{"id": "2411.16206", "title": "Scalable Batch Bayesian Optimization Via Subspace Acquisition Functions", "abstract": "Extending Bayesian optimization to batch evaluation can enable the designer to make the most use of parallel computing technology. However, most of current batch approaches do not scale well with the batch size. That is, their optimization efficiencies often deteriorate as the batch size increases. To address this issue, we propose a simple and efficient approach to extend Bayesian optimization to large-scale batch evaluation in this work. Different from existing batch approaches, the idea of the new approach is to draw a batch of axis-aligned subspaces of the original problem and select one point from each subspace using existing acquisition functions. Numerical experiments show that our proposed approach speedups the convergence significantly when compared with the sequential Bayesian optimization algorithm, and performs very competitively when compared with ten batch Bayesian optimization algorithms. The implementation of our proposed approach is available at https://github.com/zhandawei/SubSpace_Acquisition_Functions.", "date": "2024-11-25", "categories": []}
{"id": "2606.19230", "title": "A Human-in-the-Loop Bayesian Optimization Framework for Constraint-Aware Bioprocess Development", "abstract": "This work presents an extension to Pareto Front Guided Sampling (PFGS), a Human-in-the-Loop (HitL) Bayesian Optimization (BO) framework in which Gaussian process (GP) surrogate-derived quantities are reformulated as objectives of a multi-objective optimization problem, and the resulting Pareto front is exposed to a domain expert for interactive candidate selection rather than returning a single automated recommendation. The framework is extended in two directions: constrained optimization is addressed by incorporating the posterior probability of satisfying output specification limits as an explicit Pareto objective, computed analytically from the GP posterior distribution; robust optimization is addressed by a Monte Carlo sampling strategy that estimates expected lower-confidence performance over a user-defined variability of input perturbations, capturing performance degradation under likely implementation deviations. The resulting multi-dimensional Pareto representation renders trade-offs between predicted performance, model uncertainty, probabilistic constraint satisfaction, and input robustness simultaneously visible through pairwise two-dimensional projections on an interactive dashboard, enabling selection criteria to be iteratively refined as the surrogate model improves and development objectives evolve. The framework is showcased on an eight-dimensional fed-batch Chinese Hamster Ovary (CHO) cell culture simulator demonstrating systematic identification of high-performing, feasibility-compliant, and perturbation-resilient operating conditions, and illustrating how expert-defined requirements provide a principled stopping criterion and support informed allocation of experimental resources.", "date": "2026-06-17", "categories": []}
{"id": "2502.06178", "title": "Bayesian Optimization by Kernel Regression and Density-based Exploration", "abstract": "Bayesian optimization is highly effective for optimizing expensive-to-evaluate black-box functions, but it faces significant computational challenges due to the cubic per-iteration cost of Gaussian processes, which results in a total time complexity that is quartic with respect to the number of iterations. To address this limitation, we propose a novel algorithm, Bayesian optimization by kernel regression and density-based exploration (BOKE). BOKE uses kernel regression for efficient function approximation, kernel density for exploration, and integrates them into the confidence bound criteria to guide the optimization process, thus reducing computational costs to quadratic. Our theoretical analysis rigorously establishes the global convergence of BOKE under noisy evaluations. Through extensive numerical experiments on both synthetic and real-world optimization tasks, we demonstrate that BOKE not only performs competitively compared to Gaussian process-based methods and several other baseline methods but also exhibits superior computational efficiency. These results highlight BOKE's effectiveness in resource-constrained environments, providing a practical approach for optimization problems in engineering applications.", "date": "2025-02-10", "categories": []}
{"id": "2507.13263", "title": "From Sorting Algorithms to Scalable Kernels: Bayesian Optimization in High-Dimensional Permutation Spaces", "abstract": "Bayesian Optimization (BO) is a powerful tool for black-box optimization, but its application to high-dimensional permutation spaces is severely limited by the challenge of defining scalable representations. The current state-of-the-art BO approach for permutation spaces relies on an exhaustive $\\Omega(n^2)$ pairwise comparison, inducing a dense representation that is impractical for large-scale permutations. To break this barrier, we introduce a novel framework for generating efficient permutation representations via kernel functions derived from sorting algorithms. Within this framework, the Mallows kernel can be viewed as a special instance derived from enumeration sort. Further, we introduce the \\textbf{Merge Kernel} , which leverages the divide-and-conquer structure of merge sort to produce a compact, $\\Theta(n\\log n)$ to achieve the lowest possible complexity with no information loss and effectively capture permutation structure. Our central thesis is that the Merge Kernel performs competitively with the Mallows kernel in low-dimensional settings, but significantly outperforms it in both optimization performance and computational efficiency as the dimension $n$ grows. Extensive evaluations on various permutation optimization benchmarks confirm our hypothesis, demonstrating that the Merge Kernel provides a scalable and more effective solution for Bayesian optimization in high-dimensional permutation spaces, thereby unlocking the potential for tackling previously intractable problems such as large-scale feature ordering and combinatorial neural architecture search.", "date": "2025-07-17", "categories": []}
{"id": "2606.01730", "title": "Evidence-Gated LLM Priors for Multi-Objective Bayesian Optimization", "abstract": "Large language models (LLMs) are increasingly used as heuristic advisors for black-box optimization, yet their suggestions and self-reported confidence are not necessarily calibrated to downstream objective values. This issue becomes more pronounced in multi-objective Bayesian optimization, where different objectives may require different expert knowledge and where an LLM expert can be useful for one objective but misleading for another.\n  We study how to use LLM-generated expert priors in discrete multi-objective Bayesian optimization without blindly trusting them. We propose an objective-wise reputation-market mechanism that treats each expert-objective pair as a falsifiable prior source. Expert weights are updated online from observed objective feedback, discounted over time, and gated by market-level trust. We then introduce a decoupled counterfactual gate that can use the LLM prior without confidence, use it with confidence, or abstain from the LLM prior entirely.\n  Across controlled synthetic stress tests and three molecule optimization benchmarks with \\qwenflash{}-generated expert priors, we find that dynamic objective-wise calibration improves robustness over fixed LLM priors. However, raw LLM confidence is not reliably beneficial: on ESOL, confidence is positively correlated with prediction error; on FreeSolv, confidence can help; and on Lipophilicity, ignoring confidence remains strongest. Our fixed three-arm counterfactual gate improves over the first counterfactual variant on ESOL and FreeSolv, while an attempted margin portfolio exposes a useful negative result: margin selection should be acquisition-aware rather than based only on one-step prior error.", "date": "2026-06-01", "categories": []}
{"id": "2603.09276", "title": "On Regret Bounds of Thompson Sampling for Bayesian Optimization", "abstract": "We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP. Compared with the GP upper confidence bound (GP-UCB) with established high-probability and expected regret bounds, most analyses of GP-TS have been limited to expected regret. Moreover, whether the recent analyses of GP-UCB for the lenient regret and the improved cumulative regret upper bound can be applied to GP-TS remains unclear. To fill these gaps, this paper shows several regret bounds: (i) a regret lower bound for GP-TS, which implies that GP-TS suffers from a polynomial dependence on $1/\\delta$ with probability $\\delta$, (ii) an upper bound of the second moment of cumulative regret, which directly suggests an improved regret upper bound on $\\delta$, (iii) expected lenient regret upper bounds, and (iv) an improved cumulative regret upper bound on the time horizon $T$. Along the way, we provide several useful lemmas, including a relaxation of the necessary condition from recent analysis to obtain improved regret upper bounds on $T$.", "date": "2026-03-10", "categories": []}
{"id": "2606.11574", "title": "Range-Aware Bayesian Optimization for Discovering Diverse Designs within Target Property Windows", "abstract": "In many materials and product design problems, desirable candidates exhibit properties that fall within an acceptable range rather than achieve a single optimum. Recovering multiple, distinct solutions that satisfy such specifications is also practically valuable, as some candidates may be preferred for reasons of cost, processability, or robustness that are difficult to encode directly in an objective function. Here, we develop a range-aware Bayesian optimization (BO) framework in which the acquisition function directly scores the posterior probability that a candidate satisfies a target range. The framework naturally extends to parallel pursuit of multiple distinct specifications over a shared candidate space. Across benchmark tasks, range-aware acquisition consistently recovers larger and more diverse sets of valid designs than standard BO baselines and recent goal-seeking methods. Its utility is further demonstrated in two practically motivated design case studies involving optimizing reaction conditions for polymer synthesis and sequence-defined oligomer discovery for prescribed optical absorption bands, supported by quantum chemical calculations. These results suggest that range-aware BO can provide a practical and sample-efficient foundation for specification-driven design, particularly when design flexibility and solution diversity are important considerations.", "date": "2026-06-10", "categories": []}
{"id": "2503.20272", "title": "An $(\\epsilon,\\delta)$-accurate level set estimation with a stopping criterion", "abstract": "The level set estimation problem seeks to identify regions within a set of candidate points where an unknown and costly to evaluate function's value exceeds a specified threshold, providing an efficient alternative to exhaustive evaluations of function values. Traditional methods often use sequential optimization strategies to find $\\epsilon$-accurate solutions, which permit a margin around the threshold contour but frequently lack effective stopping criteria, leading to excessive exploration and inefficiencies. This paper introduces an acquisition strategy for level set estimation that incorporates a stopping criterion, ensuring the algorithm halts when further exploration is unlikely to yield improvements, thereby reducing unnecessary function evaluations. We theoretically prove that our method satisfies $\\epsilon$-accuracy with a confidence level of $1 - \\delta$, addressing a key gap in existing approaches. Furthermore, we show that this also leads to guarantees on the lower bounds of performance metrics such as F-score. Numerical experiments demonstrate that the proposed acquisition function achieves comparable precision to existing methods while confirming that the stopping criterion effectively terminates the algorithm once adequate exploration is completed.", "date": "2025-03-26", "categories": []}
{"id": "2603.29730", "title": "mlr3mbo: Bayesian Optimization in R", "abstract": "We present mlr3mbo, a modular toolbox for Bayesian optimization in R. mlr3mbo supports single- and multi-objective optimization, multi-point proposals, batch and asynchronous parallelization, and robust error handling. While it can be used for many standard Bayesian optimization variants in applied settings, researchers can also construct custom Bayesian optimization algorithms from its flexible building blocks. In addition to an introduction to the software, its design principles, and its building blocks, the paper presents two extensive empirical evaluations on the surrogate-based benchmark suite YAHPO Gym. To identify robust default configurations for both numeric and mixed-hierarchical optimization regimes, and to gain further insights into the respective impacts of individual settings, we run a coordinate descent search over the mlr3mbo configuration space and analyze its results. Furthermore, we benchmark mlr3mbo against a wide range of established optimizers, including HEBO, SMAC3, Ax, and Optuna, and find that it performs on par with state-of-the-art.", "date": "2026-03-31", "categories": []}
{"id": "2606.09889", "title": "Optuna Constrained Tree-Structured Parzen Estimator Is a Joint Density Generalization of c-TPE", "abstract": "Constrained hyperparameter optimization (HPO) is common in practice, yet Optuna's widely used constrained TPE lacks algorithmic analysis. While c-TPE proposes an expected constrained improvement (ECI) approach assuming independence between the objective and constraints, Optuna uses a single joint density over both. We show that Optuna's constrained TPE is joint c-TPE -- the same ECI acquisition function using a joint likelihood. We demonstrate joint c-TPE is invariant to constraint duplication whereas independent c-TPE degrades as the product accumulates duplicated factors. We outline practical tradeoffs between the formulations and directions for future study.", "date": "2026-06-03", "categories": []}
{"id": "2502.01226", "title": "Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling", "abstract": "Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions. The characteristics of the unknown function depend heavily on the assumed GP prior. Most work in the literature assume that this prior is known but in practice this seldom holds. Instead, practitioners often rely on maximum likelihood estimation to select the hyperparameters of the prior - which lacks theoretical guarantees. In this work, we study two algorithms for joint prior selection and regret minimization in GP bandits based on GP Thompson sampling (GP-TS): Prior-Elimination GP-TS (PE-GP-TS) that disqualifies priors with poor predictive performance, and HyperPrior GP-TS (HP-GP-TS) that utilizes a bi-level Thompson sampling scheme. We theoretically analyze the algorithms and establish a sublinear regret bound for HP-GP-TS. In addition, we demonstrate the effectiveness of these algorithms compared to the alternatives through extensive experiments with synthetic and real-world data.", "date": "2025-02-03", "categories": []}
{"id": "2606.02351", "title": "Local Preferential Bayesian Optimization", "abstract": "Bayesian optimization (BO) is a popular and effective approach for tuning expensive, noisy experiments, but requires the formulation of an explicit objective function. Preferential BO (PBO) removes this requirement by learning from pairwise human feedback, yet existing methods struggle to efficiently optimize beyond low- and medium-dimensional problems due to their global search approaches. We address this limitation by developing a family of local PBO methods that transfer key ideas from high-dimensional BO to the preferential setting. In particular, we introduce local PBO methods which adapt trust-region and derivative-informed local search to pairwise preference feedback, where the latter exploits first- and second-order derivatives of the Laplace-approximated GP posterior. Our benchmark on GP sample paths, standard optimization benchmark functions, and policy-search tasks shows that local PBO methods are especially effective in high-dimensional and complex landscapes with steep optima. Compared with global preference-based baselines, they can substantially reduce cumulative regret, making them particularly useful for real-world preference-based optimization tasks such as policy search.", "date": "2026-06-01", "categories": []}
{"id": "2606.07561", "title": "Boundary Variance Inflation Causes Acquisition Bias in Gaussian Processes", "abstract": "Gaussian processes with stationary kernels on bounded domains exhibit inflated posterior variance near the boundary. Despite being a long-recognized artifact in geostatistics and a source of over-exploration in Bayesian optimization, the causes and effects of boundary-induced acquisition bias are underexplored. We trace the root cause to a simple geometric mechanism: the truncation of the kernel correlation neighborhood at the domain boundary creates an observation-independent distortion that worsens with dimensionality. We show how this distortion manifests across three acquisition classes: variance maximization concentrates selections at the corners, whereas negative integrated posterior variance and expected predictive information gain move selections inward to axis-aligned interior shells. These patterns arise without reference to any objective function, meaning that acquisition behavior can be dominated by kernel geometry rather than the desired task-specific uncertainty. To quantify this, we introduce a function-free selection-profile diagnostic for arbitrary acquisitions, kernels, and bounded-domain geometries.", "date": "2026-05-25", "categories": []}
{"id": "2606.08438", "title": "Improving Bayesian Optimization via Training-Aware Conditional Diffusion Models", "abstract": "Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\\mathbf{x}^{\\star}$. To align with this goal, information-based acquisition functions such as Predictive Entropy Search (PES) model $\\mathbf{x}^{\\star}$ as a random variable and reduce the entropy of its distribution, but approximating this distribution via traditional GP posterior sampling is computationally expensive. To address this limitation, we leverage Conditional Diffusion Models (CDMs) to efficiently approximate the distribution of $\\mathbf{x}^{\\star}$ and develop BO-inherent training strategies for CDMs. Motivated by the structural properties of the CDM-learned distribution, we further develop an acquisition strategy termed Diffusion-based Mode Seeking (DMS) to guide the sequential evaluation. We establish a sub-optimality guarantee for the CDM-learned distribution and demonstrate through extensive experiments that DMS outperforms standard BO baselines.", "date": "2026-06-07", "categories": []}
{"id": "2606.08611", "title": "Bayesian Optimization of a Multi-Product Chemical Reactor Using Composite Models and Partial Physics Knowledge", "abstract": "We study data-driven real-time economic optimization of a multi-product chemical reactor when no reliable first-principles model is available beyond a steady-state energy balance. Instead of learning the economic objective directly as a black-box function, we use a composite formulation in which Gaussian process (GP) models predict physically meaningful outputs, including product concentrations and reactor temperature, while profit is computed analytically from these predictions together with raw-material, product, and utility prices. This preserves the structure of the economic objective, makes it parametric in changing prices without needing retraining, and allows candidate operating points to be checked against the available energy balance through a physics residual. The GPs also provide predictive uncertainty, which is exploited in a Bayesian optimization (BO) framework both for data-efficient exploration and for conservative enforcement of the reactor temperature constraint through an upper confidence bound. The acquisition function additionally penalizes large energy-balance mismatch obtained by substituting the GP-predicted outputs and candidate inputs into the available steady-state energy balance. The approach is demonstrated on a benchmark simulation of a non-isothermal multi-product reactor. Relative to a trust-region safe BO implementation, the proposed method achieves better simulated economic performance within the available iteration budget. Relative to a purely data-driven BO approach that does not use the available physics information, it avoids reactor temperature constraint violations.", "date": "2026-06-07", "categories": []}
{"id": "2606.09664", "title": "In-Context Learning for Latent Space Bayesian Optimization", "abstract": "Bayesian optimization (BO) is a central tool for sample-efficient design, and latent-space Bayesian optimization (LSBO) extends it to structured objects such as molecules and proteins. In parallel, tabular foundation models such as TabPFN and TabICL now achieve state-of-the-art regression performance and are increasingly used as BO surrogates. Because their Bayesian behavior is induced by large synthetic pretraining collections, the composition of this pretraining distribution is crucial. LSBO creates a distinctive mismatch: the induced map from latent code to objective value differs markedly from the regression tasks used to train current in-context models. We address this mismatch by complementing the pretraining stage of tabular foundation model surrogates with synthetic optimization tasks defined on the latent space of a molecular VAE. The continued-pretraining objective features a regularizer that anchors the model to the original checkpoint, preserving its broad regression prior while avoiding overspecialization to the adaptation tasks. On held-out molecular optimization benchmarks, the resulting model achieves strong performance, supporting the relevance of LSBO-specific adaptation for in-context surrogates.", "date": "2026-06-08", "categories": []}
{"id": "2603.02970", "title": "LAGO: A Local-Global Optimization Framework Combining Trust Region Methods and Bayesian Optimization", "abstract": "We introduce LAGO, a LocAl-Global Optimization framework coupling Bayesian Optimization (BO) and gradient-based trust region local refinement through an adaptive competition mechanism for smooth expensive-to-evaluate objective functions with available gradients. At each iteration, global and local optimization strategies independently propose candidate points, and the next evaluation is selected based on predicted improvement. LAGO separates global exploration from local refinement at the proposal level: the BO acquisition function is optimized outside the active trust region, while local candidates are proposed within the trust region. Points in the vicinity of the accepted local step are incorporated in the global GP dataset only when satisfying a lengthscale-based minimum-distance criterion, hence reducing the risk of numerical instability during local exploitation. LAGO enhances BO with efficient local refinement when reaching promising regions, and reverts to exploratory behavior when local steps are not competitive.", "date": "2026-03-03", "categories": []}
{"id": "2606.06984", "title": "Accelerating Multi-Objective Bayesian Optimisation via Predictive-Gradient Catalysts", "abstract": "This paper presents a general acceleration mechanism for multi-objective Bayesian optimisation (MOBO) that leverages Gaussian process predictive gradients as auxiliary signals. Rather than replacing existing Pareto-compliant acquisition functions, the proposed approach augments them with local stationarity information derived from surrogate-derived gradients, enabling faster convergence toward the global Pareto set under limited evaluation budgets. Two catalyst instantiations are investigated: an adaptive Multiple-Gradient Descent Algorithm-Based Catalyst (MGDA) and a predefined-weight variant that enables focused exploration when budgets are tight. Experiments on the DTLZ benchmark suite (using 2 objectives and 10 decision variables) show that predictive gradient catalysis can deliver significant acceleration compared to other acquisition functions (EHVI, AugTch, tMPoI, SAF) when surrogates are accurate, particularly for stationary problems.", "date": "2026-06-05", "categories": []}
{"id": "2606.07134", "title": "$\\alpha$-PFN: Fast Entropy Search via In-Context Learning", "abstract": "Information-theoretic acquisition functions such as Entropy Search (ES) offer a principled exploration-exploitation framework for Bayesian optimization (BO). However, their practical implementation relies on complicated and slow approximations, i.e., a Monte Carlo estimation of the information gain. This complexity can introduce numerical errors and requires specialized, hand-crafted implementations. We propose a two-stage amortization strategy that learns to approximate entropy search-based acquisition functions using Prior-data Fitted Networks (PFNs) in a single forward pass. A first PFN is trained to be conditioned on information about the optima; second, the $\\alpha$-PFN is trained to predict the expected information gain by training on information gains measured with the first PFN. The $\\alpha$-PFN offers a flexible learned approximation, which replaces the complex heuristic approximations with a single forward pass per candidate, enabling rapid and extensible acquisition evaluation. Empirically, our approach is competitive with state-of-the-art entropy search implementations on synthetic and real-world benchmarks, while accelerating the different entropy search variants across all our experiments, with speed ups over 50x. Source code: https://github.com/automl/AlphaPFN.", "date": "2026-06-05", "categories": []}
{"id": "2304.11127", "title": "Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance", "abstract": "Recent scientific advances require complex experiment design, necessitating the meticulous tuning of many experiment parameters. Tree-structured Parzen estimator (TPE) is a widely used Bayesian optimization method in recent parameter tuning frameworks such as Hyperopt and Optuna. Despite its popularity, the roles of each control parameter in TPE and the algorithm intuition have not been discussed so far. The goal of this paper is to identify the roles of each control parameter and their impacts on parameter tuning based on the ablation studies using diverse benchmark datasets. The recommended setting concluded from the ablation studies is demonstrated to improve the performance of TPE. Our TPE implementation used in this paper is available at https://github.com/nabenabe0928/tpe/tree/single-opt. OptunaHub now provides our standalone TPE implementation at https://hub.optuna.org/samplers/tpe_tutorial/.", "date": "2023-04-21", "categories": []}
{"id": "2606.00009", "title": "Optimal Transport-based Permutation-Invariant Bayesian Optimization of Offshore Wind Farm Layouts", "abstract": "Bayesian Optimization (BO) is widely and successfully adopted for solving optimization problems having an expensive-to-evaluate, black-box, and non-convex objective function. However, the vanilla BO algorithm is not able to exploit possible symmetries characterizing the target problem. An intuitive case is given by optimal location problems, whose decision variables refer to a finite set of points within a continuous space, with the order of points not affecting the value of the objective function. We refer to this setting as optimization over layouts to distinguish from optimization over point-clouds where, instead, the order of points counts. As an instance of optimization over layouts we consider a real-life industrial-relevant application, that is the optimization of the layout of an offshore wind farm: given identical wind turbines, switching any pair of them has not any effect on the annual energy production. Based on Optimal Transport theory, we propose a Permutation-Invariant BO approach, namely PIBO, proved to provide better wind farm layouts when compared to the vanilla BO approach while cutting computation time roughly in half.", "date": "2026-03-27", "categories": []}
{"id": "2606.00293", "title": "Accurate Large-sample Uncertainty Quantification using Stochastic Gradient Markov Chain Monte Carlo", "abstract": "Tuning algorithms such as stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD) for approximate sampling and uncertainty quantification remains challenging, particularly in the practically relevant settings when the batch size is large or the model is misspecified. Existing theory that provides tuning guidance relies on continuous-time limits or strong statistical assumptions, which can become quantitatively inaccurate in these regimes. We address these shortcomings by proposing new discrete-time approximations to SG(L)D with and without momentum, which enables accurate predictions of the stationary covariance, iterate average covariance, and integrated autocorrelation time. Moreover, we prove quantitative, non-asymptotic error bounds showing that these estimates are sufficiently accurate for practical tuning and uncertainty quantification. Numerical experiments demonstrate that our theory yields improved tuning guidance across a range of models and data-generating distributions where existing approaches fail, including when using the $\\beta$-divergence rather than log-loss to obtain statistically robust inferences.", "date": "2026-05-29", "categories": []}
{"id": "2606.00956", "title": "Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee", "abstract": "This paper studies a one-step lookahead Bayesian optimization (BO) method and its theoretical guarantee. Although the empirical effectiveness of one-step lookahead BO methods, such as entropy search, has been studied extensively, they often rely on computationally intractable approximations, and their regret guarantees remain underdeveloped. Thus, this paper proposes a one-step lookahead BO method called optimal-point variance reduction (OVR), which requires only posterior sampling and Monte Carlo approximations. We obtain a uniform error bound over an input domain for the Monte Carlo estimation in OVR. Furthermore, we show that the regularized OVR, with the slight modification to promote exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we demonstrate the effectiveness of OVR through numerical experiments.", "date": "2026-05-31", "categories": []}
{"id": "2606.01182", "title": "CA-BED: Conversation-Aware Bayesian Experimental Design", "abstract": "Large Language Models (LLMs) excel at static reasoning tasks, yet their performance often degrades in interactive scenarios where information must be actively acquired through questioning. A key challenge lies in selecting questions that reduce uncertainty while incorporating responses that may be ambiguous or only partially informative. To address this, we propose Conversation-Aware Bayesian Experimental Design (CA-BED), an inference-time probabilistic dialog planning framework that integrates Bayesian Experimental Design with LLM-based likelihood estimation to optimize question selection over multiple conversational turns. CA-BED maintains a belief distribution over hypotheses, anticipates possible answers, and propagates expected information gain through a simulated conversation tree. Across two structured entity-deduction benchmarks, CA-BED yields an average 21.8% improvement in success rates over direct prompting, with comparable gains relative to alternative information-seeking methods. It achieves these gains with an average increase of only 1.8 conversational turns compared to direct prompting.", "date": "2026-05-31", "categories": []}
{"id": "2606.01457", "title": "Transferring Information Across Interventions in Causal Bayesian Optimization", "abstract": "Bayesian optimization is a popular way to optimize expensive systems, where every experiment, simulation, or intervention costs time or money. In its standard form, it treats the variables we control as plain inputs to a black box and cannot tell apart mere correlation from a real cause and effect. Causal Bayesian optimization closes part of this gap by using a known causal graph together with observational data to decide which variables are worth intervening on. Existing methods, however, learn the effect of each possible intervention almost in isolation, even though in a causal system these effects usually share the same underlying mechanisms. We propose graph-coupled causal Bayesian optimization, which ties the different intervention effects together through the uncertainty we have about a small set of shared causal parameters. The result is a causal kernel that lets evidence collected from one intervention improve our estimate of related interventions. For identifiable linear Gaussian causal models, we show that this kernel has low rank, bounded by the number of shared parameters rather than by the size of the intervention menu. This in turn yields an information-gain bound that grows only logarithmically in the optimization horizon, and a regret bound that cleanly separates three sources of error: optimization, causal estimation, and the choice of which intervention sets to consider. We also describe nonlinear and adaptive extensions. Across theory-aligned Gaussian systems, shared-mechanism stress tests, and standard causal optimization benchmarks, the method keeps the benefits of causal Bayesian optimization while transferring information across related interventions, with the clearest gains when direct interventions on the target's parents are unavailable and sparse interventional data must be reused across a large family of candidate interventions.", "date": "2026-05-31", "categories": []}
{"id": "2507.12453", "title": "Cost-aware Stopping for Bayesian Optimization", "abstract": "In automated machine learning, scientific discovery, and other applications of Bayesian optimization, deciding when to stop evaluating expensive black-box functions in a cost-aware manner is an important but underexplored practical consideration. A natural performance metric for this purpose is the cost-adjusted simple regret, which explicitly captures the trade-off between solution quality and cumulative evaluation cost. Existing stopping rules for Bayesian optimization are either heuristic, or are theoretically grounded but designed to optimize simple regret without accounting for evaluation costs; as a result, they provide no guarantees against unnecessary evaluations when costs are high. We propose a principled cost-aware stopping rule for Bayesian optimization that adapts to varying evaluation costs without heuristic tuning. Our rule is grounded in a theoretical connection to state-of-the-art cost-aware acquisition functions, namely the Pandora's Box Gittins Index (PBGI) and log expected improvement per cost (LogEIPC). When paired with either acquisition function, we prove that the resulting policy satisfies a theoretical guarantee bounding the expected cost-adjusted simple regret. Across synthetic tasks and empirical benchmarks including hyperparameter optimization and neural architecture size search, pairing our stopping rule with PBGI or LogEIPC usually matches or outperforms other acquisition-function--stopping-rule pairs in terms of cost-adjusted simple regret.", "date": "2025-07-16", "categories": []}
{"id": "2604.15959", "title": "Multi-Objective Bayesian Optimization via Adaptive \\varepsilon-Constraints Decomposition", "abstract": "Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling $\\varepsilon$-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in $\\varepsilon$-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.", "date": "2026-04-17", "categories": []}
{"id": "2605.31050", "title": "Best-Arm Identification-Based Trust Region Selection for Bayesian Optimization on Multimodal Functions", "abstract": "Gaussian process-based Bayesian optimization (BO) is a popular approach for expensive black-box optimization, but its performance often degrades on complex multimodal or high-dimensional problems. Trust region-based BO mitigates this issue by focusing on local regions, and recent studies suggest that selecting an effective region can be formulated as a multi-armed bandit problem. We propose a trajectory-aware framework that integrates best-arm identification (BAI) with trust region-based BO to efficiently solve multimodal optimization problems. Our method extrapolates the optimization trajectories of multiple locally initialized optimizers to predict their final performance and progressively eliminates suboptimal candidates via BAI. We theoretically show that the proposed BAI-guided BO converges faster to the global optimum than conventional BO under mild assumptions, and demonstrate its effectiveness through extensive experiments on synthetic and real-world benchmarks.", "date": "2026-05-29", "categories": []}
{"id": "2511.16815", "title": "BITS for GAPS: Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogates", "abstract": "We introduce Bayesian Information-Theoretic Sampling for hierarchical GAussian Process Surrogates (BITS for GAPS), a framework enabling information-theoretic experimental design of Gaussian process-based surrogate models. Unlike standard methods, which use fixed or point-estimated hyperparameters in acquisition functions, our approach propagates hyperparameter uncertainty into the sampling criterion through Bayesian hierarchical modeling. In this framework, a latent function receives a Gaussian process prior, while hyperparameters are assigned additional priors to capture the modeler's knowledge of the governing physical phenomena. Consequently, the acquisition function incorporates uncertainties from both the latent function and its hyperparameters, ensuring that sampling is guided by both data scarcity and model uncertainty. We further establish theoretical results in this context: a closed-form approximation and a lower bound of the posterior differential entropy.\n  We demonstrate the framework's utility for hybrid modeling with a vapor-liquid equilibrium case study. Specifically, we build a surrogate model for latent activity coefficients in a binary mixture. We construct a hybrid model by embedding the surrogate into an extended form of Raoult's law. This hybrid model then informs distillation design. This case study shows how partial physical knowledge can be translated into a hierarchical Gaussian process surrogate. It also shows that using BITS for GAPS increases expected information gain and predictive accuracy by targeting high-uncertainty regions of the Wilson activity model. Overall, BITS for GAPS is a generalized uncertainty-aware framework for adaptive data acquisition in complex physical systems.", "date": "2025-11-20", "categories": []}
{"id": "2605.28746", "title": "Preference-Shaped Expected Hypervolume and R2 Improvement: Exact Computation and Monotonicity", "abstract": "This paper studies preference-shaped expected improvement criteria for Bayesian multiobjective optimization. We consider two indicator families which are often used for similar algorithmic purposes, but which are geometrically different. The hypervolume indicator is based on a dystopian reference point and measures dominated volume in objective space. The R2 indicator is based on a utopian point and evaluates approximation sets through weighted Tchebycheff scalarization envelopes. The purpose of the paper is to make precise which preference transformations preserve exact computation, Pareto compatibility, and monotonicity properties, and which transformations change the underlying geometry. On the hypervolume side, we revisit canonical EHVI through the Deng representation, formulate product-density weighted EHVI in desirability coordinates, discuss cone-based EHVI as ordinary EHVI after a linear cone transformation, and separate these cases from truncated EHVI, where variance monotonicity may fail. On the R2 side, we prove that exact integral R2 improvement is not, in general, an ordinary objective-space weighted hypervolume. The obstruction is lower-dimensional: Lebesgue-density hypervolume cannot see certain boundary contributions that Tchebycheff scalarizations still detect. We then show that exact integral R2 improvement is exactly a scalarization-space volume, namely the measure of the Tchebycheff shadow between the incumbent scalarization envelope and the reference envelope. This representation yields finite-sum ER2I algorithms for discrete R2, quadrature methods for exact integral R2, and an achievement-space Gaussian surrogate formulation in which ER2I is an integral of scalar Gaussian expected improvements.", "date": "2026-05-27", "categories": []}
{"id": "2605.26990", "title": "Constrained Bayesian Experimental Design via Online Planning", "abstract": "Bayesian experimental design (BED) is a principled framework for data-efficient design of sequential experiments. However, existing BED methods are unable to adapt to dynamic constraints inherent in real-world tasks due to budget limitations, varying costs, or physical constraints that restrict how designs evolve over time. In this paper, we introduce a novel approach to BED that enables constrained optimization of experimental designs by combining offline pre-training of an amortized policy and a posterior network with online multi-step lookahead planning using scenario trees. We empirically demonstrate that our method yields substantially more informative design sequences than existing methods across a range of constrained BED tasks, while incurring only a modest additional computational overhead.", "date": "2026-05-26", "categories": []}
{"id": "2605.27093", "title": "Gaussian Process-based learning with new MCMC-based implementation of Wishart prior on correlation matrix", "abstract": "In probabilstic supervised learning of an input-output relationship - as a sample function of a Gaussian Process (GP) - priors are typically specified for the hyperparameters of the kernel that parametrises the covariance function of the GP, where the induced covariance matrix of the (resulting multivariate Normal) likelihood, governs the learning and prediction. When the sought function is highly multivariate, multiple lengthscale parameters must be learnt simultaneously, making inference difficult. We develop a ``self-assembled'' Wishart prior for the covariance matrix, while undertaking Bayesian inference on the kernel hyperparameters using MCMC. The construction uses a look-back window over recent MCMC iterations to define a time-step dependent scale matrix, thereby introducing adaptiveness to the chain. Results suggest that direct prior specification on the covariance matrix can be useful for diagnosing weakly informative inputs within the GP-based learning paradigm. We support our prior development with two distinct empirical illustrations - one on synthetic data, and another on a real-world dataset.", "date": "2026-05-26", "categories": []}
{"id": "2605.23473", "title": "Automated Random Embedding for Practical Bayesian Optimization with Unknown Effective Dimension", "abstract": "Bayesian optimization is widely employed for optimizing complex black-box functions but struggles with the curse of dimensionality. Random embedding, as a dimension reduction strategy, simplifies tasks that possess the effective dimension by optimizing within a low-dimensional subspace. However, determining the effective dimension of a task in advance remains a significant challenge, which influences the selection of the subspace dimensionality and the optimization performance. Traditional methods use fixed subspace dimensions provided by experts or rely on trial and error to estimate subspace dimensions with resources consumed. To this end, this paper proposes an automated random embedding for high-dimensional Bayesian optimization with unknown effective dimension, called Dynamic Shared Embedding Bayesian Optimization (DSEBO). DSEBO starts with a low dimension and switches to a higher subspace if the solutions in the current subspace show preliminary convergence. DSEBO dynamically determines the dimension of the next subspace based on the quality of the solutions in different subspaces and shares the queried solutions with the new subspace for a better initialization. Theoretically, we derive a regret bound for DSEBO and demonstrate that DSEBO can better balance approximation and optimization errors. Extensive experiments on functions with dimensionality of varying magnitudes and real-world tasks with unknown effective dimensions reveal that, compared with state-of-the-art methods, alternating optimization across different subspaces results in significant improvements in high-dimensional optimization, both in terms of optimization regret and time.", "date": "2026-05-22", "categories": []}
{"id": "2508.02332", "title": "BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization", "abstract": "The performance of Bayesian optimization (BO), a highly sample-efficient method for expensive black-box problems, is critically governed by the selection of its hyperparameters, including the kernel and acquisition functions. This presents a significant practical challenge: an inappropriate combination of these can lead to poor performance and wasted evaluations. While individual improvements to kernel functions and acquisition functions have been actively explored, the joint and autonomous selection of the best pair of these fundamental hyperparameters has been largely overlooked. This forced practitioners to rely on heuristics or costly manual training. In this work, we propose a framework, BOOST (Bayesian Optimization with Optimal Kernel and Acquisition Function Selection Technique), that automates this selection. BOOST utilizes a simple offline evaluation stage to predict the performance of various kernel-acquisition function pairs and identify the most promising pair before committing to the expensive evaluation process. BOOST is a data-driven strategy selection procedure that evaluates kernel-acquisition pairs based on their empirical performance on the data-in-hand. At each iteration, previously observed points are partitioned into a reference set and a query set. These subsets play roles analogous to training and validation sets in machine learning: the reference set is used for model construction, while the query set represents unseen regions to retrospectively evaluate how effectively each candidate strategy progresses toward the target value. Experiments on synthetic benchmarks and machine learning hyperparameter optimization tasks demonstrate that BOOST consistently improves over fixed-hyperparameter BO and remains competitive with state-of-the-art adaptive methods, highlighting its robustness across diverse landscapes.", "date": "2025-08-04", "categories": []}
{"id": "2605.02409", "title": "Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications", "abstract": "Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with permutation symmetries, as the most common kernels employed are better suited for vector inputs rather than unordered sets of items. Motivated by this issue, we turn to permutation invariant Bayesian Optimization for well placement in Carbon Capture and Storage projects. The high fidelity black box simulator is instructed to operate wells under group control, giving rise to permutation symmetries within injector and producer groups that cannot be exploited with standard GP kernels. In this work, our main contribution is a novel Gaussian Process kernel (GP-Perm) that encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations, and can be combined with standard kernels for additional vector-valued inputs. As a learned invariant baseline, we also consider a Deep Kernel Learning model (DKL-DS) using the Deep Sets architecture to learn a permutation-invariant embedding. We evaluate the proposed methodology across 8 use cases, comprising seven synthetic benchmarks and one realistic CCS case study (Johansen formation)", "date": "2026-05-04", "categories": []}
{"id": "2605.22054", "title": "LABO: LLM-Accelerated Bayesian Optimization through Broad Exploration and Selective Experimentation", "abstract": "The high cost and data scarcity in scientific exploration have motivated the use of large language models (LLMs) as knowledge-driven components in Bayesian optimization (BO). However, existing approaches typically embed LLMs directly into the sampling or surrogate modeling pipeline, without fully leveraging their significantly lower evaluation cost compared to real-world experiments. To address this limitation, we propose LLM-Accelerated Bayesian Optimization (LABO), a framework that combines LLM predictions with experimental observations within a single BO loop. LABO employs a gating criterion to dynamically balance the reliance on LLM predictions versus actual experiments. By leveraging inexpensive LLM evaluations to broadly explore the search space and reserving costly real experiments only for regions with high uncertainty, LABO achieves more sample-efficient optimization. We provide a theoretical analysis with a cumulative regret bound that formalizes this efficiency gain. Empirical results across diverse scientific tasks demonstrate that LABO consistently outperforms existing methods under identical experimental budgets. Our results suggest that LABO offers a practical and theoretically grounded approach for integrating LLMs into scientific discovery workflows.", "date": "2026-05-21", "categories": []}
{"id": "2605.22561", "title": "Regret-Based $(\\epsilon,\\delta)$-optimal Stopping Criteria for Bayesian Optimization", "abstract": "Bayesian optimization (BO) is a widely used iterative black-box optimization method that utilizes Gaussian process (GP) surrogate models. In practice, BO is typically terminated after a fixed evaluation budget is exhausted, which can incur unnecessary cost and provides no optimality guarantee on solution quality. Recent research in developing a practical stopping criterion has made empirical progress, yet a theoretically sound stopping criterion remains a work in progress. In this work, we present provably tighter instantaneous regret bounds for GP upper confidence bound (GP-UCB) at any given iteration. Then, we propose stopping criteria for GP-UCB based on this tighter bound that ensures an $\\epsilon$-optimal solution with high probability $1-\\delta$ upon termination. Numerical experiments are performed to validate and demonstrate the effectiveness and efficiency of our stopping criteria.", "date": "2026-05-21", "categories": []}
{"id": "2312.01386", "title": "On the Suboptimality of GP-UCB under Polynomial Effective Optimism", "abstract": "Gaussian process upper confidence bound (GP-UCB) is widely used for sequential optimization of expensive black-box functions. Although many upper bounds on its cumulative regret have been established in the literature, whether GP-UCB is minimax optimal remains open. We study this question through the effective optimism level, defined as the product of the exploration coefficient and the regularization parameter in kernel ridge regression. Under a uniform confidence assumption, we prove a new regret lower bound for GP-UCB with Mat\\'ern kernels. The bound shows that polynomial growth of the effective optimism level, up to logarithmic factors, rules out the minimax-optimal regret rate. Since this is the regime covered by most existing analyses, our result identifies a concrete obstacle to proving minimax optimality for standard GP-UCB. More broadly, it suggests that the gap between current upper bounds and minimax lower bounds may reflect a real limitation of the algorithm, not only of the analysis.", "date": "2023-12-03", "categories": []}
{"id": "2605.13302", "title": "Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization", "abstract": "This paper extends safety guarantees for multi-task Bayesian optimization with uncertain co-regionalization matrices from intrinsic co-regionalization models to linear models of co-regionalization. The latter allows for more flexible modeling of the inter-task correlations by composing multiple features. We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-regionalization kernel. Furthermore, we show the potential performance gains of linear models of co-regionalization in a numerical comparison on a safe multi-task Bayesian optimization benchmark.", "date": "2026-05-13", "categories": []}
{"id": "2605.20249", "title": "Automated Kernel Discovery Towards Understanding High-dimensional Bayesian Optimization", "abstract": "Gaussian Process (GP) kernels are central to Bayesian optimization (BO), yet designing effective kernels for high-dimensional problems still relies on extensive manual engineering. Existing automated approaches struggle in high dimensions for two bottlenecks: their kernel search space is limited to additions and multiplications of base kernels, and LLM-based approaches require conditioning on raw observations, which becomes infeasible due to context-length limits and the difficulty of extracting meaningful patterns. We introduce \\textbf{Kernel Discovery}, a LLM-driven evolutionary framework for high-dimensional BO that searches a broader kernel space beyond predefined composition rules and does not require conditioning on observations. Motivated by the observation that directly prompting an LLM to generate kernel code yields syntactically varied but functionally identical kernels, we adopt a two-stage approach: an LLM first proposes novel mathematical forms, then a second LLM call converts each form into validated, executable code. We also propose a leave-one-out continuous ranked probability score (LOO-CRPS) as a selection criterion that penalizes overfitted kernels. On five high-dimensional BO benchmarks, our method achieves an average rank of \\textbf{1.2 out of 17}, outperforming competitive baselines.\n  We further analyze the discovered kernels to identify which kernels lead to improvements in high-dimensional BO.", "date": "2026-05-18", "categories": []}
{"id": "2605.18819", "title": "Efficient Conditioning Why Pseudo Observation Batch Bayesian Optimization Works When It Does not", "abstract": "Constant Liar (CL), Kriging Believer (KB), and fantasy models are widely used for batch selection in parallel Bayesian Optimization, yet a unified theory explaining their effectiveness and conditions under which they fail has been lacking. We identify efficient conditioning as the key surrogate property the ability to update predictions in closed form when data is augmented. We prove that Gaussian Processes satisfy this requirement, producing provably distinct batch points with separation of order l, and that this holds for any acquisition function monotonically non decreasing in posterior uncertainty (EI, UCB, PI), with qualitatively similar behavior for Thompson Sampling. We unify CL, KB, and fantasy models as instances of a single conditioning mechanism differing only in the lie value distribution, and draw quantitative connections to Local Penalization (LP) and qualitative connections to Determinantal Point Processes (DPPs). To disentangle model structure from optimizer randomness, we introduce the Structural Diversity Diagnostic (SDD), a reusable methodology for testing surrogate compatibility. Experiments on Hartmann6D, Ackley 8D, Levy10D, and SVM hyperparameter tuning validate all theoretical predictions: CL or KBs implicit penalty matches or outperforms explicit LP greedy conditioning achieves convergence on par with joint qEI efficient conditioning extends to Multiquadric RBF networks; and parametric surrogates produce degenerate batches even when fully retrained (random forests), while neural networks regain diversity only at 15x the wall clock cost of GP conditioning. Robustness is confirmed across multiple initial datasets and under observation noise.", "date": "2026-05-12", "categories": []}
{"id": "2605.19093", "title": "Embedding by Elicitation: Dynamic Representations for Bayesian Optimization of System Prompts", "abstract": "System prompts are a central control mechanism in modern AI systems, shaping behavior across conversations, tasks, and user populations. Yet they are difficult to tune when feedback is available only as aggregate metrics rather than per-example labels, failures, or critiques. We study this aggregate feedback setting as sample-constrained black-box optimization over discrete, variable-length text. We introduce ReElicit, a Bayesian optimization framework based on \\emph{embedding by elicitation}. Given a task description, previously evaluated prompts, and scalar scores, an LLM elicits a compact, interpretable feature space and maps prompts into it. Leveraging a probabilistic Gaussian process surrogate, an acquisition function then selects target feature vectors, which the LLM realizes and refines into deployable system prompts. Re-eliciting the feature space as new evaluations arrive lets the representation adapt to the observed prompt-score history. We evaluate the setting using offline benchmark accuracy as a controlled aggregate proxy: the optimizer observes one scalar score per prompt and no per-example labels, errors, or critiques. Across ten system prompt optimization tasks with a 30 total evaluation budget, ReElicit achieves the strongest aggregate performance profile among representative aggregate-only prompt-optimization baselines. These results suggest that LLMs can serve as adaptive semantic representation builders, not only prompt generators, for Bayesian optimization over natural-language artifacts.", "date": "2026-05-18", "categories": []}
{"id": "2605.19677", "title": "Agentic Discovery of Cryomicroneedle Formulations", "abstract": "Cryomicroneedles offer a route to minimally invasive intradermal delivery of living cells, but their cryogenic formulations must reconcile cell protection with constraints on toxicity and device fabrication. Here we report an AI-assisted, closed-loop workflow for cryomicroneedle cryoprotectant discovery that combines literature curation, Gaussian-process surrogate modelling, Bayesian optimization, and sequential wet-lab validation. A curated dataset of 198 mesenchymal stem-cell cryopreservation formulations from 42 studies was converted into 21 ingredient features and used to train an uncertainty-aware literature prior. This model captured moderate structure in the literature data but failed prospectively, motivating iterative wet-lab correction. Across ten validation iterations and 106 wet-lab observations, the model progressively adapted to cryomicroneedle-specific outcomes: batch RMSE decreased from 41.21 to 6.86 percentage points, later-stage rank correlations became consistently positive, and the cumulative wet-lab predicted-versus-measured summary reached $R^2 = 0.942$. The best validated formulation achieved 95.15\\% post-thaw viability with low DMSO, ectoin, ethylene glycol, and fetal bovine serum. However, high viability alone did not ensure intact cryomicroneedle formation, highlighting the need for future multi-objective optimization. These results demonstrate that agent-assisted computational infrastructure can make data-efficient formulation discovery more accessible to labs with minimal data expertise in-house. Project code is available at https://github.com/baitmeister/ML-for-CryoMN.", "date": "2026-05-19", "categories": []}
{"id": "2605.20145", "title": "Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization", "abstract": "Bayesian optimization (BO) selects evaluation points for expensive black-box objectives using Gaussian process (GP) predictive distributions. Kernel choice and hyperparameter selection can lead to miscalibrated predictive distributions and an inappropriate exploration-exploitation trade-off. For minimization, sampling criteria such as expected improvement (EI) depend on the predictive distribution below the current best value, so lower-tail miscalibration directly affects the sampling decision. This article studies goal-oriented calibration of GP predictive distributions below a low threshold $t$ in the noiseless setting, for standard GP models with hyperparameters selected by maximum likelihood. A framework for predictive reliability below $t$ is introduced, based on two notions of spatial calibration: occurrence calibration over the design space and thresholded $\\mu$-calibration on sublevel sets of the form $\\{x\\in\\mathbb{X}, f(x)\\le t\\}$. Building on this framework, we propose tcGP, a post-hoc method that calibrates GP predictive distributions below~$t$, and we show that the resulting EI-based global optimization algorithm remains dense in the design space. Experiments on standard benchmarks show improved lower-tail calibration and BO performance relative to standard GP models and globally calibrated GP models.", "date": "2026-05-19", "categories": []}
{"id": "2405.14657", "title": "Anchor-Based Heteroscedastic Noise for Preferential Bayesian Optimization", "abstract": "Preferential Bayesian optimization (PBO) learns latent utilities from pairwise comparisons, but most existing methods assume homoscedastic comparison noise. This is inadequate in human-in-the-loop settings, where a user may compare some designs reliably and others only hesitantly. We propose a heteroscedastic noise model for PBO: before optimization, the user provides a small set of reliable examples, called anchors, and a kernel density estimator (KDE) turns these anchors into an input-dependent map of user uncertainty. We incorporate this map into preferential GP surrogates and derive risk-averse acquisition functions that trade off utility and ease of comparison. We further show that a risk-adjusted variant of the popular expected utility of the best option (EUBO) preserves the one-step Bayes-optimality guarantee up to an additive constant, and that under an idealized i.i.d. anchor model the KDE estimator enjoys standard consistency and concentration rates. Experiments on synthetic problems and human-preference datasets show improved risk-adjusted performance and clarify how anchor placement affects the method.", "date": "2024-05-23", "categories": []}
{"id": "2601.21357", "title": "Beyond Objective-Based Improvement: Stationarity-Aware Expected Improvement for Bayesian Optimization", "abstract": "Bayesian Optimization (BO) is a principled framework for optimizing expensive black-box functions, with Expected Improvement (EI) among its most widely used acquisition functions. Despite its empirical success, EI is agnostic to first-order optimality conditions, relying solely on objective-value improvement. As a result, it can exhibit vanishing acquisition signals where the improvement criterion is uninformative, limiting its effectiveness in guiding search. We propose Expected Improvement via Gradient Norms (EI-GN), a novel acquisition function that extends the improvement principle to incorporate first-order stationarity, promoting sampling in regions that are both high-performing and close to stationary points. We derive a tractable closed-form expression for EI-GN and show that it remains consistent with the improvement-based acquisition framework. By embedding progress toward stationarity into the acquisition criterion, EI-GN provides a richer and more informative notion of improvement. Empirical results on standard BO benchmarks demonstrate consistent gains over baseline methods, and we further illustrate its applicability to control policy learning.", "date": "2026-01-29", "categories": []}
{"id": "2602.17679", "title": "Joint Parameter and State-Space Bayesian Optimization: Using Process Expertise to Accelerate Manufacturing Optimization", "abstract": "Bayesian optimization (BO) is a powerful method for optimizing black-box manufacturing processes, but its performance is often limited when dealing with high-dimensional multi-stage systems, where we can observe intermediate outputs. Standard BO models the process as a black box and ignores the intermediate observations and the underlying process structure. Partially Observable Gaussian Process Networks (POGPN) model the process as a Directed Acyclic Graph (DAG). However, using intermediate observations is challenging when the observations are high-dimensional state-space time series. Process-expert knowledge can be used to extract low-dimensional latent features from the high-dimensional state-space data. We propose POGPN-JPSS, a framework that combines POGPN with Joint Parameter and State-Space (JPSS) modeling to use intermediate extracted information. We demonstrate the effectiveness of POGPN-JPSS on a challenging, high-dimensional simulation of a multi-stage bioethanol production process. Our results show that POGPN-JPSS significantly outperforms state-of-the-art methods by achieving the desired performance threshold twice as fast and with greater reliability. The fast optimization directly translates to substantial savings in time and resources. This highlights the importance of combining expert knowledge with structured probabilistic models for rapid process maturation.", "date": "2026-02-04", "categories": []}
{"id": "2605.17976", "title": "Unleashing LLMs in Bayesian Optimization: Preference-Guided Framework for Scientific Discovery", "abstract": "Scientific discovery is increasingly constrained by costly experiments and limited resources, underscoring the need for efficient optimization in AI for science. Bayesian Optimization (BO), though widely adopted for balancing exploration and exploitation, often exhibits slow cold-start performance and poor scalability in high-dimensional settings, limiting its applicability in real-world scientific problems. To overcome these challenges, we propose LLM-Guided Bayesian Optimization (LGBO), the first LLM preference-guided BO framework that continuously integrates the semantic reasoning of large language models (LLMs) into the optimization loop. Unlike prior works that use LLMs only for warm-start initialization or candidate generation, LGBO introduces a region-lifted preference mechanism that embeds LLM-driven preferences into every iteration, shifting the surrogate mean in a stable and controllable way. Theoretically, we prove that LGBO does not perform significantly worse than standard BO in the worst case, while achieving significantly faster convergence when preferences align with the objective. Empirically, LGBO consistently outperforms existing methods across diverse dry benchmarks in physics, chemistry, biology, and materials science. Most notably, in a new wet-lab optimization of Fe-Cr battery electrolytes, LGBO attains \\textbf{90\\% of the best observed value within 6 iterations}, whereas standard BO and existing LLM-augmented baselines require more than 10. Together, these results suggest that LGBO offers a promising direction for integrating LLMs into scientific optimization workflows.", "date": "2026-05-18", "categories": []}
{"id": "2510.25404", "title": "SemanticOpt: Towards LLM-Based Semantic Black-Box Optimization", "abstract": "Optimizing an experimental system can be extremely challenging when each experiment is expensive, time-consuming, or difficult to perform. Existing optimizers for expensive black-box problems, such as Bayesian optimization, are typically limited to numerical or categorical observations. They do not make use of broader domain knowledge, such as expert heuristics, relevant scientific papers, or similar previous experiments. Large language models (LLMs) can interpret this semantic information; however, even state-of-the-art LLMs struggle to reliably solve black-box optimization problems. We introduce SemanticOpt, a framework for semantic black-box optimization that equips LLMs with optimization capabilities by fine-tuning them on structured Bayesian optimization trajectories augmented with natural-language context. SemanticOpt jointly uses numerical and semantic evidence when proposing new experiments, while producing interpretable predictions aligned with Bayesian surrogate models. We construct a range of real-world optimization problems paired with semantic information to create a diverse benchmark for evaluating semantic black-box optimization. Across these domains, SemanticOpt outperforms both classical optimizers and existing LLM-based approaches on average when given relevant semantic information.", "date": "2025-10-29", "categories": []}
{"id": "2304.11468", "title": "Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces", "abstract": "Recent advances have extended the scope of Bayesian optimization (BO) to expensive-to-evaluate black-box functions with dozens of dimensions, aspiring to unlock impactful applications, for example, in the life sciences, neural architecture search, and robotics. However, a closer examination reveals that the state-of-the-art methods for high-dimensional Bayesian optimization (HDBO) suffer from degrading performance as the number of dimensions increases or even risk failure if certain unverifiable assumptions are not met. This paper proposes BAxUS that leverages a novel family of nested random subspaces to adapt the space it optimizes over to the problem. This ensures high performance while removing the risk of failure, which we assert via theoretical guarantees. A comprehensive evaluation demonstrates that BAxUS achieves better results than the state-of-the-art methods for a broad set of applications.", "date": "2023-04-22", "categories": []}
{"id": "2408.16307", "title": "Safe Bayesian Optimization for Complex Control Systems via Additive Gaussian Processes", "abstract": "Automatic controller tuning is attractive for robotics and mechatronic systems whose dynamics are difficult to model accurately, but direct black-box optimization can be unsafe because each query is executed on the physical plant. Existing safe Bayesian optimization (BO) methods provide high-probability safety guarantees, yet their practical use in multi-loop control is limited by two coupled difficulties: the controller parameter space is often moderately high-dimensional, and hardware evaluations are too expensive to allow hundreds or thousands of exploratory trials. This paper proposes \\textsc{SafeCtrlBO}, a safe BO method for simultaneously tuning multiple coupled controllers. The method uses additive Gaussian-process kernels to encode low-order structure across controller gains and reduce the sample complexity associated with dense full-dimensional kernels. It also replaces the expensive potential-expander computation used in \\textsc{SafeOpt}-style exploration with a boundary-based expansion rule that preserves the intended safe-set expansion behavior under explicit geometric conditions and is validated empirically. Experiments on synthetic benchmarks and on a permanent magnet synchronous motor (PMSM) speed-control platform show that \\textsc{SafeCtrlBO} reaches high-performing controller parameters with fewer hardware evaluations than representative safe BO baselines, while maintaining the prescribed high-probability safety criterion and avoiding violations of the hard signal-safety constraint in the hardware study. The code implementation is publicly available at https://github.com/hxwangnus/SafeCtrlBO.", "date": "2024-08-29", "categories": []}
{"id": "2501.18756", "title": "A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization", "abstract": "Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to reduce uncertainty about the function's optimum and are often considered fundamentally distinct from EI. In this work, we challenge this prevailing perspective by introducing a unified theoretical framework, Variational Entropy Search, which reveals that EI and information-theoretic acquisition functions are more closely related than previously recognized. We demonstrate that EI can be interpreted as a variational inference approximation of the popular information-theoretic acquisition function, named Max-value Entropy Search. Building on this insight, we propose VES-Gamma, a novel acquisition function that balances the strengths of EI and MES. Extensive empirical evaluations across both low- and high-dimensional synthetic and real-world benchmarks demonstrate that VES-Gamma is competitive with state-of-the-art acquisition functions and in many cases outperforms EI and MES.", "date": "2025-01-30", "categories": []}
{"id": "2502.08208", "title": "Exploring Exploration in Bayesian Optimization", "abstract": "A well-balanced exploration-exploitation trade-off is crucial for successful acquisition functions in Bayesian optimization. However, there is a lack of quantitative measures for exploration, making it difficult to analyze and compare different acquisition functions. This work introduces two novel approaches - observation traveling salesman distance and observation entropy - to quantify the exploration characteristics of acquisition functions based on their selected observations. Using these measures, we examine the explorative nature of several well-known acquisition functions across a diverse set of black-box problems, uncover links between exploration and empirical performance, and reveal new relationships among existing acquisition functions. Beyond enabling a deeper understanding of acquisition functions, these measures also provide a foundation for guiding their design in a more principled and systematic manner.", "date": "2025-02-12", "categories": []}
{"id": "2502.09198", "title": "Understanding High-Dimensional Bayesian Optimization", "abstract": "Recent work reported that simple Bayesian optimization (BO) methods perform well for high-dimensional real-world tasks, seemingly contradicting prior work and tribal knowledge. This paper investigates why. We identify underlying challenges that arise in high-dimensional BO and explain why recent methods succeed. Our empirical analysis shows that vanishing gradients caused by Gaussian process (GP) initialization schemes play a major role in the failures of high-dimensional Bayesian optimization (HDBO) and that methods that promote local search behaviors are better suited for the task. We find that maximum likelihood estimation (MLE) of GP length scales suffices for state-of-the-art performance. Based on this, we propose a simple variant of MLE called MSR that leverages these findings to achieve state-of-the-art performance on a comprehensive set of real-world applications. We present targeted experiments to illustrate and confirm our findings.", "date": "2025-02-13", "categories": []}
{"id": "2510.25240", "title": "Generative Bayesian Optimization: Generative Models as Acquisition Functions", "abstract": "We present a general strategy for turning generative models into candidate solution samplers for batch Bayesian optimization (BO). The use of generative models for BO enables large batch scaling as generative sampling, optimization of non-continuous design spaces, and high-dimensional and combinatorial design. Inspired by the success of direct preference optimization (DPO), we show that one can train a generative model with noisy, simple utility values directly computed from observations to then form proposal distributions whose densities are proportional to the expected utility, i.e., BO's acquisition function values. Furthermore, this approach is generalizable beyond preference-based feedback to general types of reward signals and loss functions. This perspective avoids the construction of surrogate (regression or classification) models, common in previous methods that have used generative models for black-box optimization. Theoretically, we show that the generative models within the BO process follow a sequence of distributions which asymptotically approximate an optimal target under certain conditions. We also evaluate the performance through experiments on challenging optimization problems involving large batches in high dimensions.", "date": "2025-10-29", "categories": []}
{"id": "2602.06104", "title": "Pragmatic Curiosity: A Unified Framework for Hybrid Learning and Optimization via Active Inference", "abstract": "Many engineering and scientific workflows rely on expensive black-box evaluations, requiring sequential decisions that must both improve task performance and reduce uncertainty. Bayesian optimization (BO) and Bayesian experimental design (BED) provide powerful but largely separate treatments of goal-directed optimization and information-seeking experimentation, leaving limited guidance for hybrid settings in which learning and optimization are intrinsically coupled. We propose Pragmatic Curiosity (PraC), a unified framework for hybrid learning and optimization via active inference. PraC evaluates candidate queries by trading information gain about a task-relevant latent symbol against an expected regret-based potential over outcomes. This formulation exposes three operational design choices: which latent quantity should be clarified, how task value is encoded as regret, and how strongly information gain should be exchanged against pragmatic value. We instantiate PraC across three regimes of increasing complexity: decision-oriented plume monitoring with fixed global symbols and known downstream losses, targeted active search with induced local symbols and evolving coverage goals, and composite Bayesian optimization with hierarchical regret learning under unknown preferences. Across these regimes, PraC reduces downstream decision risk, improves coverage of critical outcome regions, and jointly learns predictive and preference structures without relying on task-specific staging rules.", "date": "2026-02-05", "categories": []}
{"id": "2605.13160", "title": "Kernel-based guarantees for nonlinear parametric models in Bayesian optimization", "abstract": "Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on Gaussian processes, kernel machines, linear models, or linearized neural approximations, leaving a gap between theory and the nonlinear models used in practice. We develop a kernel based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data. Our approach uses kernels over the parameter space to induce reproducing kernel Hilbert space structures over the corresponding model class, yielding confidence bounds for models trained with broad classes of regularized convex losses. We show how these bounds can support convergence guarantees for nonlinear acquisition and surrogate models, including randomized regularized policies that select points by maximizing a trained random model. These results provide a unified route to analyzing nonlinear parametric models in Bayesian optimization and related adaptive optimization settings.", "date": "2026-05-13", "categories": []}
{"id": "2603.14094", "title": "Maximin Robust Bayesian Experimental Design", "abstract": "We address the brittleness of Bayesian experimental design under model misspecification by formulating the problem as a max--min game between the experimenter and an adversarial nature subject to information-theoretic constraints. We demonstrate that this approach yields a robust objective governed by Sibson's $\\alpha$-mutual information (MI), which identifies the $\\alpha$-tilted posterior as the robust belief update and establishes the R\\'enyi divergence as the appropriate measure of conditional information gain. To mitigate the bias and variance of nested Monte Carlo estimators needed to estimate Sibson's $\\alpha$-MI, we adopt a PAC-Bayes framework to search over stochastic design policies, yielding rigorous high-probability lower bounds on the robust expected information gain that explicitly control finite-sample error.", "date": "2026-03-14", "categories": []}
{"id": "2605.12079", "title": "Elicitation-Augmented Bayesian Optimization", "abstract": "Human-in-the-loop Bayesian optimization (HITL BO) methods utilize human expertise to improve the sample-efficiency of BO. Most HITL BO methods assume that a domain expert can quantify their knowledge, for instance by pinpointing query locations or specifying their prior beliefs about the location of the maximum as a probability distribution. However, since human expertise is often tacit and cannot be explicitly quantified, we consider a setting where domain knowledge of an expert is elicited via pairwise comparisons of designs. We interpret the expert's pairwise judgements as noisy evidence about the values of the observable objective function and develop a principled method for combining the information obtained via direct observations and pairwise queries. Specifically, we derive a cost-aware value-of-information acquisition function that balances direct observations against pairwise queries. The proposed method approaches the convex hull of the trajectories of the individual information sources: when pairwise queries are cheap it substantially improves sample-efficiency over observation-only BO, and when pairwise queries are costly or noisy, it recovers the performance of standard BO by relying on direct observations alone.", "date": "2026-05-12", "categories": []}
{"id": "2510.17671", "title": "LILO: Bayesian Optimization with Natural Language Feedback", "abstract": "Many real-world optimization problems are guided by complex, subjective preferences that are difficult to express as explicit closed-form objectives. In response, we introduce Language-in-the-Loop Optimization (LILO), a Bayesian optimization (BO) framework that employs a large language model (LLM) to translate free-form natural language feedback and prior knowledge from a decision maker into structured preference signals, going beyond the restrictive scalar or pairwise feedback formats typically assumed in preferential BO. The LLM-derived preferences are integrated by a Gaussian process proxy model, enabling principled acquisition-driven exploration with calibrated uncertainty. By placing the LLM in a supporting role rather than as the optimizer itself, LILO preserves the sample efficiency and stability of BO while providing a flexible and expressive feedback interface. Across synthetic and real-world benchmarks, LILO consistently outperforms both conventional preference-based BO methods and LLM-only optimizers, with particularly strong gains in feedback-limited regimes.", "date": "2025-10-20", "categories": []}
{"id": "2601.22131", "title": "SMOG: Scalable Meta-Learning for Multi-Objective Bayesian Optimization", "abstract": "Multi-objective optimization aims to solve problems with competing objectives. Evaluating such problems is often slow or expensive, limiting the budget of evaluations. In many applications, historical data from related optimization tasks is available and can be leveraged via meta-learning to accelerate optimization. Bayesian optimization, as a promising technique for expensive black-box problems, has been extended independently to meta-learning and multi-objective optimization, but methods that simultaneously address both settings remain largely unexplored. We propose SMOG-a scalable and modular meta-learning model based on a multi-output Gaussian process-that explicitly learns correlations between objectives. SMOG builds a structured joint Gaussian process prior across meta- and target tasks and, after conditioning on metadata, yields a closed-form prior for the target task. This construction propagates metadata uncertainty into the target surrogate in a principled way. SMOG supports hierarchical, parallel training, achieving linear scaling with the number of meta-tasks. The resulting surrogate integrates seamlessly with standard multi-objective Bayesian optimization acquisition functions. We demonstrate that our method is consistently competitive, delivering strong data efficiency across representative benchmarks and applications.", "date": "2026-01-29", "categories": []}
{"id": "2602.07144", "title": "BONSAI: Bayesian Optimization with Natural Simplicity and Interpretability", "abstract": "Bayesian optimization (BO) is a popular technique for sample-efficient optimization of black-box functions. In many applications, the parameters being tuned come with a carefully engineered default configuration, and practitioners only want to deviate from this default when necessary. Standard BO, however, does not aim to minimize deviation from the default and, in practice, often pushes weakly relevant parameters to the boundary of the search space. This makes it difficult to distinguish between important and spurious changes and increases the burden of vetting recommendations when the optimization objective omits relevant operational considerations. We introduce BONSAI, a default-aware BO policy that prunes low-impact deviations from a default configuration while explicitly controlling the loss in acquisition value. BONSAI is compatible with a variety of acquisition functions, including expected improvement and upper confidence bound (GP-UCB). We theoretically bound the regret incurred by BONSAI, showing that, under certain conditions, it enjoys the same no-regret property as vanilla GP-UCB. Moreover, assuming known ARD lengthscales -- the same assumption underlying GP-UCB regret bounds -- BONSAI provably recovers the relevant-coordinate set at zero acquisition cost, yielding a method that matches the GP-UCB regret rate while recovering the minimal-$\\ell_0$ solution -- a guarantee not provided by prior sparse-BO methods. Across many real-world applications, we empirically find that BONSAI substantially reduces the number of non-default parameters in recommended configurations while maintaining competitive optimization performance, with little effect on wall time -- averaging only $1.5\\times$ the candidate-generation cost of standard BO, compared to $7$-$34\\times$ on average for prior sparse-BO methods (IR, ER, and SEBO).", "date": "2026-02-06", "categories": []}
{"id": "2605.09775", "title": "Bayesian Optimization with Structured Measurements: A Vector-Valued RKHS Framework", "abstract": "Bayesian optimization (BO) is an efficient framework for optimizing expensive black-box functions. However, it is typically formulated as learning an end-to-end mapping from inputs to scalar objectives, thereby discarding the potentially rich information whenever a structured system output is available. In this work, we study Bayesian optimization over a vector-valued operator with structured measurements, where each measurement observes multidimensional or functional outputs, e.g., trajectories or spatial fields, rather than a single scalar value. The objective is then defined as a linear functional of these measurements. This allows each observation to reveal substantially richer information about the underlying system compared to scalar observations. Assuming the unknown operator lies in a vector-valued reproducing kernel Hilbert space (RKHS), we derive high-probability concentration bounds for the kernel ridge regression (KRR) estimator directly in the measurement space, characterizing uncertainty in a general Hilbert space. Building on these results, we propose an algorithm based on the upper confidence bound (UCB) acquisition function with regret guarantees under mild assumptions, recovering sublinear rates for common kernels. Empirically, we demonstrate that leveraging structured measurements leads to improved sample efficiency by enabling efficient transfer of information across objectives and adaptation to time-varying settings.", "date": "2026-05-10", "categories": []}
{"id": "2605.10572", "title": "Online Sharp-Calibrated Bayesian Optimization", "abstract": "Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box functions, commonly based on Gaussian process (GP) surrogate models. Its effectiveness relies on uncertainty quantification that is both sharp (informative) and well-calibrated along the BO trajectory. In practice, GP kernel hyperparameters are unknown and are refit online from sequentially collected (non-i.i.d.) data, which can yield miscalibrated or overly conservative uncertainty and lies outside the fixed-kernel assumptions of standard BO regret theory. We propose Online Sharp-Calibrated Bayesian Optimization (OSCBO), a BO algorithm that adaptively balances GP sharpness and calibration by casting hyperparameter selection as a constrained online-learning problem. We also show that OSCBO preserves sublinear regret bounds by leveraging the theoretical guarantees of the underlying online learning algorithm. Empirically, OSCBO performs competitively across synthetic and real-world benchmarks, ranking among the strongest methods in final simple regret while maintaining robust cumulative-regret behavior.", "date": "2026-05-11", "categories": []}
{"id": "2512.14263", "title": "DT-PBO: an Interpretable Tree-based Surrogate Model for Preferential Bayesian Optimization", "abstract": "Preferential Bayesian Optimization (PBO) aims to find a decision-maker's most preferred solution in as few pairwise comparisons as possible. Existing approaches rely on Gaussian Process (GP) surrogates, which provide strong performance but limited interpretability. This limits real-world usability in high-stakes domains, such as healthcare, where interpretability and trust are essential. We propose DT-PBO, a novel tree-based surrogate model for PBO that is inherently interpretable while capturing preference uncertainty. Specifically, we introduce a novel splitting heuristic that constructs interpretable shallow decision trees directly from pairwise comparison data, and use Laplace approximation to obtain probabilistic estimates for each leaf. This enables efficient preference modeling without sacrificing interpretability. Across eight benchmark functions, our method achieves competitive convergence to GP-based PBO, particularly on functions with rugged optimization landscapes. Additional experiments show robustness against noise and a fast computational running time. Experiments on real-world datasets further demonstrate that our model provides interpretable insights into decision-maker preferences that would remain opaque under GP-based approaches.", "date": "2025-12-16", "categories": []}
{"id": "2605.07565", "title": "Ensemble Distributionally Robust Bayesian Optimisation", "abstract": "We study zeroth-order optimisation under context distributional uncertainty, a setting commonly tackled using Bayesian optimisation (BO). A prevailing strategy to make BO more robust to the complex and noisy nature of data is to employ an ensemble as the surrogate model, thereby mitigating the weaknesses of any single model. In this study, we propose a novel algorithm for Ensemble Distributionally Robust Bayesian Optimisation that remains computationally tractable while managing continuous context. We obtain theoretical sublinear regret bounds, improving current state-of-the-art results. We show that our method's empirical behaviour aligns with its theoretical guarantees.", "date": "2026-05-08", "categories": []}
{"id": "2605.07572", "title": "Open-Ended Task Discovery via Bayesian Optimization", "abstract": "When applying Bayesian optimization (BO) to scientific workflow, a major yet often overlooked source of uncertainty is the task itself -- namely, what to optimize and how to evaluate it -- which can evolve as evidence accumulates. We introduce Generate-Select-Refine (GSR), a open-ended BO framework that alternates between task generation and task optimization. Starting from a user-provided seed task, GSR generates new tasks in a coarse-to-fine manner while a task-acquisition function schedules optimization. Asymptotically, it concentrates evaluations on the best task, incurring only logarithmic regret overhead relative to single-task BO. We apply GSR to new product development, chemical synthesis scaling, algorithm analysis, and patent repurposing, where it outperforms existing LLM-based optimizers.", "date": "2026-05-08", "categories": []}
{"id": "2605.07863", "title": "ADKO: Agentic Decentralized Knowledge Optimization", "abstract": "We present Agentic Decentralized Knowledge Optimization (ADKO), a framework for collaborative black-box optimization across autonomous agents that achieves sample efficiency, privacy preservation, heterogeneous-objective handling, and communication efficiency. Each agent maintains a private Gaussian Process (GP) surrogate trained on local data and communicates only through knowledge tokens-compact, lossy summaries containing directional signals, advantage scores, and optional language-model (LM) insights-without sharing raw data or model parameters. ADKO unifies GP-Upper Confidence Bound (GP-UCB), parallel Bayesian optimization, decentralized learning, and LM-guided discovery. We provide the first formal analysis of dual information loss: token compression, quantified via mutual-information-based fidelity, and LM approximation error, decomposed into bias and stochastic noise. Our main result shows cumulative regret decomposes into GP error, LM bias, LM noise, and compression loss, with necessary and sufficient conditions for sublinear regret. We also propose fidelity-aware token pruning to preserve high-information tokens under memory budget. Experiments on neural architecture search and scientific discovery validate the theory and show consistent improvements over strong baselines.", "date": "2026-05-08", "categories": []}
{"id": "2601.12355", "title": "Tree-Structured Synergy of Large Language Models and Bayesian Optimization for Efficient CASH", "abstract": "To lower the expertise barrier in machine learning, the AutoML community has focused on the CASH problem, which jointly automates algorithm selection and hyperparameter tuning. While traditional methods like Bayesian Optimization (BO) struggle with cold-start issues, Large Language Models (LLMs) can mitigate these through semantic priors. However, existing LLM-based optimizers generalize poorly to high-dimensional, structured CASH spaces. In this paper, we propose LB-MCTS, a trajectory-structured optimization framework that uses a Monte Carlo Tree Search tree as a shared state for algorithm selection, hyperparameter refinement, and BO-LLM proposer synergy. Within this shared state, BO provides algorithm-specific surrogate modeling for quantitative search, while the LLM exploits path-aware selective memory to generate semantic proposals and reflections. As the surrogate model improves, a reliability-aware proposer policy adaptively shifts from LLM-driven to BO-driven proposals within a unified search trajectory. Experiments on 104 AMLB datasets demonstrate that LB-MCTS consistently outperforms BO-based, LLM-based, and hybrid baselines.", "date": "2026-01-18", "categories": []}
{"id": "2605.05382", "title": "Meta-learning for sample-efficient Bayesian optimisation of fed-batch processes", "abstract": "The optimisation of fed-batch (bio)chemical process recipes is subject to inherent, underlying, and unmeasurable fluctuations across batches, whose trajectories are difficult to model and costly to measure. Bayesian Optimisation (BayesOpt) is a powerful tool for sampling and optimisation of expensive-to-measure functions. Gaussian Processes (GPs), the surrogate models used in BayesOpt, are static, forecast poorly, and lack generalisation across experiments, limiting their applicability to time-varying batch processes with stochastic parameters, i.e., process fluctuations. This work investigates System-Aware Neural ODE Processes (SANODEP) as a meta-learning model to overcome the limitations of GPs and increase few-shot optimisation performance in BayesOpt. Using a penicillin batch production case study, we find that SANODEP outperforms GP-based BayesOpt in the low-data regime, resulting in improved objectives when few experimental runs are performed. These improvements are observed in both on- and off-distribution batches, highlighting the generalisation capabilities of SANODEP. Using this approach, batch process operators can accelerate the initial optimisation steps in BayesOpt by deploying meta-learning or optimise the process with fewer experiments when the experimental cost is high.", "date": "2026-05-06", "categories": []}
{"id": "2605.06187", "title": "In-Context Black-Box Optimization with Unreliable Feedback", "abstract": "Black-box optimization in science and engineering often comes with side information: experts, simulators, pretrained predictors, or heuristics can suggest which candidates look promising. This information can accelerate search, but it can also be biased, input-dependent, or misleading. Feedback-aware BO methods typically handle one task at a time, limiting their ability to generalize over multiple sources of feedback. In-context optimizers address cross-task adaptation, but usually assume that optimization history is the only available signal at test time. We study feedback-informed in-context black-box optimization (FICBO), where a pretrained optimizer conditions on both the observed history and cheap auxiliary feedback for the current candidate set. We introduce a structured feedback prior that models how feedback sources vary in their access, relevance, and distortion relative to the true objective, and use it to pretrain a feedback-aware transformer. At test time, the model estimates source reliability in context by comparing observed objective values with auxiliary signals, improving query selection. On synthetic and real-world tasks, FICBO effectively exploits informative feedback while remaining robust to weak or misleading sources, improving over other baselines. Empirical investigations further illustrate how the model perceives test-time sources, offering insights into its interpretability and decision-making process.", "date": "2026-05-07", "categories": []}
{"id": "2605.06413", "title": "Decoupled PFNs: Identifiable Epistemic-Aleatoric Decomposition via Structured Synthetic Priors", "abstract": "Prior-Fitted Networks (PFNs) amortize Bayesian prediction by meta-learning over a synthetic task prior, but their standard output is a posterior predictive distribution over noisy observations. For sequential decision-making, such as active learning and Bayesian optimization, acquisition should prioritize epistemic uncertainty about the latent signal rather than irreducible aleatoric observation noise. We show that this epistemic--aleatoric split is not identifiable in general from the posterior predictive distribution alone, even when that distribution is known exactly. We then exploit a distinctive advantage of PFNs: because the synthetic data-generating process is under our control, each task can contain an explicit latent signal and noise function, and the generator can provide query-level labels for both the noiseless target and the observation-noise variance. We use these labels to train a decoupled PFN with separate latent-signal and aleatoric heads. The observation-level predictive is induced by convolving the latent signal distribution with the learned noise model. Empirically, epistemic-only acquisition mitigates the failure mode of total-variance exploration in noisy and heteroscedastic settings. In matched comparisons, decoupled models usually improve over tuned observation-level baselines, with the clearest gains in HPO; in broader sweeps, a decoupled model obtains the best average rank in both HPO and synthetic BO.", "date": "2026-05-07", "categories": []}
{"id": "2605.06454", "title": "ORTHOBO: Orthogonal Bayesian Hyperparameter Optimization", "abstract": "Bayesian optimization is widely used for hyperparameter optimization when model evaluations are expensive; however, noisy acquisition estimates can lead to unstable decisions. We identify acquisition estimation noise as a failure mode that was previously overlooked: even when the surrogate model and acquisition target are correctly specified, finite-sample Monte Carlo error can perturb acquisition values. This can, in turn, flip candidate rankings and lead to suboptimal BO decisions. As a remedy, we aim at variance reduction and propose an orthogonal acquisition estimator that subtracts an optimally weighted score-function control variate, which yields an acquisition residual orthogonal to posterior score directions and which thus reduces Monte Carlo variance. We further introduce OrthoBO: a Bayesian optimization framework that combines our orthogonal acquisition estimator with ensemble surrogates and an outer log transformation. We show theoretically that our estimator preserves the target, leads to variance reduction, and improves pairwise ranking stability. We further verify the theoretical properties of OrthoBO through numerical experiments where our framework reduces acquisition estimation variance, stabilizes candidate rankings, and achieves strong performance. We also demonstrate the downstream utility of OrthoBO in hyperparameter optimization for neural network training and fine-tuning.", "date": "2026-05-07", "categories": []}
{"id": "2605.00237", "title": "Bayesian Optimization in Linear Time", "abstract": "Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and adaptively employing a mixture of global exploration and local exploitation, this method has been used for optimization in many fields including machine learning, automotive engineering and reinforcement learning. However, the standard method suffers from two problems: 1) with cubic computational complexity in the training-set size it eventually becomes computationally infeasible to train the model, and 2) globally modeling the objective function is not necessarily optimal given the local nature of minimization. Using flexible and recursive binary partitioning of the search space, we adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme, thereby ameliorating both standard shortcomings. We compare our method against a commonly used Bayesian optimization library on seven challenging test functions, ranging in dimensionality from $6$ to $124$, and show that our method achieves superior optimization performance in all tests. In addition our method has linear computational complexity.", "date": "2026-04-30", "categories": []}
{"id": "2605.04895", "title": "Regime-Conditioned Evaluation in Multi-Context Bayesian Optimization", "abstract": "Published transfer-BO comparisons often estimate an average treatment effect of acquisition choice over hidden regime variables, while practitioners need the conditional effect for their specific prior quality, budget ratio, and metric. An audit of 40 transfer-BO papers from NeurIPS, ICML, ICLR, AISTATS, UAI, TMLR, JMLR, and AutoML-Conf (2022-2025) finds that 98% never vary B/|A| as a controlled axis. On the same GDSC2 benchmark, changing only the budget reverses the ranking: at B=50, Greedy outperforms UCB by 0.050 Hit@1, while at B=100, UCB outperforms Greedy by 0.035. We capture this transition with the Portable Regime Score PRS=(B/|A|)(1-rho), where rho is the prior rank correlation and can be estimated from pilot contexts before the main comparison. Across 79 conditions spanning chemistry, drug-response biology, and HPO, a hierarchical model gives beta=0.50 (p=1.1e-9), and 19% of conditions fall in an equivalence zone where |advantage|<0.01 Hit@1. In five published reversal cases, PRS predicts the winner from pre-comparison observables. A No-Free-Leaderboard proposition explains why unconditional rankings are unstable: when CATE changes sign across regimes, the reported ATE becomes a function of benchmark mixture. RegimePlanner, which estimates rho online and switches acquisition accordingly, wins all 16 HPO-B search spaces at B=100 and exceeds the matched {Greedy,UCB} per-context oracle on GDSC2 by 18%. Pre-registered predictions achieve 27/40=67.5% overall accuracy and above 90% within EMA prior families. The practical protocol is simple: report B/|A|, rho, K, and metric alongside any claimed acquisition advantage.", "date": "2026-05-06", "categories": []}
{"id": "2503.06917", "title": "Sample-Efficient Optimization over Generative Priors via Coarse Learnability", "abstract": "We study zeroth-order optimization where solutions must minimize a cost $d(s)$ while maintaining high probability under a complex generative prior $L(s)$ (e.g., a parameterized model). This reduces to sampling from a target distribution proportional to $L(s) e^{-T \\cdot d(s)}$. Since classical model-based optimization (MBO) lacks finite-sample guarantees for expressive approximate learners, we introduce \"coarse learnability\", a flexible statistical assumption requiring only that a learned model covers the target's probability mass within a polynomial factor. Leveraging this assumption, we design an iterative MBO algorithm called \\alift with a sample correction step that provably approximates the target using only a polynomial number of samples. We apply this framework to globally optimizing non-convex objectives bounded by a quadratic envelope in $R^n$, where we show this assumption is naturally satisfied for a family of \"optimistic\" posterior distributions. To reach global $\\varepsilon$-optimality, this implies a sample complexity of $\\widetilde{O}(\\log 1/\\varepsilon)$, a rate characteristic of optimistic space-partitioning methods. We further justify coarse learnability as an assumption for generative priors theoretically, proving that in simple settings, parametric maximum likelihood estimation and over-smoothed kernel density estimators naturally satisfy it. Finally, one motivation for our framework comes from inference-time alignment. Though our primary contribution pertains to the theoretical foundations of MBO, we provide qualitative evidence that, in simple settings, even primitive LLMs can shift their distributions toward lower-cost regions when fine-tuned with zeroth-order feedback.", "date": "2025-03-10", "categories": []}
{"id": "2506.12818", "title": "Taking the GP Out of the Loop", "abstract": "Bayesian optimization (BO) has traditionally solved black-box problems where function evaluation is expensive and, therefore, observations are few. Recently, however, there has been growing interest in applying BO to problems where function evaluation is cheaper and observations are more plentiful. In this regime, scaling to many observations $N$ is impeded by Gaussian-process (GP) surrogates: GP hyperparameter fitting scales as $\\mathcal{O}(N^3)$ (reduced to roughly $\\mathcal{O}(N^2)$ in modern implementations), and it is repeated at every BO iteration. Many methods improve scaling at acquisition time, but hyperparameter fitting still scales poorly, making it the bottleneck. We propose Epistemic Nearest Neighbors (ENN), a lightweight alternative to GPs that estimates function values and uncertainty (epistemic and aleatoric) from $K$-nearest-neighbor observations. ENN scales as $\\mathcal{O}(N)$ for both fitting and acquisition. Our BO method, TuRBO-ENN, replaces the GP surrogate in TuRBO with ENN and its Thompson-sampling acquisition with $\\mathrm{UCB} = \\mu(x) + \\sigma(x)$. For the special case of noise-free problems, we can omit fitting altogether by replacing $\\mathrm{UCB}$ with a non-dominated sort over $\\mu(x)$ and $\\sigma(x)$. We show empirically that TuRBO-ENN reduces proposal time (i.e., fitting time + acquisition time) by one to two orders of magnitude compared to TuRBO at up to 50,000 observations.", "date": "2025-06-15", "categories": []}
{"id": "2501.10859", "title": "What price to pay? Auto-tuning a building MPC controller for optimal economic cost", "abstract": "Demand-side management (DSM) programs introduce complex pricing, requiring advanced control for cost minimization. Model Predictive Control (MPC) offers a solution but its performance hinges on appropriate hyperparameter tuning. We propose using Constrained Bayesian Optimization (CONFIG) to automate this process. In a case study, our optimized MPC reduced electricity costs by 26.90% compared to a rule-based controller and by 17.46% versus an manually tuned MPC. Analysis of real contracts further showed that optimal DSM program selection can lower monthly bills by up to 20.18%, demonstrating a data-driven path to significant consumer savings.", "date": "2025-01-18", "categories": []}
{"id": "2507.21803", "title": "Bayesian Neural Network Surrogates for Bayesian Optimization of Carbon Capture and Storage Operations", "abstract": "Carbon Capture and Storage (CCS) stands as a pivotal technology for fostering a sustainable future. The process, which involves injecting supercritical CO$_2$ into underground formations, a method already widely used for Enhanced Oil Recovery, serves a dual purpose: it not only curbs CO$_2$ emissions and addresses climate change but also extends the operational lifespan and sustainability of oil fields and platforms, easing the shift toward greener practices. This paper delivers a thorough comparative evaluation of strategies for optimizing decision variables in CCS project development, employing a derivative-free technique known as Bayesian Optimization. In addition to Gaussian Processes, which usually serve as the gold standard in BO, various novel stochastic models were examined and compared within a BO framework. This research investigates the effectiveness of utilizing more exotic stochastic models than GPs for BO in environments where GPs have been shown to underperform, such as in cases with a large number of decision variables or multiple objective functions that are not similarly scaled. By incorporating Net Present Value (NPV) as a key objective function, the proposed framework demonstrates its potential to improve economic viability while ensuring the sustainable deployment of CCS technologies. Ultimately, this study represents the first application in the reservoir engineering industry of the growing body of BO research, specifically in the search for more appropriate stochastic models, highlighting its potential as a preferred method for enhancing sustainability in the energy sector.", "date": "2025-07-29", "categories": []}
{"id": "2605.00909", "title": "Accelerating battery research with an AI interface between FINALES and Kadi4Mat", "abstract": "The time-consuming formation process critically impacts the longevity of sodium-ion coin cells and End Of Life (EOL) performance. This study aims to optimize formation protocols for duration efficiency, targeting high-performance outcomes while minimizing the number of experiments to reduce resource consumption and accelerate discovery. Specifically, we consider two potentially competing objectives: minimizing formation time and maximizing EOL performance. Beyond this application focus, we also present a methodological contribution: a framework designed to enable interoperability between the FINALES and Kadi RDM ecosystems, which we employ to tackle our optimization problem. In this setup, the FINALES framework orchestrates experiment planning and execution on the POLiS MAP, while an active-learning agent implemented within Kadi4Mat guides experiment selection, using multi-objective batched Bayesian optimization to efficiently explore the parameter space. This interoperability enhancement enables coordinated, distributed collaboration across automated systems and human-operated workflows, bridging multiple research centers. Using this approach, we iteratively explore the trade-off between formation time and EOL performance and identify candidate solutions approximating the Pareto front. The resulting workflow demonstrates the capability of interoperable infrastructures to facilitate data-driven optimization in battery research, and establishes a transferable framework applicable to diverse materials science and engineering optimization tasks.", "date": "2026-04-29", "categories": []}
{"id": "2605.02690", "title": "Caliper-in-the-Loop: Black-Box Optimization for Hyperledger Fabric Performance Tuning", "abstract": "Hyperledger Fabric performance depends on many interacting configuration parameters, making manual tuning difficult. We study automated throughput tuning by treating benchmarking as a noisy black-box optimization problem and applying Bayesian optimization (BO) with dimensionality reduction (DR). We implement an end-to-end Caliper-in-the-loop pipeline that deploys candidate configurations, benchmarks them, and updates the optimizer from observed throughput. The search space, derived from Fabric configuration files, has 317 dimensions. In a cloud testbed, we evaluate 16 BO+DR variants and a random-search baseline. The best method, DYCORS-PCA, achieves a 12% TPS improvement relative to the first evaluated configuration, while MPI-REMBO achieves 9%. These results suggest that BO with DR is a practical approach for high-dimensional Hyperledger Fabric tuning, while also highlighting the role of measurement noise in interpreting gains.", "date": "2026-05-04", "categories": []}
{"id": "2605.00068", "title": "Human-in-the-Loop Meta Bayesian Optimization for Fusion Energy and Scientific Applications", "abstract": "Inertial Confinement Fusion (ICF) holds transformative promise for sustainable, near-limitless clean energy, yet remains constrained by prohibitively high costs and limited experimental opportunities. This paper presents Human-in-the-Loop Meta Bayesian Optimization (HL-MBO), a framework that integrates expert knowledge with few-shot, uncertainty-aware machine learning to accelerate discovery in data-scarce, high-stakes scientific domains. HL-MBO introduces a meta-learned surrogate model with an expert-informed acquisition function to recommend candidate experiments. To foster trust and enable informed decisions, HL-MBO also provides interpretable explanations of its suggestions. We show HL-MBO outperforms current BO methods on ICF energy yield optimization, as well as benchmarks in molecular optimization and critical temperature maximization for superconducting materials.", "date": "2026-04-30", "categories": []}
{"id": "2504.13529", "title": "Improving Bayesian Optimization for Portfolio Management with an Adaptive Scheduling", "abstract": "Existing black-box portfolio management systems are prevalent in the financial industry due to commercial and safety constraints, though their performance can fluctuate dramatically with changing market regimes. Evaluating these non-transparent systems is computationally expensive, as fixed budgets limit the number of possible observations. Therefore, achieving stable and sample-efficient optimization for these systems has become a critical challenge. This work presents a novel Bayesian optimization framework (TPE-AS) that improves search stability and efficiency for black-box portfolio models under these limited observation budgets. Standard Bayesian optimization, which solely maximizes expected return, can yield erratic search trajectories and misalign the surrogate model with the true objective, thereby wasting the limited evaluation budget. To mitigate these issues, we propose a weighted Lagrangian estimator that leverages an adaptive schedule and importance sampling. This estimator dynamically balances exploration and exploitation by incorporating both the maximization of model performance and the minimization of the variance of model observations. It guides the search from broad, performance-seeking exploration towards stable and desirable regions as the optimization progresses. Extensive experiments and ablation studies, which establish our proposed method as the primary approach and other configurations as baselines, demonstrate its effectiveness across four backtest settings with three distinct black-box portfolio management models.", "date": "2025-04-18", "categories": []}
{"id": "2305.06709", "title": "NUBO: A Transparent Python Package for Bayesian Optimization", "abstract": "NUBO, short for Newcastle University Bayesian Optimisation, is a Bayesian optimization framework for the optimization of expensive-to-evaluate black-box functions, such as physical experiments and computer simulators. Bayesian optimization is a costefficient optimization strategy that uses surrogate modelling via Gaussian processes to represent an objective function and acquisition functions to guide the selection of candidate points to approximate the global optimum of the objective function. NUBO itself focuses on transparency and user experience to make Bayesian optimization easily accessible to researchers from all disciplines. Clean and understandable code, precise references, and thorough documentation ensure transparency, while user experience is ensured by a modular and flexible design, easy-to-write syntax, and careful selection of Bayesian optimization algorithms. NUBO allows users to tailor Bayesian optimization to their specific problem by writing the optimization loop themselves using the provided building blocks. It supports sequential single-point, parallel multi-point, and asynchronous optimization of bounded, constrained, and/or mixed (discrete and continuous) parameter input spaces. Only algorithms and methods that are extensively tested and validated to perform well are included in NUBO. This ensures that the package remains compact and does not overwhelm the user with an unnecessarily large number of options. The package is written in Python but does not require expert knowledge of Python to optimize your simulators and experiments. NUBO is distributed as open-source software under the BSD 3-Clause license.", "date": "2023-05-11", "categories": []}
{"id": "2511.03125", "title": "Provable Accelerated Bayesian Optimization with Knowledge Transfer", "abstract": "We study how to accelerate Bayesian optimization (BO) on a target task by transferring historical knowledge from related source tasks. Existing work on BO with knowledge transfer either lacks theoretical guarantees or achieves the same regret as BO in the non-transfer setting, $\\widetilde{O}(\\sqrt{T \\gamma_f})$, where $T$ is the number of evaluations of the target function and $\\gamma_f$ denotes its information gain. In this paper, we propose the DeltaBO algorithm, which builds a novel uncertainty-quantification approach on the difference function $\\delta$ between the source and target functions, which are allowed to belong to different Reproducing Kernel Hilbert Spaces (RKHSs). Under mild assumptions, we prove that the regret of DeltaBO is of order $\\widetilde{O}(\\sqrt{T (T/N + \\gamma_\\delta)})$, where $N$ denotes the number of evaluations from source tasks and typically $N \\gg T$. In many applications, source and target tasks are similar, which implies that $\\gamma_\\delta$ can be much smaller than $\\gamma_f$. Empirical studies on both real-world hyperparameter-tuning tasks and synthetic functions show that DeltaBO outperforms other baseline methods and also verify our theoretical claims. Our code is available on GitHub.", "date": "2025-11-05", "categories": []}
{"id": "2604.25025", "title": "A Finite Time Analysis of Thompson Sampling for Bayesian Optimization with Preferential Feedback", "abstract": "Preference feedback, in the form of pairwise comparisons rather than scalar scores, has seen increasing use in applications such as human-, laboratory-, and expert-in-the-loop design, as well as scientific discovery. We propose a Thompson Sampling (TS) approach to Bayesian optimization with preferential feedback that models comparisons using a monotone link on latent utility differences and leverages the dueling kernel induced by a base kernel. We provide a finite-time analysis showing that the performance of the proposed method matches that of standard TS for conventional Bayesian optimization with scalar feedback. The analysis exploits the anchor invariance of TS for challenger selection and introduces a double-TS pairing variant. We also demonstrate the performance of the method on both synthetic and real-world examples.", "date": "2026-04-27", "categories": []}
{"id": "2512.07868", "title": "Bayesian Optimization for Function-Valued Responses under Min-Max Criteria", "abstract": "Bayesian optimization is widely used for optimizing expensive black box functions, but most existing approaches focus on scalar responses. In many scientific and engineering settings the response is functional, varying smoothly over an index such as time or wavelength, which makes classical formulations inadequate. Existing methods often minimize integrated error, which captures average performance but neglects worst case deviations. To address this limitation we propose min-max Functional Bayesian Optimization (MM-FBO), a framework that directly minimizes the maximum error across the functional domain. Functional responses are represented using functional principal component analysis, and Gaussian process surrogates are constructed for the principal component scores. Building on this representation, MM-FBO introduces an integrated uncertainty acquisition function that balances exploitation of worst case expected error with exploration across the functional domain. We provide two theoretical guarantees: a discretization bound for the worst case objective, and a consistency result showing that as the surrogate becomes accurate and uncertainty vanishes, the acquisition converges to the true min-max objective. We validate the method through experiments on synthetic benchmarks and physics inspired case studies involving electromagnetic scattering by metaphotonic devices and vapor phase infiltration. Results show that MM-FBO consistently outperforms existing baselines and highlights the importance of explicitly modeling functional uncertainty in Bayesian optimization.", "date": "2025-11-26", "categories": []}
{"id": "2604.22967", "title": "Rethinking Trust Region Bayesian Optimization in High Dimensions", "abstract": "Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO's local GP may remain either excessively complex or overly simple as the dimension $D$ and trust region side length $L$ vary. To address this issue, we propose a straightforward variant, AdaScale-TuRBO, which scales the GP lengthscale with both the problem dimension and trust region size, thereby preserving kernel geometry and maintaining consistent prior complexity. Empirically, we show that AdaScale-TuRBO can robustly outperform standard TuRBO and other popular high-dimensional BO methods on synthetic benchmarks and real-world trajectory planning tasks.", "date": "2026-04-24", "categories": []}
{"id": "2411.00171", "title": "EARL-BO: Reinforcement Learning for Multi-Step Lookahead, High-Dimensional Bayesian Optimization", "abstract": "To avoid myopic behavior, multi-step lookahead Bayesian optimization (BO) algorithms consider the sequential nature of BO and have demonstrated promising results in recent years. However, owing to the curse of dimensionality, most of these methods make significant approximations or suffer scalability issues. This paper presents a novel reinforcement learning (RL)-based framework for multi-step lookahead BO in high-dimensional black-box optimization problems. The proposed method enhances the scalability and decision-making quality of multi-step lookahead BO by efficiently solving the sequential dynamic program of the BO process in a near-optimal manner using RL. We first introduce an Attention-DeepSets encoder to represent the state of knowledge to the RL agent and subsequently propose a multi-task, fine-tuning procedure based on end-to-end (encoder-RL) on-policy learning. We evaluate the proposed method, EARL-BO (Encoder Augmented RL for BO), on synthetic benchmark functions and hyperparameter tuning problems, finding significantly improved performance compared to existing multi-step lookahead and high-dimensional BO methods.", "date": "2024-10-31", "categories": []}
{"id": "2604.20938", "title": "HARBOR: Automated Harness Optimization", "abstract": "Long-horizon language-model agents are dominated, in lines of code and in operational complexity, not by their underlying model but by the harness that wraps it: context compaction, tool caching, semantic memory, trajectory reuse, speculative tool prediction, and the glue that binds the model to a sandboxed execution environment. We argue that harness design is a first-class machine-learning problem and that automated configuration search dominates manual stacking once the flag space exceeds a handful of bits. We defend this claim in two steps. First, we formalize automated harness optimization as constrained noisy Bayesian optimization over a mixed-variable, cost-heterogeneous configuration space with cold-start-corrected rewards and a posterior chance-constrained safety check, and give a reference solver, HARBOR (Harness Axis-aligned Regularized Bayesian Optimization Routine), built from a block-additive SAAS surrogate, multi-fidelity cost-aware acquisition, and TuRBO trust regions. Second, we instantiate the problem in a flag-gated harness over a production coding agent and report a controlled four-round manual-tuning case study against a fixed task suite and an end-to-end HARBOR run. The formulation itself is task-class agnostic: the configuration space, reward correction, acquisition, and safety check apply to any agent harness with a bounded flag space and a reproducible task suite.", "date": "2026-04-22", "categories": []}
{"id": "2410.16893", "title": "Global Optimization of Gaussian Process Acquisition Functions Using a Piecewise-Linear Kernel Approximation", "abstract": "Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms employ sampling- or gradient-based methods, which do not provably converge to global optima. This work investigates mixed-integer programming (MIP) as a paradigm for global acquisition function optimization. Specifically, our Piecewise-linear Kernel Mixed Integer Quadratic Programming (PK-MIQP) formulation introduces a piecewise-linear approximation for Gaussian process kernels and admits a corresponding MIQP representation for acquisition functions. The proposed method is applicable to uncertainty-based acquisition functions for any stationary or dot-product kernel. We analyze the theoretical regret bounds of the proposed approximation, and empirically demonstrate the framework on synthetic functions, constrained benchmarks, and a hyperparameter tuning task.", "date": "2024-10-22", "categories": []}
{"id": "2604.18912", "title": "Collaborative Contextual Bayesian Optimization", "abstract": "Discovering optimal designs through sequential data collection is essential in many real-world applications. While Bayesian Optimization (BO) has achieved remarkable success in this setting, growing attention has recently turned to context-specific optimal design, formalized as Contextual Bayesian Optimization (CBO). Unlike BO, CBO is inherently more challenging as it must approximate an entire mapping from the context space to its corresponding optimal design, requiring simultaneous exploration across contexts and exploitation within each. In many modern applications, such tasks arise across multiple potentially heterogeneous but related clients, where collaboration can significantly improve learning efficiency. We propose CCBO, Collaborative Contextual Bayesian Optimization, a unified framework enabling multiple clients to jointly perform CBO with controllable contexts, supporting both online collaboration and offline initialization from peers' historical beliefs, with an optional privacy-preserving communication mechanism. We establish sublinear regret guarantees and demonstrate, through extensive simulations and a real-world hot rolling application, that CCBO achieves substantial improvements over existing approaches even under client heterogeneity. The code to reproduce the results can be found at https://github.com/cchihyu/Collaborative-Contextual-Bayesian-Optimization", "date": "2026-04-20", "categories": []}
{"id": "2604.13672", "title": "Optimization with SpotOptim", "abstract": "The `spotoptim` package implements surrogate-model-based optimization of expensive black-box functions in Python. Building on two decades of Sequential Parameter Optimization (SPO) methodology, it provides a Kriging-based optimization loop with Expected Improvement, support for continuous, integer, and categorical variables, noise-aware evaluation via Optimal Computing Budget Allocation (OCBA), and multi-objective extensions. A steady-state parallelization strategy overlaps surrogate search with objective evaluation on multi-core hardware, and a success-rate-based restart mechanism detects stagnation while preserving the best solution found. The package returns scipy-compatible `OptimizeResult` objects and accepts any scikit-learn-compatible surrogate model. Built-in TensorBoard logging provides real-time monitoring of convergence and surrogate quality. This report describes the architecture and module structure of spotoptim, provides worked examples including neural network hyperparameter tuning, and compares the framework with BoTorch, Optuna, Ray Tune, BOHB, SMAC, and Hyperopt. The package is open-source.", "date": "2026-04-15", "categories": []}
{"id": "2604.12005", "title": "BayMOTH: Bayesian optiMizatiOn with meTa-lookahead -- a simple approacH", "abstract": "Bayesian optimization (BO) has for sequential optimization of expensive black-box functions demonstrated practicality and effectiveness in many real-world settings. Meta-Bayesian optimization (meta-BO) focuses on improving the sample efficiency of BO by making use of information from related tasks. Although meta-BO is sample-efficient when task structure transfers, poor alignment between meta-training and test tasks can cause suboptimal queries to be suggested during online optimization. To this end, we propose a simple meta-BO algorithm that utilizes related-task information when determined useful, falling back to lookahead otherwise, within a unified framework. We demonstrate competitiveness of our method with existing approaches on function optimization tasks, while retaining strong performance in low task-relatedness regimes where test tasks share limited structure with the meta-training set.", "date": "2026-04-13", "categories": []}
{"id": "2604.08569", "title": "Memory-Guided Trust-Region Bayesian Optimization (MG-TuRBO) for High Dimensions", "abstract": "Traffic simulation and digital-twin calibration is a challenging optimization problem with a limited simulation budget. Each trial requires an expensive simulation run, and the relationship between calibration inputs and model error is often nonconvex, and noisy. The problem becomes more difficult as the number of calibration parameters increases. We compare a commonly used automatic calibration method, a genetic algorithm (GA), with Bayesian optimization methods (BOMs): classical Bayesian optimization (BO), Trust-Region BO (TuRBO), Multi-TuRBO, and a proposed Memory-Guided TuRBO (MG-TuRBO) method. We compare performance on 2 real-world traffic simulation calibration problems with 14 and 84 decision variables, representing lower- and higher-dimensional (14D and 84D) settings. For BOMs, we study two acquisition strategies, Thompson sampling and a novel adaptive strategy. We evaluate performance using final calibration quality, convergence behavior, and consistency across runs. The results show that BOMs reach good calibration targets much faster than GA in the lower-D problem. MG-TuRBO performs comparably in our 14D setting, it demonstrates noticeable advantages in the 84D problem, particularly when paired with our adaptive strategy. Our results suggest that MG-TuRBO is especially useful for high-D traffic simulation calibration and potentially for high-D problems in general.", "date": "2026-03-25", "categories": []}
{"id": "2604.08891", "title": "Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization", "abstract": "In Bayesian optimization, Thompson sampling selects the evaluation point by sampling from the posterior distribution over the objective function maximizer. Because this sampling problem is intractable for Gaussian process (GP) surrogates, the posterior distribution is typically restricted to fixed discretizations (i.e., candidate points) that become exponentially sparse as dimensionality increases. While previous works aim to increase candidate point density through scalable GP approximations, our orthogonal approach increases density by adaptively reducing the search space during sampling. Specifically, we introduce Adaptive Candidate Thompson Sampling (ACTS), which generates candidate points in subspaces guided by the gradient of a surrogate model sample. ACTS is a simple drop-in replacement for existing TS methods -- including those that use trust regions or other local approximations -- producing better samples of maxima and improved optimization across synthetic and real-world benchmarks.", "date": "2026-04-10", "categories": []}
{"id": "2604.09417", "title": "Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?", "abstract": "Many-objective optimisation, a subset of multi-objective optimisation, involves optimisation problems with more than three objectives. As the number of objectives increases, the number of solutions needed to adequately represent the entire Pareto front typically grows substantially. This makes it challenging, if not infeasible, to design a search algorithm capable of effectively exploring the entire Pareto front. This difficulty is particularly acute in the Bayesian optimisation paradigm, where sample efficiency is critical and only a limited number of solutions (often a few hundred) are evaluated. Moreover, after the optimisation process, the decision-maker eventually selects just one solution for deployment, regardless of how many high-quality, diverse solutions are available. In light of this, we argue an idea that under a very limited evaluation budget, it may be more useful to focus on finding a single solution of the highest possible quality for the decision-maker, rather than aiming to approximate the entire Pareto front as existing many-/multi-objective Bayesian optimisation methods typically do. Bearing this idea in mind, this paper proposes a \\underline{s}ingle \\underline{p}oint-based \\underline{m}ulti-\\underline{o}bjective search framework (SPMO) that aims to improve the quality of solutions along a direction that leads to a good tradeoff between objectives. Within SPMO, we present a simple acquisition function, called expected single-point improvement (ESPI), working under both noiseless and noisy scenarios. We show that ESPI can be optimised effectively with gradient-based methods via the sample average approximation (SAA) approach and theoretically prove its convergence guarantees under the SAA. We also empirically demonstrate that the proposed SPMO is computationally tractable and outperforms state-of-the-arts on a wide range of benchmark and real-world problems.", "date": "2026-04-10", "categories": []}
{"id": "2512.00170", "title": "We Still Don't Understand High-Dimensional Bayesian Optimization", "abstract": "Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly, we demonstrate that these approaches are outperformed by arguably the simplest method imaginable: Bayesian linear regression. After applying a geometric transformation to avoid boundary-seeking behavior, Gaussian processes with linear kernels match state-of-the-art performance on tasks with 60- to 6,000-dimensional search spaces. Linear models offer numerous advantages over their non-parametric counterparts: they afford closed-form sampling and their computation scales linearly with data, a fact we exploit on molecular optimization tasks with >20,000 observations. Coupled with empirical analyses, our results suggest the need to depart from past intuitions about BO methods in high-dimensions.", "date": "2025-11-28", "categories": []}
{"id": "2604.07416", "title": "Bayesian Optimization for Mixed-Variable Problems in the Natural Sciences", "abstract": "Optimizing expensive black-box objectives over mixed search spaces is a common challenge across the natural sciences. Bayesian optimization (BO) offers sample-efficient strategies through probabilistic surrogate models and acquisition functions. However, its effectiveness diminishes in mixed or high-cardinality discrete spaces, where gradients are unavailable and optimizing the acquisition function becomes computationally demanding. In this work, we generalize the probabilistic reparameterization (PR) approach of Daulton et al. to handle non-equidistant discrete variables, enabling gradient-based optimization in fully mixed-variable settings with Gaussian process (GP) surrogates. With real-world scientific optimization tasks in mind, we conduct systematic benchmarks on synthetic and experimental objectives to obtain an optimized kernel formulations and demonstrate the robustness of our generalized PR method. We additionally show that, when combined with a modified BO workflow, our approach can efficiently optimize highly discontinuous and discretized objective landscapes. This work establishes a practical BO framework for addressing fully mixed optimization problems in the natural sciences, and is particularly well suited to autonomous laboratory settings where noise, discretization, and limited data are inherent.", "date": "2026-04-08", "categories": []}
{"id": "2504.03943", "title": "Multi-Variable Batch Bayesian Optimization in Materials Research: Synthetic Data Analysis of Noise Sensitivity and Problem Landscape Effects", "abstract": "Bayesian Optimization (BO) machine learning method is increasingly used to guide experimental optimization tasks in materials science. To emulate the large number of input variables and noise-containing results in experimental materials research, we perform batch BO simulation of six design variables with a range of noise levels. Two test cases relevant for materials science problems are examined: a needle-in-a-haystack case (Ackley function) that may be encountered in, e.g., molecule optimizations, and a smooth landscape with a local optimum in addition to the global optimum (Hartmann function) that may be encountered in, e.g., material composition optimization. We show learning curves, performance metrics, and visualization to effectively track the optimization progression and evaluate how the optimization outcomes are affected by noise, batch-picking method, choice of acquisition function, and exploration hyperparameter values. We find that the effects of noise depend on the problem landscape: noise degrades the optimization results of a needle-in-a-haystack search (Ackley) dramatically more. However, with increasing noise, we observe an increasing probability of landing on the local optimum in Hartmann. Therefore, prior knowledge of the problem domain structure and noise level is essential when designing BO for materials research experiments. Synthetic data studies -- with known ground truth and controlled noise levels -- enable us to isolate and evaluate the impact of different batch BO components, {\\it e.g.}, acquisition policy, objective metrics, and hyperparameter values, before transitioning to the inherent uncertainties of real experimental systems. The results and methodology of this study will facilitate a greater utilization of BO in guiding experimental materials research, specifically in settings with a large number of design variables to optimize.", "date": "2025-04-04", "categories": []}
{"id": "2510.07421", "title": "Bayesian Optimization of Multi-Bit Pulse Encoding in In2O3/Al2O3 Thin-film Transistors for Temporal Data Processing", "abstract": "Utilizing the intrinsic history-dependence and nonlinearity of hardware, physical reservoir computing is a promising neuromorphic approach to encode time-series data for in-sensor computing. The accuracy of this encoding critically depends on the distinguishability of multi-state outputs, which is often limited by suboptimal and empirically chosen reservoir operation conditions. In this work, we demonstrate a machine learning approach, Bayesian optimization, to improve the encoding fidelity of solution-processed Al2O3/In2O3 thin-film transistors (TFTs). We show high-fidelity 6-bit temporal encoding by exploring five key pulse parameters and using the normalized degree of separation (nDoS) as the metric of output state separability. Additionally, we show that a model trained on simpler 4-bit data can effectively guide optimization of more complex 6-bit encoding tasks, reducing experimental cost. Specifically, for the encoding and reconstruction of binary-patterned images of a moving car across 6 sequential frames, we demonstrate that the encoding is more accurate when operating the TFT using optimized pulse parameters and the 4-bit optimized operating condition performs almost as well as the 6-bit optimized condition. Finally, interpretability analysis via Shapley Additive Explanations (SHAP) reveals that gate pulse amplitude and drain voltage are the most influential parameters in achieving higher state separation. This work presents the first systematic method to identify optimal operating conditions for reservoir devices, and the approach can be extended to other physical reservoir implementations across different material platforms.", "date": "2025-10-08", "categories": []}
{"id": "2510.11727", "title": "Multi-objective Bayesian Optimization with Human-in-the-Loop for Flexible Neuromorphic Electronics Fabrication", "abstract": "Neuromorphic computing hardware enables edge computing and can be implemented in flexible electronics for novel applications. Metal oxide materials are promising candidates for fabricating flexible neuromorphic electronics, but suffer from processing constraints due to the incompatibilities between oxides and polymer substrates. In this work, we use photonic curing to fabricate flexible metal-insulator-metal capacitors with solution-processible aluminum oxide dielectric tailored for neuromorphic applications. Because photonic curing outcomes depend on many input parameters, identifying an optimal processing condition through a traditional grid-search approach is unfeasible. Here, we apply multi-objective Bayesian optimization (MOBO) to determine photonic curing conditions that optimize the trade-off between desired electrical properties of large capacitance-frequency dispersion and low leakage current. Furthermore, we develop a human-in-the-loop (HITL) framework for incorporating failed experiments into the MOBO machine learning workflow, demonstrating that this framework accelerates optimization by reducing the number of experimental rounds required. Once optimization is concluded, we analyze different Pareto-optimal conditions to tune the dielectrics properties and provide insight into the importance of different inputs through Shapley Additive exPlanations analysis. The demonstrated framework of combining MOBO with HITL feedback can be adapted to a wide range of multi-objective experimental problems that have interconnected inputs and high experimental failure rates to generate usable results for machine learning models.", "date": "2025-10-08", "categories": []}
{"id": "2604.01328", "title": "Efficient and Principled Scientific Discovery through Bayesian Optimization: A Tutorial", "abstract": "Traditional scientific discovery relies on an iterative hypothesise-experiment-refine cycle that has driven progress for centuries, but its intuitive, ad-hoc implementation often wastes resources, yields inefficient designs, and misses critical insights. This tutorial presents Bayesian Optimisation (BO), a principled probability-driven framework that formalises and automates this core scientific cycle. BO uses surrogate models (e.g., Gaussian processes) to model empirical observations as evolving hypotheses, and acquisition functions to guide experiment selection, balancing exploitation of known knowledge and exploration of uncharted domains to eliminate guesswork and manual trial-and-error. We first frame scientific discovery as an optimisation problem, then unpack BO's core components, end-to-end workflows, and real-world efficacy via case studies in catalysis, materials science, organic synthesis, and molecule discovery. We also cover critical technical extensions for scientific applications, including batched experimentation, heteroscedasticity, contextual optimisation, and human-in-the-loop integration. Tailored for a broad audience, this tutorial bridges AI advances in BO with practical natural science applications, offering tiered content to empower cross-disciplinary researchers to design more efficient experiments and accelerate principled scientific discovery.", "date": "2026-04-01", "categories": []}
{"id": "2603.28999", "title": "Transfer Learning in Bayesian Optimization for Aircraft Design", "abstract": "The use of transfer learning within Bayesian optimization addresses the disadvantages of the so-called \\textit{cold start} problem by using source data to aid in the optimization of a target problem. We present a method that leverages an ensemble of surrogate models using transfer learning and integrates it in a constrained Bayesian optimization framework. We identify challenges particular to aircraft design optimization related to heterogeneous design variables and constraints. We propose the use of a partial-least-squares dimension reduction algorithm to address design space heterogeneity, and a \\textit{meta} data surrogate selection method to address constraint heterogeneity. Numerical benchmark problems and an aircraft conceptual design optimization problem are used to demonstrate the proposed methods. Results show significant improvement in convergence in early optimization iterations compared to standard Bayesian optimization, with improved prediction accuracy for both objective and constraint surrogate models.", "date": "2026-03-30", "categories": []}
{"id": "2603.28410", "title": "Mixture-Model Preference Learning for Many-Objective Bayesian Optimization", "abstract": "Preference-based many-objective optimization faces two obstacles: an expanding space of trade-offs and heterogeneous, context-dependent human value structures. Towards this, we propose a Bayesian framework that learns a small set of latent preference archetypes rather than assuming a single fixed utility function, modelling them as components of a Dirichlet-process mixture with uncertainty over both archetypes and their weights. To query efficiently, we designing hybrid queries that target information about (i) mode identity and (ii) within-mode trade-offs. Under mild assumptions, we provide a simple regret guarantee for the resulting mixture-aware Bayesian optimization procedure. Empirically, our method outperforms standard baselines on synthetic and real-world many-objective benchmarks, and mixture-aware diagnostics reveal structure that regret alone fails to capture.", "date": "2026-03-30", "categories": []}
{"id": "2510.05516", "title": "NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information", "abstract": "Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a curvature-aware local BO method that targets a (modified) Newton step by jointly learning gradient and Hessian information with Gaussian process (GP) surrogates, and selecting evaluations via a one-step lookahead bound on the Newton-step error. We show that this bound contracts with batch size, so NeST-BO drives the step error to zero; in well-behaved neighborhoods it recovers the fast local convergence behavior of inexact/modified Newton methods, while standard safeguards support global convergence to stationary points. To improve scaling with problem dimension, we optimize the acquisition in low-dimensional embedded subspaces (random or learned), reducing the dominant cost of learning curvature from $O(d^2)$ to $O(m^2)$ with $m \\ll d$ while preserving step targeting. Across high-dimensional synthetic and real-world problems, including cases with thousands of variables and unknown active subspaces, NeST-BO consistently yields faster convergence and better final values than state-of-the-art local and high-dimensional BO baselines.", "date": "2025-10-07", "categories": []}
{"id": "2510.27643", "title": "Bayesian Optimization on Networks", "abstract": "This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that sequentially update a Gaussian process surrogate model of the objective to guide the acquisition of query points. To ensure that the surrogates are tailored to the network's geometry, we adopt Whittle-Mat\\'ern Gaussian process prior models defined via stochastic partial differential equations on metric graphs. In addition to establishing regret bounds for optimizing sufficiently smooth objective functions, we analyze the practical case in which the smoothness of the objective is unknown and the Whittle-Mat\\'ern prior is represented using finite elements. Numerical results demonstrate the effectiveness of our algorithms for optimizing benchmark objective functions on a synthetic metric graph and for Bayesian inversion via maximum a posteriori estimation on a telecommunication network.", "date": "2025-10-31", "categories": []}
{"id": "2603.26339", "title": "Curvature-aware Expected Free Energy as an Acquisition Function for Bayesian Optimization", "abstract": "We propose an Expected Free Energy-based acquisition function for Bayesian optimization to solve the joint learning and optimization problem, i.e., optimize and learn the underlying function simultaneously. We show that, under specific assumptions, Expected Free Energy reduces to Upper Confidence Bound, Lower Confidence Bound, and Expected Information Gain. We prove that Expected Free Energy has unbiased convergence guarantees for concave functions. Using the results from these derivations, we introduce a curvature-aware update law for Expected Free Energy and show its proof of concept using a system identification problem on a Van der Pol oscillator. Through rigorous simulation experiments, we show that our adaptive Expected Free Energy-based acquisition function outperforms state-of-the-art acquisition functions with the least final simple regret and error in learning the Gaussian process.", "date": "2026-03-27", "categories": []}
{"id": "2508.12738", "title": "A Hierarchical Surrogate Model for Efficient Multi-Task Parameter Learning in Closed-Loop Control", "abstract": "Many control problems require repeated tuning and adaptation of controllers across distinct closed-loop tasks, where data efficiency and adaptability are critical. We propose a hierarchical Bayesian optimization (BO) framework that is tailored to efficient controller parameter learning in sequential decision-making and control scenarios for distinct tasks. Instead of treating the closed-loop cost as a black-box, our method exploits structural knowledge of the underlying problem, consisting of a dynamical system, a control law, and an associated closed-loop cost function. We construct a hierarchical surrogate model using Gaussian processes that capture the closed-loop state evolution under different parameterizations, while the task-specific weighting and accumulation into the closed-loop cost are computed exactly via known closed-form expressions. This allows knowledge transfer and enhanced data efficiency between different closed-loop tasks. The proposed framework retains sublinear regret guarantees on par with standard black-box BO, while enabling multi-task or transfer learning. Simulation experiments with model predictive control demonstrate substantial benefits in both sample efficiency and adaptability when compared to purely black-box BO approaches.", "date": "2025-08-18", "categories": []}
{"id": "2603.25311", "title": "Practical Efficient Global Optimization is No-regret", "abstract": "Efficient global optimization (EGO) is one of the most widely used noise-free Bayesian optimization algorithms.It comprises the Gaussian process (GP) surrogate model and expected improvement (EI) acquisition function. In practice, when EGO is applied, a scalar matrix of a small positive value (also called a nugget or jitter) is usually added to the covariance matrix of the deterministic GP to improve numerical stability. We refer to this EGO with a positive nugget as the practical EGO. Despite its wide adoption and empirical success, to date, cumulative regret bounds for practical EGO have yet to be established. In this paper, we present for the first time the cumulative regret upper bound of practical EGO. In particular, we show that practical EGO has sublinear cumulative regret bounds and thus is a no-regret algorithm for commonly used kernels including the squared exponential (SE) and Mat\\'{e}rn kernels ($\\nu>\\frac{1}{2}$). Moreover, we analyze the effect of the nugget on the regret bound and discuss the theoretical implication on its choice. Numerical experiments are conducted to support and validate our findings.", "date": "2026-03-26", "categories": []}
{"id": "2602.18148", "title": "Gradient-Informed Bayesian and Interior Point Optimization for Efficient Inverse Design in Nanophotonics", "abstract": "Inverse design, particularly geometric shape optimization, provides a systematic approach for developing high-performance nanophotonic devices. While numerous optimization algorithms exist, previous global approaches exhibit slow convergence and conversely local search strategies frequently become trapped in local optima. To address the limitations inherent to both local and global approaches, we introduce BONNI: Bayesian optimization through neural network ensemble surrogates with interior point optimization. It augments global optimization with an efficient incorporation of gradient information to determine optimal sampling points. This capability allows BONNI to circumvent the local optima found in many nanophotonic applications, while capitalizing on the efficiency of gradient-based optimization. We demonstrate BONNI's capabilities in the design of a distributed Bragg reflector as well as a dual-layer grating coupler through an exhaustive comparison against other optimization algorithms commonly used in literature. Using BONNI, we were able to design a 10-layer distributed Bragg reflector with only 4.5% mean spectral error, compared to the previously reported results of 7.8% error with 16 layers. Further designs of a broadband waveguide taper and photonic crystal waveguide transition validate the capabilities of BONNI.", "date": "2026-02-20", "categories": []}
{"id": "2603.24138", "title": "Efficient Controller Learning from Human Preferences and Numerical Data Via Multi-Modal Surrogate Models", "abstract": "Tuning control policies manually to meet high-level objectives is often time-consuming. Bayesian optimization provides a data-efficient framework for automating this process using numerical evaluations of an objective function. However, many systems, particularly those involving humans, require optimization based on subjective criteria. Preferential Bayesian optimization addresses this by learning from pairwise comparisons instead of quantitative measurements, but relying solely on preference data can be inefficient. We propose a multi-fidelity, multi-modal Bayesian optimization framework that integrates low-fidelity numerical data with high-fidelity human preferences. Our approach employs Gaussian process surrogate models with both hierarchical, autoregressive and non-hierarchical, coregionalization-based structures, enabling efficient learning from mixed-modality data. We illustrate the framework by tuning an autonomous vehicle's trajectory planner, showing that combining numerical and preference data significantly reduces the need for experiments involving the human decision maker while effectively adapting driving style to individual preferences.", "date": "2026-03-25", "categories": []}
{"id": "2603.24567", "title": "Trust Region Constrained Bayesian Optimization with Penalized Constraint Handling", "abstract": "Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that combines a penalty formulation, a surrogate model, and a trust region strategy. The constrained problem is converted to an unconstrained form by penalizing constraint violations, which provides a unified modeling framework. A trust region restricts the search to a local region around the current best solution, which improves stability and efficiency in high dimensions. Within this region, we use the Expected Improvement acquisition function to select evaluation points by balancing improvement and uncertainty. The proposed Trust Region method integrates penalty-based constraint handling with local surrogate modeling. This combination enables efficient exploration of feasible regions while maintaining sample efficiency. We compare the proposed method with state-of-the-art methods on synthetic and real-world high-dimensional constrained optimization problems. The results show that the method identifies high-quality feasible solutions with fewer evaluations and maintains stable performance across different settings.", "date": "2026-03-25", "categories": []}
{"id": "2509.19988", "title": "BioBO: Biology-informed Bayesian Optimization for Perturbation Design", "abstract": "Efficient design of genomic perturbation experiments is crucial for accelerating drug discovery and therapeutic target identification, yet exhaustive perturbation of the human genome remains infeasible due to the vast search space of potential genetic interactions and experimental constraints. Bayesian optimization (BO) has emerged as a powerful framework for selecting informative interventions, but existing approaches often fail to exploit domain-specific biological prior knowledge. We propose Biology-Informed Bayesian Optimization (BioBO), a method that integrates Bayesian optimization with multimodal gene embeddings and enrichment analysis, a widely used tool for gene prioritization in biology, to enhance surrogate modeling and acquisition strategies. BioBO combines biologically grounded priors with acquisition functions in a principled framework, which biases the search toward promising genes while maintaining the ability to explore uncertain regions. Through experiments on established public benchmarks and datasets, we demonstrate that BioBO improves labeling efficiency by 25-40%, and consistently outperforms conventional BO by identifying top-performing perturbations more effectively. Moreover, by incorporating enrichment analysis, BioBO yields pathway-level explanations for selected perturbations, offering mechanistic interpretability that links designs to biologically coherent regulatory circuits.", "date": "2025-09-24", "categories": []}
{"id": "2603.21525", "title": "BOxCrete: A Bayesian Optimization Open-Source AI Model for Concrete Strength Forecasting and Mix Optimization", "abstract": "Modern concrete must simultaneously satisfy evolving demands for mechanical performance, workability, durability, and sustainability, making mix designs increasingly complex. Recent studies leveraging Artificial Intelligence (AI) and Machine Learning (ML) models show promise for predicting compressive strength and guiding mix optimization, but most existing efforts are based on proprietary industrial datasets and closed-source implementations. Here we introduce BOxCrete, an open-source probabilistic modeling and optimization framework trained on a new open-access dataset of over 500 strength measurements (1-15 ksi) from 123 mixtures - 69 mortar and 54 concrete mixes tested at five curing ages (1, 3, 5, 14, and 28 days). BOxCrete leverages Gaussian Process (GP) regression to predict strength development, achieving average R$^2$ = 0.94 and RMSE = 0.69 ksi, quantify uncertainty, and carry out multi-objective optimization of compressive strength and embodied carbon. The dataset and model establish a reproducible open-source foundation for data-driven development of AI-based optimized mix designs.", "date": "2026-03-23", "categories": []}
{"id": "2505.17393", "title": "CatBOX: A Categorical-Continuous Bayesian Optimization with Spectral Mixture Kernels for Accelerated Catalysis Experiments", "abstract": "Identifying optimal catalyst compositions and reaction conditions is central in catalysis research, yet remains challenging due to the vast multidimensional design spaces encompassing both continuous and categorical parameters. In this work, we present CatBOX, a Bayesian Optimization method for accelerated catalytic experimental design that jointly optimizes categorical and continuous experimental parameters. Our approach introduces a novel spectral mixture kernel that combines the inverse Fourier transform of Gaussian and Cauchy mixtures to provide a flexible representation of the continuous parameter space, capturing both smooth and non-smooth variations. Categorical choices, such as catalyst compositions and support types, are navigated via trust regions based on Hamming distance. For performance evaluation, CatBOX was theoretically verified based on information theory and benchmarked on a series of synthetic functions, achieving more than a 3-fold improvement relative to the best-performing baseline and a 19-fold improvement relative to random search on average across tasks. Additionally, three real-life catalytic experiments, including oxidative coupling of methane, urea-selective catalytic reduction, and direct arylation of imidazoles, were further used for in silico benchmarking, where CatBOX reliably identified top catalyst recipes and reaction conditions with the highest efficiencies in the absence of any a priori knowledge. Finally, we develop an open-source, code-free online platform to facilitate trial deployment in real experimental settings, particularly for self-driving laboratory environments.", "date": "2025-05-23", "categories": []}
{"id": "2603.18417", "title": "Self-Tuning Sparse Attention: Multi-Fidelity Hyperparameter Optimization for Transformer Acceleration", "abstract": "Sparse attention mechanisms promise to break the quadratic bottleneck of long-context transformers, yet production adoption remains limited by a critical usability gap: optimal hyperparameters vary substantially across layers and models, and current methods (e.g., SpargeAttn) rely on manual grid search to identify them. We propose AFBS-BO (Adaptive Fidelity Binary Search with Bayesian Optimization), a fully automated framework that discovers optimal layer- and head-specific hyperparameters without human intervention. Our hybrid algorithm combines Bayesian Optimization for global exploration with binary search for local refinement, leveraging multi-fidelity evaluation across sequence lengths to reduce tuning cost. On Llama-2-7B, AFBS-BO accelerates hyperparameter discovery by 3.4x with 8.8x fewer evaluations than grid search, and identifies high-sparsity configurations that outperform existing sparse attention baselines while closely matching dense attention quality. By transforming sparse attention from a manually tuned heuristic into a self-optimizing primitive, AFBS-BO enables plug-and-play acceleration across diverse transformer architectures and domains.", "date": "2026-03-19", "categories": []}
{"id": "2509.01437", "title": "Sampling as Bandits: Evaluation-Efficient Design for Black-Box Densities", "abstract": "We propose bandit importance sampling (BIS), a powerful importance sampling framework tailored for settings in which evaluating the target density is computationally expensive. BIS facilitates accurate sampling while minimizing the required number of target-density evaluations. In contrast to adaptive importance sampling, which optimizes a proposal distribution, BIS directly optimizes the set of samples through a sequential selection process driven by multi-armed bandits. BIS serves as a general framework that accommodates user-defined bandit strategies. Theoretically, the weak convergence of the weighted samples, and thus the consistency of the Monte Carlo estimator, is established regardless of the specific strategy employed. In this paper, we present a practical strategy that leverages Gaussian process surrogates to guide sample selection, adapting the principles of Bayesian optimization for sampling. Comprehensive numerical studies demonstrate the superior performance of BIS across multimodal, heavy-tailed distributions, and real-world Bayesian inference tasks involving Markov random fields.", "date": "2025-09-01", "categories": []}
{"id": "2603.13501", "title": "Standard Acquisition Is Sufficient for Asynchronous Bayesian Optimization", "abstract": "Asynchronous Bayesian optimization is widely used for gradient-free optimization in domains with independent parallel experiments and varying evaluation times. Existing methods posit that standard acquisitions lead to redundant and repeated queries, proposing complex solutions to enforce diversity in queries. Challenging this fundamental premise, we show that methods, like the Upper Confidence Bound, can in fact achieve theoretical guarantees essentially equivalent to those of sequential Thompson sampling. A conceptual analysis of asynchronous Bayesian optimization reveals that existing works neglect intermediate posterior updates, which we find to be generally sufficient to avoid redundant queries. Further investigation shows that by penalizing busy locations, diversity-enforcing methods can over-explore in asynchronous settings, reducing their performance. Our extensive experiments demonstrate that simple standard acquisition functions match or outperform purpose-built asynchronous methods across synthetic and real-world tasks.", "date": "2026-03-13", "categories": []}
{"id": "2603.12618", "title": "Human-AI Collaborative Autonomous Experimentation With Proxy Modeling for Comparative Observation", "abstract": "Optimization for different tasks like material characterization, synthesis, and functional properties for desired applications over multi-dimensional control parameters need a rapid strategic search through active learning such as Bayesian optimization (BO). However, such high-dimensional experimental physical descriptors are complex and noisy, from which realization of a low-dimensional mathematical scalar metrics or objective functions can be erroneous. Moreover, in traditional purely data-driven autonomous exploration, such objective functions often ignore the subtle variation and key features of the physical descriptors, thereby can fail to discover unknown phenomenon of the material systems. To address this, here we present a proxy-modelled Bayesian optimization (px-BO) via on-the-fly teaming between human and AI agents. Over the loop of BO, instead of defining a mathematical objective function directly from the experimental data, we introduce a voting system on the fly where the new experimental outcome will be compared with existing experiments, and the human agents will choose the preferred samples. These human-guided comparisons are then transformed into a proxy-based objective function via fitting Bradley-Terry (BT) model. Then, to minimize human interaction, this iteratively trained proxy model also acts as an AI agent for future surrogate human votes. Finally, these surrogate votes are periodically validated by human agents, and the corrections are then learned by the proxy model on-the-fly. We demonstrated the performance of the proposed px-BO framework into simulated and BEPS data generated from PTO sample. We find that our approach provided better control of the domain experts for an improved search over traditional data-driven exploration, thus, signifies the importance of human-AI teaming in an accelerated and meaningful material space exploration.", "date": "2026-03-13", "categories": []}
{"id": "2603.01470", "title": "Randomized Kriging Believer for Parallel Bayesian Optimization with Regret Bounds", "abstract": "We consider an optimization problem of an expensive-to-evaluate black-box function, in which we can obtain noisy function values in parallel. For this problem, parallel Bayesian optimization (PBO) is a promising approach, which aims to optimize with fewer function evaluations by selecting a diverse input set for parallel evaluation. However, existing PBO methods suffer from poor practical performance or lack theoretical guarantees. In this study, we propose a PBO method, called randomized kriging believer (KB), based on a well-known KB heuristic and inheriting the advantages of the original KB: low computational complexity, a simple implementation, versatility across various BO methods, and applicability to asynchronous parallelization. Furthermore, we show that our randomized KB achieves Bayesian expected regret guarantees. We demonstrate the effectiveness of the proposed method through experiments on synthetic and benchmark functions and emulators of real-world data.", "date": "2026-03-02", "categories": []}
{"id": "2603.11199", "title": "Bayesian Optimization of Partially Known Systems using Hybrid Models", "abstract": "Bayesian optimization (BO) has gained attention as an efficient algorithm for black-box optimization of expensive-to-evaluate systems, where the BO algorithm iteratively queries the system and suggests new trials based on a probabilistic model fitted to previous samples. Still, the standard BO loop may require a prohibitively large number of experiments to converge to the optimum, especially for high-dimensional and nonlinear systems. We present a hybrid model-based BO formulation that combines the iterative Bayesian learning of BO with partially known mechanistic physical models. Instead of learning a direct mapping from inputs to the objective, we write all known equations for a physics-based model and infer expressions for variables missing equations using a probabilistic model, in our case, a Gaussian process (GP). The final formulation then includes the GP as a constraint in the hybrid model, thereby allowing other physics-based nonlinear and implicit model constraints. This hybrid model formulation yields a constrained, nonlinear stochastic program, which we discretize using the sample-average approximation. In an in-silico optimization of a single-stage distillation, the hybrid BO model based on mass conservation laws yields significantly better designs than a standard BO loop. Furthermore, the hybrid model converges in as few as one iteration, depending on the initial samples, whereas, the standard BO does not converge within 25 for any of the seeds. Overall, the proposed hybrid BO scheme presents a promising optimization method for partially known systems, leveraging the strengths of both mechanistic modeling and data-driven optimization.", "date": "2026-03-11", "categories": []}
{"id": "2603.09793", "title": "Information Theoretic Bayesian Optimization over the Probability Simplex", "abstract": "Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions. Many applications involve optimizing probabilities and mixtures which naturally belong to the probability simplex, a constrained non-Euclidean domain defined by non-negative entries summing to one. This paper introduces $\\alpha$-GaBO, a novel family of Bayesian optimization algorithms over the probability simplex. Our approach is grounded in information geometry, a branch of Riemannian geometry which endows the simplex with a Riemannian metric and a class of connections. Based on information geometry theory, we construct Mat\\'ern kernels that reflect the geometry of the probability simplex, as well as a one-parameter family of geometric optimizers for the acquisition function. We validate our method on benchmark functions and on a variety of real-world applications including mixtures of components, mixtures of classifiers, and a robotic control task, showing its increased performance compared to constrained Euclidean approaches.", "date": "2026-03-10", "categories": []}
{"id": "2603.07965", "title": "Local Constrained Bayesian Optimization", "abstract": "Bayesian optimization (BO) for high-dimensional constrained problems remains a significant challenge due to the curse of dimensionality. We propose Local Constrained Bayesian Optimization (LCBO), a novel framework tailored for such settings. Unlike trust-region methods that are prone to premature shrinking when confronting tight or complex constraints, LCBO leverages the differentiable landscape of constraint-penalized surrogates to alternate between rapid local descent and uncertainty-driven exploration. Theoretically, we prove that LCBO achieves a convergence rate for the Karush-Kuhn-Tucker (KKT) residual that depends polynomially on the dimension $d$ for common kernels under mild assumptions, offering a rigorous alternative to global BO where regret bounds typically scale exponentially. Extensive evaluations on high-dimensional benchmarks (up to 100D) demonstrate that LCBO consistently outperforms state-of-the-art baselines.", "date": "2026-03-09", "categories": []}
{"id": "2512.19739", "title": "OASI: Objective-Aware Surrogate Initialization for Multi-Objective Bayesian Optimization in TinyML Keyword Spotting", "abstract": "Voice-triggered interfaces rely on keyword spotting (KWS) models that must operate continuously under strict memory, latency, and energy constraints on microcontroller-class hardware. Designing such models therefore requires not only high recognition accuracy but also predictable deployability within limited Flash and SRAM budgets. Bayesian optimization is known to handle accuracy-efficiency trade-offs effectively in multi-objective optimization; however, it is highly sensitive to initialization, particularly in the low-budget regimes of TinyML model optimization. We propose Objective-Aware Surrogate Initialization (OASI), which seeds surrogate optimization with Pareto-biased solutions generated via multi-objective simulated annealing. Unlike space-filling or heuristic warm-start methods, OASI initializes the surrogate conditioning process with a bias toward feasible accuracy-memory trade-offs, thus avoiding SRAM-violating configurations. OASI improves hypervolume and convergence robustness over Latin hypercube, Sobol, and random initializations under the same budget constraints on a TinyML KWS problem. Hardware-in-the-loop experiments on STM32 microcontrollers verify the existence of deployable and memory-feasible models without incurring extra optimization costs.", "date": "2025-12-17", "categories": []}
{"id": "2510.04676", "title": "Counterfactual Credit Guided Bayesian Optimization", "abstract": "Bayesian optimization has emerged as a prominent methodology for optimizing expensive black-box functions by leveraging Gaussian process surrogates, which focus on capturing the global characteristics of the objective function. However, in numerous practical scenarios, the primary objective is not to construct an exhaustive global surrogate, but rather to quickly pinpoint the global optimum. Due to the aleatoric nature of the sequential optimization problem and its dependence on the quality of the surrogate model and the initial design, it is restrictive to assume that all observed samples contribute equally to the discovery of the optimum in this context. In this paper, we introduce Counterfactual Credit Guided Bayesian Optimization (CCGBO), a novel framework that explicitly quantifies the contribution of individual historical observations through counterfactual credit. By incorporating counterfactual credit into the acquisition function, our approach can selectively allocate resources in areas where optimal solutions are most likely to occur. We prove that CCGBO retains sublinear regret. Empirical evaluations on various synthetic and real-world benchmarks demonstrate that CCGBO consistently reduces simple regret and accelerates convergence to the global optimum.", "date": "2025-10-06", "categories": []}
{"id": "2602.00640", "title": "Combinatorial Bandit Bayesian Optimization for Tensor Outputs", "abstract": "Bayesian optimization (BO) has been widely used to optimize expensive and black-box functions across various domains. However, existing BO methods have not addressed tensor-output functions. To fill this gap, we propose a novel tensor-output BO framework. Specifically, we first introduce a tensor-output Gaussian process (TOGP) with two classes of tensor-output kernels as a surrogate model of the tensor-output function, which can effectively capture the structural dependencies within the tensor. Based on it, we develop an upper confidence bound (UCB) acquisition function to select query points. Furthermore, we introduce a more practical and challenging problem setting, termed combinatorial bandit Bayesian optimization (CBBO), where only a subset of the tensor outputs can be selected to contribute to the objective. To tackle this, we propose a tensor-output CBBO method, which extends TOGP to handle partially observed tensor outputs, and accordingly design a novel combinatorial multi-arm bandit-UCB2 (CMAB-UCB2) criterion to sequentially select both the query points and the output subset. We establish theoretical regret bounds for both methods, guaranteeing sublinear regret. Extensive experiments on synthetic and real-world datasets demonstrate the superiority of our methods.", "date": "2026-01-31", "categories": []}
{"id": "2603.00935", "title": "Time-Aware Latent Space Bayesian Optimization", "abstract": "Latent-space Bayesian optimization (LSBO) extends Bayesian optimization to structured domains, such as molecular design, by searching in the continuous latent space of a generative model. However, most LSBO methods assume a fixed objective, whereas real design campaigns often face temporal drift (e.g., evolving preferences or shifting targets). Bringing time-varying BO into LSBO is nontrivial: drift can affect not only the surrogate, but also the latent search space geometry induced by the representation. We propose Time-Aware Latent-space Bayesian Optimization (TALBO), which incorporates time in both the surrogate and the learned generative representation via a GP-prior variational autoencoder, yielding a latent space aligned as objectives evolve. To evaluate timevarying LSBO systematically, we adapt widely used molecular design tasks to drifting multi-property objectives and introduce metrics tailored to changing targets. Across these benchmarks, TALBO consistently outperforms strong LSBO baselines and remains robust across drift speeds and design choices, while remaining competitive under actually time-invariant objectives.", "date": "2026-03-01", "categories": []}
{"id": "2510.13328", "title": "Thompson Sampling via Fine-Tuning of LLMs", "abstract": "Bayesian optimization in large unstructured discrete spaces is often hindered by the computational cost of maximizing acquisition functions due to the absence of gradients. We propose a scalable alternative based on Thompson sampling that eliminates the need for acquisition function maximization by directly parameterizing the probability that a candidate yields the maximum reward. Our approach, Thompson Sampling via Fine-Tuning (ToSFiT) leverages the prior knowledge embedded in prompt-conditioned large language models, and incrementally adapts them toward the posterior. Theoretically, we derive a novel regret bound for a variational formulation of Thompson Sampling that matches the strong guarantees of its standard counterpart. Our analysis reveals the critical role of careful adaptation to the posterior probability of maximality -- a principle that underpins our ToSFiT algorithm. Empirically, we validate our method on three diverse tasks: FAQ response refinement, thermally stable protein search, and quantum circuit design. Within a collection of methods covering in-context Bayesian optimization, reinforcement learning, and evolutionary search, ToSFiT exhibits both state-of-the-art sample efficiency and computational efficiency.", "date": "2025-10-15", "categories": []}
{"id": "2509.21725", "title": "Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems", "abstract": "A bilevel optimization problem consists of two optimization problems nested as an upper- and a lower-level problem, in which the optimality of the lower-level problem defines a constraint for the upper-level problem. This paper considers Bayesian optimization (BO) for the case that both the upper- and lower-levels involve expensive black-box functions. Because of its nested structure, bilevel optimization has a complex problem definition, by which bilevel BO has not been widely studied compared with other standard extensions of BO such as multi-objective or constraint problems. We propose an information-theoretic approach that considers the information gain of both the upper- and lower-optimal solutions and values. This enables us to define a unified criterion that measures the benefit for both level problems, simultaneously. Further, we also show a practical lower bound based approach to evaluating the information gain. We empirically demonstrate the effectiveness of our proposed method through several benchmark datasets.", "date": "2025-09-26", "categories": []}
{"id": "2602.08351", "title": "The Chicken and Egg Dilemma: Co-optimizing Data and Model Configurations for LLMs", "abstract": "Co-optimizing data and model configurations for training LLMs presents a classic chicken-and-egg dilemma: The best training data configuration (e.g., data mixture) for a downstream task depends on the chosen model configuration (e.g., model architecture), and vice versa. However, jointly optimizing both data and model configurations is often deemed intractable, and existing methods focus on either data or model optimization without considering their interaction. We introduce JoBS, an approach that uses a scaling-law-inspired performance predictor to aid Bayesian optimization (BO) in jointly optimizing LLM training data and model configurations efficiently. JoBS allocates a portion of the optimization budget to learn an LLM performance predictor that predicts how promising a training configuration is from a small number of training steps. The remaining budget is used to perform BO entirely with the predictor, effectively amortizing the cost of running full-training runs. We study JoBS's average regret and devise the optimal budget allocation to minimize regret. JoBS outperforms existing multi-fidelity BO baselines, as well as data and model optimization approaches across diverse LLM tasks under the same optimization budget.", "date": "2026-02-09", "categories": []}
{"id": "2511.15315", "title": "Robust Bayesian Optimisation with Unbounded Corruptions", "abstract": "Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient magnitude. To address this, we introduce a new adversary whose budget is only bounded in the frequency of corruptions, not in their magnitude. We then derive RCGP-UCB, an algorithm coupling the famous upper confidence bound (UCB) approach with a Robust Conjugate Gaussian Process (RCGP). We present stable and adaptive versions of RCGP-UCB, and prove that they achieve sublinear regret in the presence of up to $O(T^{1/4})$ and $O(T^{1/7})$ corruptions with possibly infinite magnitude. This robustness comes at near zero cost: without outliers, RCGP-UCB's regret bounds match those of the standard GP-UCB algorithm.", "date": "2025-11-19", "categories": []}
{"id": "2511.19628", "title": "Optimization and Regularization Under Arbitrary Objectives", "abstract": "This study investigates the limitations of applying Markov Chain Monte Carlo (MCMC) methods to arbitrary objective functions, focusing on a two-block MCMC framework which alternates between Metropolis-Hastings and Gibbs sampling. While such approaches are often considered advantageous for enabling data-driven regularization, we show that their performance critically depends on the sharpness of the employed likelihood form. By introducing a sharpness parameter and exploring alternative likelihood formulations proportional to the target objective function, we demonstrate how likelihood curvature governs both in-sample performance and the degree of regularization inferred by the training data. Empirical applications are conducted on reinforcement learning tasks: including a navigation problem and the game of tic-tac-toe. The study concludes with a separate analysis examining the implications of extreme likelihood sharpness on arbitrary objective functions stemming from the classic game of blackjack, where the first block of the two-block MCMC framework is replaced with an iterative optimization step. The resulting hybrid approach achieves performance nearly identical to the original MCMC framework, indicating that excessive likelihood sharpness effectively collapses posterior mass onto a single dominant mode.", "date": "2025-11-24", "categories": []}
{"id": "2602.13398", "title": "Accelerated Discovery of Cryoprotectant Cocktails via Multi-Objective Bayesian Optimization", "abstract": "Designing cryoprotectant agent (CPA) cocktails for vitrification is challenging because formulations must be concentrated enough to suppress ice formation yet non-toxic enough to preserve cell viability. This tradeoff creates a large, multi-objective design space in which traditional discovery is slow, often relying on expert intuition or exhaustive experimentation. We present a data-efficient framework that accelerates CPA cocktail design by combining high-throughput screening with an active-learning loop based on multi-objective Bayesian optimization. From an initial set of measured cocktails, we train probabilistic surrogate models to predict concentration and viability and quantify uncertainty across candidate formulations. We then iteratively select the next experiments by prioritizing cocktails expected to improve the Pareto front, maximizing expected Pareto improvement under uncertainty, and update the models as new assay results are collected. Wet-lab validation shows that our approach efficiently discovers cocktails that simultaneously achieve high CPA concentrations and high post-exposure viability. Relative to a naive strategy and a strong baseline, our method improves dominated hypervolume by 9.5\\% and 4.5\\%, respectively, while reducing the number of experiments needed to reach high-quality solutions. In complementary synthetic studies, it recovers a comparably strong set of Pareto-optimal solutions using only 30\\% of the evaluations required by the prior state-of-the-art multi-objective approach, which amounts to saving approximately 10 weeks of experimental time. Because the framework assumes only a suitable assay and defined formulation space, it can be adapted to different CPA libraries, objective definitions, and cell lines to accelerate cryopreservation development.", "date": "2026-02-13", "categories": []}
{"id": "2602.14472", "title": "Frequentist Regret Analysis of Gaussian Process Thompson Sampling via Fractional Posteriors", "abstract": "We study Gaussian Process Thompson Sampling (GP-TS) for sequential decision-making over compact, continuous action spaces and provide a frequentist regret analysis based on fractional Gaussian process posteriors, without relying on domain discretization as in prior work. We show that the variance inflation commonly assumed in existing analyses of GP-TS can be interpreted as Thompson Sampling with respect to a fractional posterior with tempering parameter $\\alpha \\in (0,1)$. We derive a kernel-agnostic regret bound expressed in terms of the information gain parameter $\\gamma_t$ and the posterior contraction rate $\\epsilon_t$, and identify conditions on the Gaussian process prior under which $\\epsilon_t$ can be controlled. As special cases of our general bound, we recover regret of order $\\tilde{\\mathcal{O}}(T^{\\frac{1}{2}})$ for the squared exponential kernel, $\\tilde{\\mathcal{O}}(T^{\\frac{2\\nu+3d}{2(2\\nu+d)}} )$ for the Mat\\'ern-$\\nu$ kernel, and a bound of order $\\tilde{\\mathcal{O}}(T^{\\frac{2\\nu+3d}{2(2\\nu+d)}})$ for the rational quadratic kernel. Overall, our analysis provides a unified and discretization-free regret framework for GP-TS that applies broadly across kernel classes.", "date": "2026-02-16", "categories": []}
{"id": "2602.14791", "title": "Extending Multi-Source Bayesian Optimization With Causality Principles", "abstract": "Multi-Source Bayesian Optimization (MSBO) serves as a variant of the traditional Bayesian Optimization (BO) framework applicable to situations involving optimization of an objective black-box function over multiple information sources such as simulations, surrogate models, or real-world experiments. However, traditional MSBO assumes the input variables of the objective function to be independent and identically distributed, limiting its effectiveness in scenarios where causal information is available and interventions can be performed, such as clinical trials or policy-making. In the single-source domain, Causal Bayesian Optimization (CBO) extends standard BO with the principles of causality, enabling better modeling of variable dependencies. This leads to more accurate optimization, improved decision-making, and more efficient use of low-cost information sources. In this article, we propose a principled integration of the MSBO and CBO methodologies in the multi-source domain, leveraging the strengths of both to enhance optimization efficiency and reduce computational complexity in higher-dimensional problems. We present the theoretical foundations of both Causal and Multi-Source Bayesian Optimization, and demonstrate how their synergy informs our Multi-Source Causal Bayesian Optimization (MSCBO) algorithm. We compare the performance of MSCBO against its foundational counterparts for both synthetic and real-world datasets with varying levels of noise, highlighting the robustness and applicability of MSCBO. Based on our findings, we conclude that integrating MSBO with the causality principles of CBO facilitates dimensionality reduction and lowers operational costs, ultimately improving convergence speed, performance, and scalability.", "date": "2026-02-16", "categories": []}
{"id": "2602.12112", "title": "Few-Shot Design Optimization by Exploiting Auxiliary Information", "abstract": "Many real-world design problems involve optimizing an expensive black-box function $f(x)$, such as hardware design or drug discovery. Bayesian Optimization has emerged as a sample-efficient framework for this problem. However, the basic setting considered by these methods is simplified compared to real-world experimental setups, where experiments often generate a wealth of useful information. We introduce a new setting where an experiment generates high-dimensional auxiliary information $h(x)$ along with the performance measure $f(x)$; moreover, a history of previously solved tasks from the same task family is available for accelerating optimization. A key challenge of our setting is learning how to represent and utilize $h(x)$ for efficiently solving new optimization tasks beyond the task history. We develop a novel approach for this setting based on a neural model which predicts $f(x)$ for unseen designs given a few-shot context containing observations of $h(x)$. We evaluate our method on two challenging domains, robotic hardware design and neural network hyperparameter tuning, and introduce a novel design problem and large-scale benchmark for the former. On both domains, our method utilizes auxiliary feedback effectively to achieve more accurate few-shot prediction and faster optimization of design tasks, significantly outperforming several methods for multi-task optimization.", "date": "2026-02-12", "categories": []}
{"id": "2502.14121", "title": "Multi-Objective Bayesian Optimization for Networked Black-Box Systems: A Path to Greener Profits and Smarter Designs", "abstract": "Designing modern industrial systems requires balancing several competing objectives, such as profitability, resilience, and sustainability, while accounting for complex interactions between technological, economic, and environmental factors. Multi-objective optimization (MOO) methods are commonly used to navigate these tradeoffs, but selecting the appropriate algorithm to tackle these problems is often unclear, particularly when system representations vary from fully equation-based (white-box) to entirely data-driven (black-box) models. While grey-box MOO methods attempt to bridge this gap, they typically impose rigid assumptions on system structure, requiring models to conform to the underlying structural assumptions of the solver rather than the solver adapting to the natural representation of the system of interest. In this chapter, we introduce a unifying approach to grey-box MOO by leveraging network representations, which provide a general and flexible framework for modeling interconnected systems as a series of function nodes that share various inputs and outputs. Specifically, we propose MOBONS, a novel Bayesian optimization-inspired algorithm that can efficiently optimize general function networks, including those with cyclic dependencies, enabling the modeling of feedback loops, recycle streams, and multi-scale simulations - features that existing methods fail to capture. Furthermore, MOBONS incorporates constraints, supports parallel evaluations, and preserves the sample efficiency of Bayesian optimization while leveraging network structure for improved scalability. We demonstrate the effectiveness of MOBONS through two case studies, including one related to sustainable process design. By enabling efficient MOO under general graph representations, MOBONS has the potential to significantly enhance the design of more profitable, resilient, and sustainable engineering systems.", "date": "2025-02-19", "categories": []}
{"id": "2602.10670", "title": "Domain Knowledge Guided Bayesian Optimization For Autonomous Alignment Of Complex Scientific Instruments", "abstract": "Bayesian Optimization (BO) is a powerful tool for optimizing complex non-linear systems. However, its performance degrades in high-dimensional problems with tightly coupled parameters and highly asymmetric objective landscapes, where rewards are sparse. In such needle-in-a-haystack scenarios, even advanced methods like trust-region BO (TurBO) often lead to unsatisfactory results. We propose a domain knowledge guided Bayesian Optimization approach, which leverages physical insight to fundamentally simplify the search problem by transforming coordinates to decouple input features and align the active subspaces with the primary search axes. We demonstrate this approach's efficacy on a challenging 12-dimensional, 6-crystal Split-and-Delay optical system, where conventional approaches, including standard BO, TuRBO and multi-objective BO, consistently led to unsatisfactory results. When combined with an reverse annealing exploration strategy, this approach reliably converges to the global optimum. The coordinate transformation itself is the key to this success, significantly accelerating the search by aligning input co-ordinate axes with the problem's active subspaces. As increasingly complex scientific instruments, from large telescopes to new spectrometers at X-ray Free Electron Lasers are deployed, the demand for robust high-dimensional optimization grows. Our results demonstrate a generalizable paradigm: leveraging physical insight to transform high-dimensional, coupled optimization problems into simpler representations can enable rapid and robust automated tuning for consistent high performance while still retaining current optimization algorithms.", "date": "2026-02-11", "categories": []}
{"id": "2602.09181", "title": "Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks", "abstract": "Exploiting the analogy between Gaussian Distributions and Gaussian Processes' posterior, we present how the weighted Wasserstein Barycenter of Gaussian Processes (W2BGP) can be used to unify, under a common framework, different exotic Bayesian Optimization (BO) tasks. Specifically, collaborative/federated BO, (synchronous) batch BO, and multi-fidelity BO are considered in this paper. Our empirical analysis proves that each one of these tasks requires just an appropriate weighting schema for the W2BGP, while the entire framework remains untouched. Moreover, we demonstrate that the most well-known BO acquisition functions can be easily re-interpreted under the proposed framework and also enable a more computationally efficient way to deal with the computation of the Wasserstein Barycenter, compared with state-of-the-art methods from the Machine Learning literature. Finally, research perspectives branching from the proposed approach are presented.", "date": "2026-02-09", "categories": []}
{"id": "2602.07411", "title": "Nonparametric Bayesian Optimization for General Rewards", "abstract": "This work focuses on Bayesian optimization (BO) under reward model uncertainty. We propose the first BO algorithm that achieves no-regret guarantee in a general reward setting, requiring only Lipschitz continuity of the objective function and accommodating a broad class of measurement noise. The core of our approach is a novel surrogate model, termed as infinite Gaussian process ($\\infty$-GP). It is a Bayesian nonparametric model that places a prior on the space of reward distributions, enabling it to represent a substantially broader class of reward models than classical Gaussian process (GP). The $\\infty$-GP is used in combination with Thompson Sampling (TS) to enable effective exploration and exploitation. Correspondingly, we develop a new TS regret analysis framework for general rewards, which relates the regret to the total variation distance between the surrogate model and the true reward distribution. Furthermore, with a truncated Gibbs sampling procedure, our method is computationally scalable, incurring minimal additional memory and computational complexities compared to classical GP. Empirical results demonstrate state-of-the-art performance, particularly in settings with non-stationary, heavy-tailed, or other ill-conditioned rewards.", "date": "2026-02-07", "categories": []}
{"id": "2602.07904", "title": "Adaptive Acquisition Selection for Bayesian Optimization with Large Language Models", "abstract": "Bayesian Optimization critically depends on the choice of acquisition function, but no single strategy is universally optimal; the best choice is non-stationary and problem-dependent. Existing adaptive portfolio methods often base their decisions on past function values while ignoring richer information like remaining budget or surrogate model characteristics. To address this, we introduce LMABO, a novel framework that casts a pre-trained Large Language Model (LLM) as a zero-shot, online strategist for the BO process. At each iteration, LMABO uses a structured state representation to prompt the LLM to select the most suitable acquisition function from a diverse portfolio. In an evaluation across 50 benchmark problems, LMABO demonstrates a significant performance improvement over strong static, adaptive portfolio, and other LLM-based baselines. We show that the LLM's behavior is a comprehensive strategy that adapts to real-time progress, proving its advantage stems from its ability to process and synthesize the complete optimization state into an effective, adaptive policy.", "date": "2026-02-08", "categories": []}
{"id": "2602.08774", "title": "Default Machine Learning Hyperparameters Do Not Provide Informative Initialization for Bayesian Optimization", "abstract": "Bayesian Optimization (BO) is a standard tool for hyperparameter tuning thanks to its sample efficiency on expensive black-box functions. While most BO pipelines begin with uniform random initialization, default hyperparameter values shipped with popular ML libraries such as scikit-learn encode implicit expert knowledge and could serve as informative starting points that accelerate convergence. This hypothesis, despite its intuitive appeal, has remained largely unexamined. We formalize the idea by initializing BO with points drawn from truncated Gaussian distributions centered at library defaults and compare the resulting trajectories against a uniform-random baseline. We conduct an extensive empirical evaluation spanning three BO back-ends (BoTorch, Optuna, Scikit-Optimize), three model families (Random Forests, Support Vector Machines, Multilayer Perceptrons), and five benchmark datasets covering classification and regression tasks. Performance is assessed through convergence speed and final predictive quality, and statistical significance is determined via one-sided binomial tests. Across all conditions, default-informed initialization yields no statistically significant advantage over purely random sampling, with p-values ranging from 0.141 to 0.908. A sensitivity analysis on the prior variance confirms that, while tighter concentration around the defaults improves early evaluations, this transient benefit vanishes as optimization progresses, leaving final performance unchanged. Our results provide no evidence that default hyperparameters encode useful directional information for optimization. We therefore recommend that practitioners treat hyperparameter tuning as an integral part of model development and favor principled, data-driven search strategies over heuristic reliance on library defaults.", "date": "2026-02-09", "categories": []}
{"id": "2602.02388", "title": "Personalized Image Generation via Human-in-the-loop Bayesian Optimization", "abstract": "Imagine Alice has a specific image $x^\\ast$ in her mind, say, the view of the street in which she grew up during her childhood. To generate that exact image, she guides a generative model with multiple rounds of prompting and arrives at an image $x^{p*}$. Although $x^{p*}$ is reasonably close to $x^\\ast$, Alice finds it difficult to close that gap using language prompts. This paper aims to narrow this gap by observing that even after language has reached its limits, humans can still tell when a new image $x^+$ is closer to $x^\\ast$ than $x^{p*}$. Leveraging this observation, we develop MultiBO (Multi-Choice Preferential Bayesian Optimization) that carefully generates $K$ new images as a function of $x^{p*}$, gets preferential feedback from the user, uses the feedback to guide the diffusion model, and ultimately generates a new set of $K$ images. We show that within $B$ rounds of user feedback, it is possible to arrive much closer to $x^\\ast$, even though the generative model has no information about $x^\\ast$. Qualitative scores from $30$ users, combined with quantitative metrics compared across $5$ baselines, show promising results, suggesting that multi-choice feedback from humans can be effectively harnessed for personalized image generation.", "date": "2026-02-02", "categories": []}
{"id": "2301.12412", "title": "Contextual Causal Bayesian Optimisation", "abstract": "We introduce a unified framework for contextual and causal Bayesian optimisation, which aims to design intervention policies maximising the expectation of a target variable. Our approach leverages both observed contextual information and known causal graph structures to guide the search. Within this framework, we propose a novel algorithm that jointly optimises over policies and the sets of variables on which these policies are defined. This thereby extends and unifies two previously distinct approaches: Causal Bayesian Optimisation and Contextual Bayesian Optimisation, while also addressing their limitations in scenarios that yield suboptimal results. We derive worst-case and instance-dependent high-probability regret bounds for our algorithm. We report experimental results across diverse environments, corroborating that our approach achieves sublinear regret and reduces sample complexity in high-dimensional settings.", "date": "2023-01-29", "categories": []}
{"id": "2511.02570", "title": "Dynamic Priors in Bayesian Optimization for Hyperparameter Optimization", "abstract": "Bayesian optimization (BO) is a widely used approach to hyperparameter optimization (HPO). However, most existing HPO methods only incorporate expert knowledge during initialization, limiting practitioners' ability to influence the optimization process as new insights emerge. This limits the applicability of BO in iterative machine learning development workflows. We propose DynaBO, a BO framework that enables continuous user control of the optimization process. Over time, DynaBO leverages provided user priors by augmenting the acquisition function with decaying, prior-weighted preferences while preserving asymptotic convergence guarantees. To reinforce robustness, we introduce a data-driven safeguard that detects and can be used to reject misleading priors. We prove theoretical results on near-certain convergence, robustness to adversarial priors, and accelerated convergence when informative priors are provided. Extensive experiments across various HPO benchmarks show that DynaBO consistently outperforms our state-of-the-art competitors across all benchmarks and for all prior kinds. Our results demonstrate that DynaBO enables reliable and efficient collaborative BO, bridging automated and manually controlled model development.", "date": "2025-11-04", "categories": []}
{"id": "2602.03232", "title": "BayeSQP: Bayesian Optimization through Sequential Quadratic Programming", "abstract": "We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for both the objective and constraints to jointly model the function values, gradients, and Hessian from only zero-order information. At each iteration, a local subproblem is constructed using the GP posterior estimates and solved to obtain a search direction. Crucially, the formulation of the subproblem explicitly incorporates uncertainty in both the function and derivative estimates, resulting in a tractable second-order cone program for high probability improvements under model uncertainty. A subsequent one-dimensional line search via constrained Thompson sampling selects the next evaluation point. Empirical results show thatBayeSQP outperforms state-of-the-art methods in specific high-dimensional settings. Our algorithm offers a principled and flexible framework that bridges classical optimization techniques with modern approaches to black-box optimization.", "date": "2026-02-03", "categories": []}
{"id": "2602.00788", "title": "Multi-Objective Multi-Fidelity Bayesian Optimization with Causal Priors", "abstract": "Multi-fidelity Bayesian optimization (MFBO) accelerates the search for the global optimum of black-box functions by integrating inexpensive, low-fidelity approximations. The central task of an MFBO policy is to balance the cost-efficiency of low-fidelity proxies against their reduced accuracy to ensure effective progression toward the high-fidelity optimum. Existing MFBO methods primarily capture associational dependencies between inputs, fidelities, and objectives, rather than causal mechanisms, and can perform poorly when lower-fidelity proxies are poorly aligned with the target fidelity. We propose RESCUE (REducing Sampling cost with Causal Understanding and Estimation), a multi-objective MFBO method that incorporates causal calculus to systematically address this challenge. RESCUE learns a structural causal model capturing causal relationships between inputs, fidelities, and objectives, and uses it to construct a probabilistic multi-fidelity (MF) surrogate that encodes intervention effects. Exploiting the causal structure, we introduce a causal hypervolume knowledge-gradient acquisition strategy to select input-fidelity pairs that balance expected multi-objective improvement and cost. We show that RESCUE improves sample efficiency over state-of-the-art MF optimization methods on synthetic and real-world problems in robotics, machine learning (AutoML), and healthcare.", "date": "2026-01-31", "categories": []}
{"id": "2602.01774", "title": "Cost-Aware Bayesian Optimization for Prototyping Interactive Devices", "abstract": "Deciding which idea is worth prototyping is a central concern in iterative design. A prototype should be produced when the expected improvement is high and the cost is low. However, this is hard to decide, because costs can vary drastically: a simple parameter tweak may take seconds, while fabricating hardware consumes material and energy. Such asymmetries, can discourage a designer from exploring the design space. In this paper, we present an extension of cost-aware Bayesian optimization to account for diverse prototyping costs. The method builds on the power of Bayesian optimization and requires only a minimal modification to the acquisition function. The key idea is to use designer-estimated costs to guide sampling toward more cost-effective prototypes. In technical evaluations, the method achieved comparable utility to a cost-agnostic baseline while requiring only ${\\approx}70\\%$ of the cost; under strict budgets, it outperformed the baseline threefold. A within-subjects study with 12 participants in a realistic joystick design task demonstrated similar benefits. These results show that accounting for prototyping costs can make Bayesian optimization more compatible with real-world design projects.", "date": "2026-02-02", "categories": []}
{"id": "2602.02432", "title": "Maximizing Reliability with Bayesian Optimization", "abstract": "Bayesian optimization (BO) is a popular, sample-efficient technique for expensive, black-box optimization. One such problem arising in manufacturing is that of maximizing the reliability, or equivalently minimizing the probability of a failure, of a design which is subject to random perturbations - a problem that can involve extremely rare failures ($P_\\mathrm{fail} = 10^{-6}-10^{-8}$). In this work, we propose two BO methods based on Thompson sampling and knowledge gradient, the latter approximating the one-step Bayes-optimal policy for minimizing the logarithm of the failure probability. Both methods incorporate importance sampling to target extremely small failure probabilities. Empirical results show the proposed methods outperform existing methods in both extreme and non-extreme regimes.", "date": "2026-02-02", "categories": []}
{"id": "2402.02277", "title": "Causal Bayesian Optimization via Exogenous Distribution Learning", "abstract": "Maximizing a target variable as an operational objective within a structural causal model is a fundamental problem. Causal Bayesian Optimization (CBO) approaches typically achieve this either by performing interventions that modify the causal structure to increase the reward or by introducing action nodes to endogenous variables, thereby adjusting the data-generating mechanisms to meet the objective. In this paper, we propose a novel method that learns the distribution of exogenous variables-an aspect often ignored or marginalized through expectation in existing CBO frameworks. By modeling the exogenous distribution, we enhance the approximation fidelity of the data-generating structural causal models (SCMs) used in surrogate models, which are commonly trained on limited observational data. Furthermore, the ability to recover exogenous variables enables the application of our approach to more general causal structures beyond the confines of Additive Noise Models (ANMs) and single-mode Gaussian, allowing the use of more expressive priors for context noise. We incorporate the learned exogenous distribution into a new CBO method, demonstrating its advantages across diverse datasets and application scenarios.", "date": "2024-02-03", "categories": []}
{"id": "2601.22315", "title": "Gaussian Process Bandit Optimization with Machine Learning Predictions and Application to Hypothesis Generation", "abstract": "Many real-world optimization problems involve an expensive ground-truth oracle (e.g., human evaluation, physical experiments) and a cheap, low-fidelity prediction oracle (e.g., machine learning models, simulations). Meanwhile, abundant offline data (e.g., past experiments and predictions) are often available and can be used to pretrain powerful predictive models, as well as to provide an informative prior. We propose Prediction-Augmented Gaussian Process Upper Confidence Bound (PA-GP-UCB), a novel Bayesian optimization algorithm that leverages both oracles and offline data to achieve provable gains in sample efficiency for the ground-truth oracle queries. PA-GP-UCB employs a control-variates estimator derived from a joint Gaussian process posterior to correct prediction bias and reduce uncertainty. We prove that PA-GP-UCB preserves the standard regret rate of GP-UCB while achieving a strictly smaller leading constant that is explicitly controlled by prediction quality and offline data coverage. Empirically, PA-GP-UCB converges faster than Vanilla GP-UCB and naive prediction-augmented GP-UCB baselines on synthetic benchmarks and on a real-world hypothesis evaluation task grounded in human behavioral data, where predictions are provided by large language models. These results establish PA-GP-UCB as a general and sample-efficient framework for hypothesis generation under expensive feedback.", "date": "2026-01-29", "categories": []}
{"id": "2601.22335", "title": "Knowledge Gradient for Preference Learning", "abstract": "The knowledge gradient is a popular acquisition function in Bayesian optimization (BO) for optimizing black-box objectives with noisy function evaluations. Many practical settings, however, allow only pairwise comparison queries, yielding a preferential BO problem where direct function evaluations are unavailable. Extending the knowledge gradient to preferential BO is hindered by its computational challenge. At its core, the look-ahead step in the preferential setting requires computing a non-Gaussian posterior, which was previously considered intractable. In this paper, we address this challenge by deriving an exact and analytical knowledge gradient for preferential BO. We show that the exact knowledge gradient performs strongly on a suite of benchmark problems, often outperforming existing acquisition functions. In addition, we also present a case study illustrating the limitation of the knowledge gradient in certain scenarios.", "date": "2026-01-29", "categories": []}
{"id": "2507.14057", "title": "Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design", "abstract": "We develop a semi-amortized, policy-based, approach to Bayesian experimental design (BED) called Stepwise Deep Adaptive Design (Step-DAD). Like existing, fully amortized, policy-based BED approaches, Step-DAD trains a design policy upfront before the experiment. However, rather than keeping this policy fixed, Step-DAD periodically updates it as data is gathered, refining it to the particular experimental instance. This test-time adaptation improves both the flexibility and the robustness of the design strategy compared with existing approaches. Empirically, Step-DAD consistently demonstrates superior decision-making and robustness compared with current state-of-the-art BED methods.", "date": "2025-07-18", "categories": []}
{"id": "2511.04403", "title": "Online Bayesian Experimental Design for Partially Observed Dynamical Systems", "abstract": "Bayesian experimental design (BED) provides a principled framework for optimizing data collection by choosing experiments that are maximally informative about unknown parameters. However, existing methods cannot deal with the joint challenge of (a) partially observable dynamical systems, where only noisy and incomplete observations are available, and (b) fully online inference, which updates posterior distributions and selects designs sequentially in a computationally efficient manner. Under partial observability, dynamical systems are naturally modeled as state-space models (SSMs), where latent states mediate the link between parameters and data, making the likelihood -- and thus information-theoretic objectives like the expected information gain (EIG) -- intractable. We address these challenges by deriving new estimators of the EIG and its gradient that explicitly marginalize latent states, enabling scalable stochastic optimization in nonlinear SSMs. Our approach leverages nested particle filters for efficient online state-parameter inference with convergence guarantees. Applications to realistic models, such as the susceptible-infectious-recovered (SIR) and a moving source location task, show that our framework successfully handles both partial observability and online inference.", "date": "2025-11-06", "categories": []}
{"id": "2601.20043", "title": "Regime-Adaptive Bayesian Optimization via Dirichlet Process Mixtures of Gaussian Processes", "abstract": "Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across heterogeneous molecular scaffolds. A single GP either oversmooths sharp transitions or hallucinates noise in smooth regions, yielding miscalibrated uncertainty. We propose RAMBO, a Dirichlet Process Mixture of Gaussian Processes that automatically discovers latent regimes during optimization, each modeled by an independent GP with locally-optimized hyperparameters. We derive collapsed Gibbs sampling that analytically marginalizes latent functions for efficient inference, and introduce adaptive concentration parameter scheduling for coarse-to-fine regime discovery. Our acquisition functions decompose uncertainty into intra-regime and inter-regime components. Experiments on synthetic benchmarks and real-world applications, including molecular conformer optimization, virtual screening for drug discovery, and fusion reactor design, demonstrate consistent improvements over state-of-the-art baselines on multi-regime objectives.", "date": "2026-01-27", "categories": []}
{"id": "2508.19028", "title": "GRADSTOP: Early Stopping of Gradient Descent via Posterior Sampling", "abstract": "Machine learning models are often learned by minimising a loss function on the training data using a gradient descent algorithm. These models often suffer from overfitting, leading to a decline in predictive performance on unseen data. A standard solution is early stopping using a hold-out validation set, which halts the minimisation when the validation loss stops decreasing. However, this hold-out set reduces the data available for training. This paper presents GRADSTOP, a novel stochastic early stopping method that only uses information in the gradients, which are produced by the gradient descent algorithm ``for free.'' Our main contributions are that we estimate the Bayesian posterior by the gradient information, define the early stopping problem as drawing sample from this posterior, and use the approximated posterior to obtain a stopping criterion. Our empirical evaluation shows that GRADSTOP achieves a small loss on test data and compares favourably to a validation-set-based stopping criterion. By leveraging the entire dataset for training, our method is particularly advantageous in data-limited settings, such as transfer learning. It can be incorporated as an optional feature in gradient descent libraries with only a small computational overhead. The source code is available at https://github.com/edahelsinki/gradstop.", "date": "2025-08-26", "categories": []}
{"id": "2601.18972", "title": "Towards Self-Optimizing Electron Microscope: Robust Tuning of Aberration Coefficients via Physics-Aware Multi-Objective Bayesian Optimization", "abstract": "Realizing high-throughput aberration-corrected Scanning Transmission Electron Microscopy (STEM) exploration of atomic structures requires rapid tuning of multipole probe correctors while compensating for the inevitable drift of the optical column. While automated alignment routines exist, conventional approaches rely on serial, gradient-free searches (e.g., Nelder-Mead) that are sample-inefficient and struggle to correct multiple interacting parameters simultaneously. Conversely, emerging deep learning methods offer speed but often lack the flexibility to adapt to varying sample conditions without extensive retraining. Here, we introduce a Multi-Objective Bayesian Optimization (MOBO) framework for rapid, data-efficient aberration correction. Importantly, this framework does not prescribe a single notion of image quality; instead, it enables user-defined, physically motivated reward formulations (e.g., symmetry-induced objectives) and uses Pareto fronts to expose the resulting trade-offs between competing experimental priorities. By using Gaussian Process regression to model the aberration landscape probabilistically, our workflow actively selects the most informative lens settings to evaluate next, rather than performing an exhaustive blind search. We demonstrate that this active learning loop is more robust than traditional optimization algorithms and effectively tunes focus, astigmatism, and higher-order aberrations. By balancing competing objectives, this approach enables \"self-optimizing\" microscopy by dynamically sustaining optimal performance during experiments.", "date": "2026-01-26", "categories": []}
{"id": "2601.16425", "title": "Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance", "abstract": "Designing experiments that systematically gather data from complex physical systems is central to accelerating scientific discovery. While Bayesian experimental design (BED) provides a principled, information-based framework that integrates experimental planning with probabilistic inference, the selection of utility functions in BED is a long-standing and active topic, where different criteria emphasize different notions of information. Although Kullback--Leibler (KL) divergence has been one of the most common choices, recent studies have proposed Wasserstein distance as an alternative. In this work, we first employ a toy example to illustrate an issue of Wasserstein distance - the value of Wasserstein distance of a fixed-shape posterior depends on the relative position of its main mass within the support and can exhibit false rewards unrelated to information gain, especially with a non-informative prior (e.g., uniform distribution). We then further provide a systematic comparison between these two criteria through a classical source inversion problem in the BED literature, revealing that the KL divergence tends to lead to faster convergence in the absence of model discrepancy, while Wasserstein metrics provide more robust sequential BED results if model discrepancy is non-negligible. These findings clarify the trade-offs between KL divergence and Wasserstein metrics for the utility function and provide guidelines for selecting suitable criteria in practical BED applications.", "date": "2026-01-23", "categories": []}
{"id": "2601.15640", "title": "An Empirical Study on Ensemble-Based Transfer Learning Bayesian Optimisation with Mixed Variable Types", "abstract": "Bayesian optimisation is a sample efficient method for finding a global optimum of expensive black-box objective functions. Historic datasets from related problems can be exploited to help improve performance of Bayesian optimisation by adapting transfer learning methods to various components of the Bayesian optimisation pipeline. In this study we perform an empirical analysis of various ensemble-based transfer learning Bayesian optimisation methods and pipeline components. We expand on previous work in the literature by contributing some specific pipeline components, and three new real-time transfer learning Bayesian optimisation benchmarks. In particular we propose to use a weighting strategy for ensemble surrogate model predictions based on regularised regression with weights constrained to be positive, and a related component for handling the case when transfer learning is not improving Bayesian optimisation performance. We find that in general, two components that help improve transfer learning Bayesian optimisation performance are warm start initialisation and constraining weights used with ensemble surrogate model to be positive.", "date": "2026-01-22", "categories": []}
{"id": "2506.21894", "title": "Thompson Sampling in Function Spaces via Neural Operators", "abstract": "We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that queries to the operator (such as running a high-fidelity simulator or physical experiment) are costly, while functional evaluations on the operator's output are inexpensive. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process (GP) posterior. We derive regret bounds and theoretical results connecting neural operators with GPs in infinite-dimensional settings. Experiments benchmark our method against other Bayesian optimization baselines on functional optimization tasks involving partial differential equations of physical systems, demonstrating better sample efficiency and significant performance gains.", "date": "2025-06-27", "categories": []}
{"id": "2509.21661", "title": "Automating Sensor Characterization with Bayesian Optimization", "abstract": "The development of novel instrumentation requires an iterative cycle with three stages: design, prototyping, and testing. Recent advancements in simulation and nanofabrication techniques have significantly accelerated the design and prototyping phases. Nonetheless, detector characterization continues to be a major bottleneck in device development. During the testing phase, a significant time investment is required to characterize the device in different operating conditions and find optimal operating parameters. The total effort spent on characterization and parameter optimization can occupy a year or more of an expert's time. In this work, we present a novel technique for automated sensor characterization that aims to accelerate the testing stage of the development cycle. This technique leverages closed-loop Bayesian optimization (BO), using real-time measurements to guide parameter selection and identify optimal operating states. We demonstrate the method with a novel low-noise CCD, showing that the machine learning-driven tool can efficiently characterize and optimize operation of the sensor in a couple of days without supervision of a device expert.", "date": "2025-09-25", "categories": []}
{"id": "2501.18792", "title": "Bayesian Optimization with Preference Exploration using a Monotonic Neural Network Ensemble", "abstract": "Many real-world black-box optimization problems have multiple conflicting objectives. Rather than attempting to approximate the entire set of Pareto-optimal solutions, interactive preference learning allows to focus the search on the most relevant subset. However, few previous studies have exploited the fact that utility functions are usually monotonic. In this paper, we address the Bayesian Optimization with Preference Exploration (BOPE) problem and propose using a neural network ensemble as a utility surrogate model. This approach naturally integrates monotonicity and supports pairwise comparison data. Our experiments demonstrate that the proposed method outperforms state-of-the-art approaches and exhibits robustness to noise in utility evaluations. An ablation study highlights the critical role of monotonicity in enhancing performance.", "date": "2025-01-30", "categories": []}
{"id": "2601.08172", "title": "VBO-MI: A Fully Gradient-Based Bayesian Optimization Framework Using Variational Mutual Information Estimation", "abstract": "Many real-world tasks require optimizing expensive black-box functions accessible only through noisy evaluations, a setting commonly addressed with Bayesian optimization (BO). While Bayesian neural networks (BNNs) have recently emerged as scalable alternatives to Gaussian Processes (GPs), traditional BNN-BO frameworks remain burdened by expensive posterior sampling and acquisition function optimization. In this work, we propose {VBO-MI} (Variational Bayesian Optimization with Mutual Information), a fully gradient-based BO framework that leverages recent advances in variational mutual information estimation. To enable end-to-end gradient flow, we employ an actor-critic architecture consisting of an {action-net} to navigate the input space and a {variational critic} to estimate information gain. This formulation effectively eliminates the traditional inner-loop acquisition optimization bottleneck, achieving up to a {$10^2 \\times$ reduction in FLOPs} compared to BNN-BO baselines. We evaluate our method on a diverse suite of benchmarks, including high-dimensional synthetic functions and complex real-world tasks such as PDE optimization, the Lunar Lander control problem, and categorical Pest Control. Our experiments demonstrate that VBO-MI consistently provides the same or superior optimization performance and computational scalability over the baselines.", "date": "2026-01-13", "categories": []}
{"id": "2505.11323", "title": "Convergence Rates of Constrained Expected Improvement", "abstract": "Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints. One of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural extension of expected improvement (EI) when constraints are incorporated. However, the theoretical convergence rate of CEI has not been established. In this work, we study the convergence rate of CEI by analyzing its simple regret upper bound. First, we show that when the objective function $f$ and constraint function $c$ are assumed to each lie in a reproducing kernel Hilbert space (RKHS), CEI achieves the convergence rates of $\\mathcal{O} \\left(t^{-\\frac{1}{2}}\\log^{\\frac{d+1}{2}}(t) \\right) \\ \\text{and }\\ \\mathcal{O}\\left(t^{\\frac{-\\nu}{2\\nu+d}} \\log^{\\frac{\\nu}{2\\nu+d}}(t)\\right)$ for the commonly used squared exponential and Mat\\'{e}rn kernels ($\\nu>\\frac{1}{2}$), respectively. Second, we show that when $f$ is assumed to be sampled from Gaussian processes (GPs), CEI achieves similar convergence rates with a high probability. Numerical experiments are performed to validate the theoretical analysis.", "date": "2025-05-16", "categories": []}
{"id": "2601.06505", "title": "Neural Nonmyopic Bayesian Optimization in Dynamic Cost Settings", "abstract": "Bayesian optimization (BO) is a common framework for optimizing black-box functions, yet most existing methods assume static query costs and rely on myopic acquisition strategies. We introduce LookaHES, a nonmyopic BO framework designed for dynamic, history-dependent cost environments, where evaluation costs vary with prior actions, such as travel distance in spatial tasks or edit distance in sequence design. LookaHES combines a multi-step variant of $H$-Entropy Search with pathwise sampling and neural policy optimization, enabling long-horizon planning beyond twenty steps without the exponential complexity of existing nonmyopic methods. The key innovation is the integration of neural policies, including large language models, to effectively navigate structured, combinatorial action spaces such as protein sequences. These policies amortize lookahead planning and can be integrated with domain-specific constraints during rollout. Empirically, LookaHES outperforms strong myopic and nonmyopic baselines across nine synthetic benchmarks from two to eight dimensions and two real-world tasks: geospatial optimization using NASA night-light imagery and protein sequence design with constrained token-level edits. In short, LookaHES provides a general, scalable, and cost-aware solution for robust long-horizon optimization in complex decision spaces, which makes it a useful tool for researchers in machine learning, statistics, and applied domains. Our implementation is available at https://github.com/sangttruong/nonmyopia.", "date": "2026-01-10", "categories": []}
{"id": "2601.07094", "title": "Robust Bayesian Optimization via Tempered Posteriors", "abstract": "Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function such as expected improvement (EI). In practice, BO often concentrates evaluations near the current incumbent, causing the surrogate to become overconfident and to understate predictive uncertainty in the region guiding subsequent decisions. We develop a robust GP-based BO via tempered posterior updates, which downweight the likelihood by a power $\\alpha \\in (0,1]$ to mitigate overconfidence under local misspecification. We establish cumulative regret bounds for tempered BO under a family of generalized improvement rules, including EI, and show that tempering yields strictly sharper worst-case regret guarantees than the standard posterior $(\\alpha=1)$, with the most favorable guarantees occurring near the classical EI choice.\n  Motivated by our theoretic findings, we propose a prequential procedure for selecting $\\alpha$ online: it decreases $\\alpha$ when realized prediction errors exceed model-implied uncertainty and returns $\\alpha$ toward one as calibration improves. Empirical results demonstrate that tempering provides a practical yet theoretically grounded tool for stabilizing BO surrogates under localized sampling.", "date": "2026-01-11", "categories": []}
{"id": "2601.07258", "title": "Simulated Annealing-based Candidate Optimization for Batch Acquisition Functions", "abstract": "Bayesian Optimization with multi-objective acquisition functions such as q-Expected Hypervolume Improvement (qEHVI) requires efficient candidate optimization to maximize acquisition function values. Traditional approaches rely on continuous optimization methods like Sequential Least Squares Programming (SLSQP) for candidate selection. However, these gradient-based methods can become trapped in local optima, particularly in complex or high-dimensional objective landscapes. This paper presents a simulated annealing-based approach for candidate optimization in batch acquisition functions as an alternative to conventional continuous optimization methods. We evaluate our simulated annealing approach against SLSQP across four benchmark multi-objective optimization problems: ZDT1 (30D, 2 objectives), DTLZ2 (7D, 3 objectives), Kursawe (3D, 2 objectives), and Latent-Aware (4D, 2 objectives). Our results demonstrate that simulated annealing consistently achieves superior hypervolume performance compared to SLSQP in most test functions. The improvement is particularly pronounced for DTLZ2 and Latent-Aware problems, where simulated annealing reaches significantly higher hypervolume values and maintains better convergence characteristics. The histogram analysis of objective space coverage further reveals that simulated annealing explores more diverse and optimal regions of the Pareto front. These findings suggest that metaheuristic optimization approaches like simulated annealing can provide more robust and effective candidate optimization for multi-objective Bayesian optimization, offering a promising alternative to traditional gradient-based methods for batch acquisition function optimization.", "date": "2026-01-12", "categories": []}
{"id": "2601.05528", "title": "Autonomous Probe Microscopy with Robust Bag-of-Features Multi-Objective Bayesian Optimization: Pareto-Front Mapping of Nanoscale Structure-Property Trade-Offs", "abstract": "Combinatorial materials libraries are an efficient route to generate large families of candidate compositions, but their impact is often limited by the speed and depth of characterization and by the difficulty of extracting actionable structure-property relations from complex characterization data. Here we develop an autonomous scanning probe microscopy (SPM) framework that integrates automated atomic force and magnetic force microscopy (AFM/MFM) to rapidly explore magnetic and structural properties across combinatorial spread libraries. To enable automated exploration of systems without a clear optimization target, we introduce a combination of a static physics-informed bag-of-features (BoF) representation of measured surface morphology and magnetic structure with multi-objective Bayesian optimization (MOBO) to discover the relative significance and robustness of features. The resulting closed-loop workflow selectively samples the compositional gradient and reconstructs feature landscapes consistent with dense grid \"ground truth\" measurements. The resulting Pareto structure reveals where multiple nanoscale objectives are simultaneously optimized, where trade-offs between roughness, coherence, and magnetic contrast are unavoidable, and how families of compositions cluster into distinct functional regimes, thereby turning multi-feature imaging data into interpretable maps of competing structure-property trends. While demonstrated for Au-Co-Ni and AFM/MFM, the approach is general and can be extended to other combinatorial systems, imaging modalities, and feature sets, illustrating how feature-based MOBO and autonomous SPM can transform microscopy images from static data products into active feedback for real-time, multi-objective materials discovery.", "date": "2026-01-09", "categories": []}
{"id": "2601.05868", "title": "Sequential Bayesian Optimal Experimental Design in Infinite Dimensions via Policy Gradient Reinforcement Learning", "abstract": "Sequential Bayesian optimal experimental design (SBOED) for PDE-governed inverse problems is computationally challenging, especially for infinite-dimensional random field parameters. High-fidelity approaches require repeated forward and adjoint PDE solves inside nested Bayesian inversion and design loops. We formulate SBOED as a finite-horizon Markov decision process and learn an amortized design policy via policy-gradient reinforcement learning (PGRL), enabling online design selection from the experiment history without repeatedly solving an SBOED optimization problem. To make policy training and reward evaluation scalable, we combine dual dimension reduction -- active subspace projection for the parameter and principal component analysis for the state -- with an adjusted derivative-informed latent attention neural operator (LANO) surrogate that predicts both the parameter-to-solution map and its Jacobian. We use a Laplace-based D-optimality reward while noting that, in general, other expected-information-gain utilities such as KL divergence can also be used within the same framework. We further introduce an eigenvalue-based evaluation strategy that uses prior samples as proxies for maximum a posteriori (MAP) points, avoiding repeated MAP solves while retaining accurate information-gain estimates. Numerical experiments on sequential multi-sensor placement for contaminant source tracking demonstrate approximately $100\\times$ speedup over high-fidelity finite element methods, improved performance over random sensor placements, and physically interpretable policies that discover an ``upstream'' tracking strategy.", "date": "2026-01-09", "categories": []}
{"id": "2511.12063", "title": "TextBO: Bayesian Optimization in Language Space for Eval-Efficient Self-Improving AI", "abstract": "Large Language Models (LLMs) have enabled self-improving AI systems that iteratively generate, evaluate, and refine their outcomes. Recent studies show that prompt-optimization-based self-improvement can outperform state-of-the-art reinforcement-learning fine-tuning of LLMs, but performance is typically measured by generation efficiency. However, in many applications, the constraint is evaluation efficiency: obtaining reliable feedback is far more costly than generating candidates. To optimize for evaluation efficiency, we extend Upper Confidence Bound-Bayesian Optimization (UCB-BO), a framework known for optimal evaluation-efficiency guarantees, to the language domain. Doing so is challenging for two reasons: (i) gradients needed for UCB-BO are ill-defined in discrete prompt space; and (ii) UCB-style exploration relies on a surrogate model and acquisition function, which only live implicitly in the LLM. We overcome these challenges by proving that combining simple textual gradients (LLM-proposed local edits) with the Best-of-N selection strategy statistically emulates ascent along the gradient of the canonical UCB acquisition function. Based on this result, we propose TextBO, a simple, evaluation-efficient self-improving algorithm that operates purely in language space without explicit surrogates or calibrated uncertainty models. We empirically validate TextBO on automated ad-alignment tasks using a persona-induced preference distribution, demonstrating superior performance per evaluation compared to strong baselines such as Best-of-N and GEPA. We also evaluate TextBO's Best-of-N multi-step textual-gradient mechanism on agentic AI benchmarks by augmenting GEPA with it and show that it significantly outperforms standard GEPA. In sum, TextBO is a simple and principled framework for AI self-improving system design that bridges prompt optimization with classical Bayesian optimization.", "date": "2025-11-15", "categories": []}
{"id": "2601.00855", "title": "Physically-Constrained Autoencoder-Assisted Bayesian Optimization for Refinement of High-Dimensional Defect-Sensitive Single Crystalline Structure", "abstract": "Physical properties and functionalities of materials are dictated by global crystal structures as well as local defects. To establish a structure-property relationship, not only the crystallographic symmetry but also quantitative knowledge about defects are required. Here we present a hybrid Machine Learning framework that integrates a physically-constrained variational-autoencoder (pcVAE) with different Bayesian Optimization (BO) methods to systematically accelerate and improve crystal structure refinement with resolution of defects. We chose the pyrochlore structured Ho2Ti2O7 as a model system and employed the GSAS2 package for benchmarking crystallographic parameters from Rietveld refinement. However, the function space of these material systems is highly nonlinear, which limits optimizers like traditional Rietveld refinement, into trapping at local minima. Also, these naive methods don't provide an extensive learning about the overall function space, which is essential for large space, large time consuming explorations to identify various potential regions of interest. Thus, we present the approach of exploring the high Dimensional structure parameters of defect sensitive systems via pretrained pcVAE assisted BO and Sparse Axis Aligned BO. The pcVAE projects high-Dimensional diffraction data consisting of thousands of independently measured diffraction orders into a lowD latent space while enforcing scaling invariance and physical relevance. Then via BO methods, we aim to minimize the L2 norm based chisq errors in the real and latent spaces separately between experimental and simulated diffraction patterns, thereby steering the refinement towards potential optimum crystal structure parameters. We investigated and compared the results among different pcVAE assisted BO, non pcVAE assisted BO, and Rietveld refinement.", "date": "2025-12-29", "categories": []}
{"id": "2512.05940", "title": "Designing an Optimal Sensor Network via Minimizing Information Loss", "abstract": "Optimal experimental design is a classic topic in statistics, with many well-studied problems, applications, and solutions. The design problem we study is the placement of sensors to monitor spatiotemporal processes, explicitly accounting for the temporal dimension in our modeling and optimization. We observe that recent advancements in computational sciences often yield large datasets based on physics-based simulations, which are rarely leveraged in experimental design. We introduce a novel model-based sensor placement criterion, along with a highly-efficient optimization algorithm, which integrates physics-based simulations and Bayesian experimental design principles to identify sensor networks that \"minimize information loss\" from simulated data. Our technique relies on sparse variational inference and (separable) Gauss-Markov priors, and thus may adapt many techniques from Bayesian experimental design. We validate our method through a case study monitoring air temperature in Phoenix, Arizona, using state-of-the-art physics-based simulations. Our results show our framework to be superior to random or quasi-random sampling, particularly with a limited number of sensors. We conclude by discussing practical considerations and implications of our framework, including more complex modeling tools and real-world deployments.", "date": "2025-12-05", "categories": []}
{"id": "2311.13050", "title": "Multi-fidelity Bayesian Optimization: A Review", "abstract": "Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.", "date": "2023-11-21", "categories": []}
{"id": "2512.22999", "title": "JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference", "abstract": "We consider problems of parameter estimation where design variables can be actively optimized to maximize information gain. To this end, we introduce JADAI, a framework that jointly amortizes Bayesian adaptive design and inference by training a policy, a history network, and an inference network end-to-end. The networks minimize a generic loss that aggregates incremental reductions in posterior error along experimental sequences. Inference networks are instantiated with diffusion-based posterior estimators that can approximate high-dimensional and multimodal posteriors at every experimental step. Across standard adaptive design benchmarks, JADAI achieves superior or competitive performance.", "date": "2025-12-28", "categories": []}
{"id": "2507.13704", "title": "A study of EHVI vs fixed scalarization for molecule design", "abstract": "Multi-objective Bayesian optimization (MOBO) provides a principled framework for navigating trade-offs in molecular design. However, its empirical advantages over scalarized alternatives remain underexplored. We benchmark a simple Pareto-based MOBO strategy - Expected Hypervolume Improvement (EHVI) - against a simple fixed-weight scalarized baseline using Expected Improvement (EI), under a tightly controlled setup with identical Gaussian Process surrogates and molecular representations. Across three molecular optimization tasks, EHVI consistently outperforms scalarized EI in terms of Pareto front coverage, convergence speed, and chemical diversity. While scalarization encompasses flexible variants - including random or adaptive schemes - our results show that even strong deterministic instantiations can underperform in low-data regimes. These findings offer concrete evidence for the practical advantages of Pareto-aware acquisition in de novo molecular optimization, especially when evaluation budgets are limited and trade-offs are nontrivial.", "date": "2025-07-18", "categories": []}
{"id": "2512.18980", "title": "OPBO: Order-Preserving Bayesian Optimization", "abstract": "Bayesian optimization is an effective method for solving expensive black-box optimization problems. Most existing methods use Gaussian processes (GP) as the surrogate model for approximating the black-box objective function, it is well-known that it can fail in high-dimensional space (e.g., dimension over 500). We argue that the reliance of GP on precise numerical fitting is fundamentally ill-suited in high-dimensional space, where it leads to prohibitive computational complexity. In order to address this, we propose a simple order-preserving Bayesian optimization (OPBO) method, where the surrogate model preserves the order, instead of the value, of the black-box objective function. Then we can use a simple but effective OP neural network (NN) to replace GP as the surrogate model. Moreover, instead of searching for the best solution from the acquisition model, we select good-enough solutions in the ordinal set to reduce computational cost. The experimental results show that for high-dimensional (over 500) black-box optimization problems, the proposed OPBO significantly outperforms traditional BO methods based on regression NN and GP. The source code is available at https://github.com/pengwei222/OPBO.", "date": "2025-12-22", "categories": []}
{"id": "2512.17569", "title": "Bayesian Optimisation: Which Constraints Matter?", "abstract": "Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems with \\emph{decoupled} black-box constraints, in which subsets of the objective and constraint functions may be evaluated independently. In particular, our methods aim to take into account that often only a handful of the constraints may be binding at the optimum, and hence we should evaluate only relevant constraints when trying to optimise a function. We empirically benchmark these methods against existing methods and demonstrate their superiority over the state-of-the-art.", "date": "2025-12-19", "categories": []}
{"id": "2412.20375", "title": "Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes", "abstract": "Bayesian optimization is an effective technique for black-box optimization, but its applicability is typically limited to low-dimensional and small-budget problems due to the cubic complexity of computing the Gaussian process (GP) surrogate. While various approximate GP models have been employed to scale Bayesian optimization to larger sample sizes, most suffer from overly-smooth estimation and focus primarily on problems that allow for large online samples. In this work, we argue that Bayesian optimization algorithms with sparse GPs can more efficiently allocate their representational power to relevant regions of the search space. To achieve this, we propose focalized GP, which leverages a novel variational loss function to achieve stronger local prediction, as well as FocalBO, which hierarchically optimizes the focalized GP acquisition function over progressively smaller search spaces. Experimental results demonstrate that FocalBO can efficiently leverage large amounts of offline and online data to achieve state-of-the-art performance on robot morphology design and to control a 585-dimensional musculoskeletal system.", "date": "2024-12-29", "categories": []}
{"id": "2503.03625", "title": "Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?", "abstract": "Bayesian Optimization (BO) with Gaussian Processes relies on optimizing an acquisition function to determine sampling. We investigate the advantages and disadvantages of using a deterministic global solver (MAiNGO) compared to conventional local and stochastic global solvers (L-BFGS-B and multi-start, respectively) for the optimization of the acquisition function. For CPU efficiency, we set a time limit for MAiNGO, taking the best point as optimal. We perform repeated numerical experiments, initially using the Muller-Brown potential as a benchmark function, utilizing the lower confidence bound acquisition function; we further validate our findings with three alternative benchmark functions. Statistical analysis reveals that when the acquisition function is more exploitative (as opposed to exploratory), BO with MAiNGO converges in fewer iterations than with the local solvers. However, when the dataset lacks diversity, or when the acquisition function is overly exploitative, BO with MAiNGO, compared to the local solvers, is more likely to converge to a local rather than a global ly near-optimal solution of the black-box function. L-BFGS-B and multi-start mitigate this risk in BO by introducing stochasticity in the selection of the next sampling point, which enhances the exploration of uncharted regions in the search space and reduces dependence on acquisition function hyperparameters. Ultimately, suboptimal optimization of poorly chosen acquisition functions may be preferable to their optimal solution. When the acquisition function is more exploratory, BO with MAiNGO, multi-start, and L-BFGS-B achieve comparable probabilities of convergence to a globally near-optimal solution (although BO with MAiNGO may require more iterations to converge under these conditions).", "date": "2025-03-05", "categories": []}
{"id": "2512.15483", "title": "Multi-stage Bayesian optimisation for dynamic decision-making in self-driving labs", "abstract": "Self-driving laboratories (SDLs) are combining recent technological advances in robotics, automation, and machine learning based data analysis and decision-making to perform autonomous experimentation toward human-directed goals without requiring any direct human intervention. SDLs are successfully used in materials science, chemistry, and beyond, to optimise processes, materials, and devices in a systematic and data-efficient way. At present, the most widely used algorithm to identify the most informative next experiment is Bayesian optimisation. While relatively simple to apply to a wide range of optimisation problems, standard Bayesian optimisation relies on a fixed experimental workflow with a clear set of optimisation parameters and one or more measurable objective functions. This excludes the possibility of making on-the-fly decisions about changes in the planned sequence of operations and including intermediate measurements in the decision-making process. Therefore, many real-world experiments need to be adapted and simplified to be converted to the common setting in self-driving labs. In this paper, we introduce an extension to Bayesian optimisation that allows flexible sampling of multi-stage workflows and makes optimal decisions based on intermediate observables, which we call proxy measurements. We systematically compare the advantage of taking into account proxy measurements over conventional Bayesian optimisation, in which only the final measurement is observed. We find that over a wide range of scenarios, proxy measurements yield a substantial improvement, both in the time to find good solutions and in the overall optimality of found solutions. This not only paves the way to use more complex and thus more realistic experimental workflows in autonomous labs but also to smoothly combine simulations and experiments in the next generation of SDLs.", "date": "2025-12-17", "categories": []}
{"id": "2512.13935", "title": "Informing Acquisition Functions via Foundation Models for Molecular Discovery", "abstract": "Bayesian Optimization (BO) is a key methodology for accelerating molecular discovery by estimating the mapping from molecules to their properties while seeking the optimal candidate. Typically, BO iteratively updates a probabilistic surrogate model of this mapping and optimizes acquisition functions derived from the model to guide molecule selection. However, its performance is limited in low-data regimes with insufficient prior knowledge and vast candidate spaces. Large language models (LLMs) and chemistry foundation models offer rich priors to enhance BO, but high-dimensional features, costly in-context learning, and the computational burden of deep Bayesian surrogates hinder their full utilization. To address these challenges, we propose a likelihood-free BO method that bypasses explicit surrogate modeling and directly leverages priors from general LLMs and chemistry-specific foundation models to inform acquisition functions. Our method also learns a tree-structured partition of the molecular search space with local acquisition functions, enabling efficient candidate selection via Monte Carlo Tree Search. By further incorporating coarse-grained LLM-based clustering, it substantially improves scalability to large candidate sets by restricting acquisition function evaluations to clusters with statistically higher property values. We show through extensive experiments and ablations that the proposed method substantially improves scalability, robustness, and sample efficiency in LLM-guided BO for molecular discovery.", "date": "2025-12-15", "categories": []}
{"id": "2510.23681", "title": "Informed Initialization for Bayesian Optimization and Active Learning", "abstract": "Bayesian Optimization is a widely used method for optimizing expensive black-box functions, relying on probabilistic surrogate models such as Gaussian Processes. The quality of the surrogate model is crucial for good optimization performance, especially in the few-shot setting where only a small number of batches of points can be evaluated. In this setting, the initialization plays a critical role in shaping the surrogate's predictive quality and guiding subsequent optimization. Despite this, practitioners typically rely on (quasi-)random designs to cover the input space. However, such approaches neglect two key factors: (a) space-filling designs may not be desirable to reduce predictive uncertainty, and (b) efficient hyperparameter learning during initialization is essential for high-quality prediction, which may conflict with space-filling designs. To address these limitations, we propose Hyperparameter-Informed Predictive Exploration (HIPE), a novel acquisition strategy that balances predictive uncertainty reduction with hyperparameter learning using information-theoretic principles. We derive a closed-form expression for HIPE in the Gaussian Process setting and demonstrate its effectiveness through extensive experiments in active learning and few-shot BO. Our results show that HIPE outperforms standard initialization strategies in terms of predictive accuracy, hyperparameter identification, and subsequent optimization performance, particularly in large-batch, few-shot settings relevant to many real-world Bayesian Optimization applications.", "date": "2025-10-27", "categories": []}
{"id": "2512.11580", "title": "Safe Bayesian optimization across noise models via scenario programming", "abstract": "Safe Bayesian optimization (BO) with Gaussian processes is an effective tool for tuning control policies in safety-critical real-world systems, specifically due to its sample efficiency and safety guarantees. However, most safe BO algorithms assume homoscedastic sub-Gaussian measurement noise, an assumption that does not hold in many relevant applications. In this article, we propose a straightforward yet rigorous approach for safe BO across noise models, including homoscedastic sub-Gaussian and heteroscedastic heavy-tailed distributions. We provide a high-probability bound on the measurement noise via the scenario approach, integrate these bounds into high probability confidence intervals, and prove safety and optimality for our proposed safe BO algorithm. We deploy our algorithm in synthetic examples and in tuning a controller for the Franka Emika manipulator in simulation.", "date": "2025-12-12", "categories": []}
{"id": "2506.01393", "title": "Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimization", "abstract": "This paper addresses the Bayesian optimization problem (also referred to as the Bayesian setting of the Gaussian process bandit), where the learner seeks to minimize the regret under a function drawn from a known Gaussian process (GP). Under a Mat\\'ern kernel with a certain degree of smoothness, we show that the Gaussian process upper confidence bound (GP-UCB) algorithm achieves $\\tilde{O}(\\sqrt{T})$ cumulative regret with high probability. Furthermore, our analysis yields $O(\\sqrt{T \\ln^2 T})$ regret under a squared exponential kernel. These results fill the gap between the existing regret upper bound for GP-UCB and the best-known bound provided by Scarlett (2018). The key idea in our proof is to capture the concentration behavior of the input sequence realized by GP-UCB, enabling a more refined analysis of the GP's information gain.", "date": "2025-06-02", "categories": []}
{"id": "2506.01625", "title": "Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks", "abstract": "We address the problem of Gaussian Process (GP) optimization in the presence of unknown and potentially varying adversarial perturbations. Unlike traditional robust optimization approaches that focus on maximizing performance under worst-case scenarios, we consider a robust satisficing objective, where the goal is to consistently achieve a predefined performance threshold $\\tau$, even under adversarial conditions. We propose two novel algorithms based on distinct formulations of robust satisficing, and show that they are instances of a general robust satisficing framework. Further, each algorithm offers different guarantees depending on the nature of the adversary. Specifically, we derive two regret bounds: one that is sublinear over time, assuming certain conditions on the adversary and the satisficing threshold $\\tau$, and another that scales with the perturbation magnitude but requires no assumptions on the adversary. Through extensive experiments, we demonstrate that our approach outperforms the established robust optimization methods in achieving the satisficing objective, particularly when the ambiguity set of the robust optimization framework is inaccurately specified.", "date": "2025-06-02", "categories": []}
{"id": "2511.12783", "title": "Function-on-Function Bayesian Optimization", "abstract": "Bayesian optimization (BO) has been widely used to optimize expensive and gradient-free objective functions across various domains. However, existing BO methods have not addressed the objective where both inputs and outputs are functions, which increasingly arise in complex systems as advanced sensing technologies. To fill this gap, we propose a novel function-on-function Bayesian optimization (FFBO) framework. Specifically, we first introduce a function-on-function Gaussian process (FFGP) model with a separable operator-valued kernel to capture the correlations between function-valued inputs and outputs. Compared to existing Gaussian process models, FFGP is modeled directly in the function space. Based on FFGP, we define a scalar upper confidence bound (UCB) acquisition function using a weighted operator-based scalarization strategy. Then, a scalable functional gradient ascent algorithm (FGA) is developed to efficiently identify the optimal function-valued input. We further analyze the theoretical properties of the proposed method. Extensive experiments on synthetic and real-world data demonstrate the superior performance of FFBO over existing approaches.", "date": "2025-11-16", "categories": []}
{"id": "2511.13625", "title": "Batch Acquisition Function Evaluations and Decouple Optimizer Updates for Faster Bayesian Optimization", "abstract": "Bayesian optimization (BO) efficiently finds high-performing parameters by maximizing an acquisition function, which models the promise of parameters. A major computational bottleneck arises in acquisition function optimization, where multi-start optimization (MSO) with quasi-Newton (QN) methods is required due to the non-convexity of the acquisition function. BoTorch, a widely used BO library, currently optimizes the summed acquisition function over multiple points, leading to the speedup of MSO owing to PyTorch batching. Nevertheless, this paper empirically demonstrates the suboptimality of this approach in terms of off-diagonal approximation errors in the inverse Hessian of a QN method, slowing down its convergence. To address this problem, we propose to decouple QN updates using a coroutine while batching the acquisition function calls. Our approach not only yields the theoretically identical convergence to the sequential MSO but also drastically reduces the wall-clock time compared to the previous approaches. Our approach is available in GPSampler in Optuna, effectively reducing its computational overhead.", "date": "2025-11-17", "categories": []}
{"id": "2512.05127", "title": "Bayesian Optimization and Convolutional Neural Networks for Zernike-Based Wavefront Correction in High Harmonic Generation", "abstract": "High harmonic generation (HHG) is a nonlinear process that enables table-top generation of tunable, high-energy, coherent, ultrashort radiation pulses in the extreme ultraviolet (EUV) to soft X-ray range. These pulses find applications in photoemission spectroscopy in condensed matter physics, pump-probe spectroscopy for high-energy-density plasmas, and attosecond science. However, optical aberrations in the high-power laser systems required for HHG degrade beam quality and reduce efficiency. We present a machine learning approach to optimize aberration correction using a spatial light modulator. We implemented and compared Bayesian optimization and convolutional neural network (CNN) methods to predict optimal Zernike polynomial coefficients for wavefront correction. Our CNN achieved promising results with 80.39% accuracy on test data, demonstrating the potential for automated aberration correction in HHG systems.", "date": "2025-11-23", "categories": []}
{"id": "2512.03772", "title": "Bayesian Optimization for Automatic Tuning of Torque-Level Nonlinear Model Predictive Control", "abstract": "This paper presents an auto-tuning framework for torque-based Nonlinear Model Predictive Control (nMPC), where the MPC serves as a real-time controller for optimal joint torque commands. The MPC parameters, including cost function weights and low-level controller gains, are optimized using high-dimensional Bayesian Optimization (BO) techniques, specifically Sparse Axis-Aligned Subspace (SAASBO) with a digital twin (DT) to achieve precise end-effector trajectory real-time tracking on an UR10e robot arm. The simulation model allows efficient exploration of the high-dimensional parameter space, and it ensures safe transfer to hardware. Our simulation results demonstrate significant improvements in tracking performance (+41.9%) and reduction in solve times (-2.5%) compared to manually-tuned parameters. Moreover, experimental validation on the real robot follows the trend (with a +25.8% improvement), emphasizing the importance of digital twin-enabled automated parameter optimization for robotic operations.", "date": "2025-12-03", "categories": []}
{"id": "2512.01245", "title": "Bayesian Optimization for Non-Cooperative Game-Based Radio Resource Management", "abstract": "Radio resource management in modern cellular networks often calls for the optimization of complex utility functions that are potentially conflicting between different base stations (BSs). Coordinating the resource allocation strategies efficiently across BSs to ensure stable network service poses significant challenges, especially when each utility is accessible only via costly, black-box evaluations. This paper considers formulating the resource allocation among spectrum sharing BSs as a non-cooperative game, with the goal of aligning their allocation incentives toward a stable outcome. To address this challenge, we propose PPR-UCB, a novel Bayesian optimization (BO) strategy that learns from sequential decision-evaluation pairs to approximate pure Nash equilibrium (PNE) solutions. PPR-UCB applies martingale techniques to Gaussian process (GP) surrogates and constructs high probability confidence bounds for utilities uncertainty quantification. Experiments on downlink transmission power allocation in a multi-cell multi-antenna system demonstrate the efficiency of PPR-UCB in identifying effective equilibrium solutions within a few data samples.", "date": "2025-12-01", "categories": []}
{"id": "2511.23141", "title": "Automated Discovery of Laser Dicing Processes with Bayesian Optimization for Semiconductor Manufacturing", "abstract": "Laser dicing of semiconductor wafers is a critical step in microelectronic manufacturing, where multiple sequential laser passes precisely separate individual dies from the wafer. Adapting this complex sequential process to new wafer materials typically requires weeks of expert effort to balance process speed, separation quality, and material integrity. We present the first automated discovery of production-ready laser dicing processes on an industrial LASER1205 dicing system. We formulate the problem as a high-dimensional, constrained multi-objective Bayesian optimization task, and introduce a sequential two-level fidelity strategy to minimize expensive destructive die-strength evaluations. On bare silicon and product wafers, our method autonomously delivers feasible configurations that match or exceed expert baselines in production speed, die strength, and structural integrity, using only technician-level operation. Post-hoc validation of different weight configurations of the utility functions reveals that multiple feasible solutions with qualitatively different trade-offs can be obtained from the final surrogate model. Expert-refinement of the discovered process can further improve production speed while preserving die strength and structural integrity, surpassing purely manual or automated methods.", "date": "2025-11-28", "categories": []}
{"id": "2410.14533", "title": "The Traveling Bandit: A Framework for Bayesian Optimization with Movement Costs", "abstract": "This paper introduces a framework for Bayesian Optimization (BO) with metric movement costs, addressing a critical challenge in practical applications where input alterations incur varying costs. Our approach is a convenient plug-in that seamlessly integrates with the existing literature on batched algorithms, where designs within batches are observed following the solution of a Traveling Salesman Problem. The proposed method provides a theoretical guarantee of convergence in terms of movement costs for BO. Empirically, our method effectively reduces average movement costs over time while maintaining comparable regret performance to conventional BO methods. This framework also shows promise for broader applications in various bandit settings with movement costs.", "date": "2024-10-18", "categories": []}
{"id": "2508.03827", "title": "Scalable neural network-based blackbox optimization", "abstract": "Bayesian Optimization (BO) is a widely used approach for blackbox optimization that leverages a Gaussian process (GP) model and an acquisition function to guide future sampling. While effective in low-dimensional settings, BO faces scalability challenges in high-dimensional spaces and with large number of function evaluations due to the computational complexity of GP models. In contrast, neural networks (NNs) offer better scalability and can model complex functions, which led to the development of NN-based BO approaches. However, these methods typically rely on estimating model uncertainty in NN prediction -- a process that is often computationally intensive and complex, particularly in high dimensions. To address these limitations, a novel method, called scalable neural network-based blackbox optimization (SNBO), is proposed that does not rely on model uncertainty estimation. Specifically, SNBO adds new samples using separate criteria for exploration and exploitation, while adaptively controlling the sampling region to ensure efficient optimization. SNBO is evaluated on a range of optimization problems spanning from 10 to 102 dimensions and compared against four state-of-the-art baseline algorithms. Across the majority of test problems, SNBO attains function values better than the best-performing baseline algorithm, while requiring 40-60% fewer function evaluations and reducing the runtime by at least an order of magnitude.", "date": "2025-08-05", "categories": []}
{"id": "2504.20319", "title": "Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approach", "abstract": "Bayesian experimental design (BED) offers a principled framework for optimizing data acquisition by leveraging probabilistic inference. However, practical implementations of BED are often compromised by model discrepancy, i.e., the mismatch between predictive models and true physical systems, which can potentially lead to biased parameter estimates. While data-driven approaches have been recently explored to characterize the model discrepancy, the resulting high-dimensional parameter space poses severe challenges for both Bayesian updating and design optimization. In this work, we propose a hybrid BED framework enabled by auto-differentiable ensemble Kalman inversion (AD-EKI) that addresses these challenges by providing a computationally efficient, gradient-free alternative to estimate the information gain for high-dimensional network parameters. The AD-EKI allows a differentiable evaluation of the utility function in BED and thus facilitates the use of standard gradient-based methods for design optimization. In the proposed hybrid framework, we iteratively optimize experimental designs, decoupling the inference of low-dimensional physical parameters handled by standard BED methods, from the high-dimensional model discrepancy handled by AD-EKI. The identified optimal designs for the model discrepancy enable us to systematically collect informative data for its calibration. The performance of the proposed method is studied by a classical convection-diffusion BED example, and the hybrid framework enabled by AD-EKI efficiently identifies informative data to calibrate the model discrepancy and robustly infers the unknown physical parameters in the modeled system. Besides addressing the challenges of BED with model discrepancy, AD-EKI also potentially fosters efficient and scalable frameworks in many other areas with bilevel optimization, such as meta-learning and structure optimization.", "date": "2025-04-29", "categories": []}
{"id": "2511.17850", "title": "Efficient Dynamic and Momentum Aperture Optimization for Lattice Design Using Multipoint Bayesian Algorithm Execution", "abstract": "We demonstrate that multipoint Bayesian algorithm execution can overcome fundamental computational challenges in storage ring design optimization. Dynamic (DA) and momentum (MA) optimization is a multipoint, multiobjective design task for storage rings, ultimately informing the flux of x-ray sources and luminosity of colliders. Current state-of-art black-box optimization methods require extensive particle-tracking simulations for each trial configuration; the high computational cost restricts the extent of the search to $\\sim 10^3$ configurations, and therefore limits the quality of the final design. We remove this bottleneck using multipointBAX, which selects, simulates, and models each trial configuration at the single particle level. We demonstrate our approach on a novel design for a fourth-generation light source, with neural-network powered multipointBAX achieving equivalent Pareto front results using more than two orders of magnitude fewer tracking computations compared to genetic algorithms. The significant reduction in cost positions multipointBAX as a promising alternative to black-box optimization, and we anticipate multipointBAX will be instrumental in the design of future light sources, colliders, and large-scale scientific facilities.", "date": "2025-11-22", "categories": []}
{"id": "2511.18891", "title": "Reproducibility Study of Large Language Model Bayesian Optimization", "abstract": "In this reproducibility study, we revisit the LLAMBO framework of Daxberger et al. (2024), a prompting-based Bayesian optimization (BO) method that uses large language models as discriminative surrogates and acquisition optimizers via text-only interactions. We replicate the core Bayesmark and HPOBench experiments under the original evaluation protocol, but replace GPT-3.5 with the open-weight Llama 3.1 70B model used for all text encoding components.\n  Our results broadly confirm the main claims of LLAMBO. Contextual warm starting via textual problem and hyperparameter descriptions substantially improves early regret behaviour and reduces variance across runs. LLAMBO's discriminative surrogate is weaker than GP or SMAC as a pure single task regressor, yet benefits from cross task semantic priors induced by the language model. Ablations that remove textual context markedly degrade predictive accuracy and calibration, while the LLAMBO candidate sampler consistently generates higher quality and more diverse proposals than TPE or random sampling. Experiments with smaller backbones (Gemma 27B, Llama 3.1 8B) yield unstable or invalid predictions, suggesting insufficient capacity for reliable surrogate behaviour.\n  Overall, our study shows that the LLAMBO architecture is robust to changing the language model backbone and remains effective when instantiated with Llama 3.1 70B.", "date": "2025-11-24", "categories": []}
{"id": "2511.19241", "title": "Local Entropy Search over Descent Sequences for Bayesian Optimization", "abstract": "Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent. We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences of iterative optimizers. The algorithm propagates the posterior belief over the objective through the optimizer, resulting in a probability distribution over descent sequences. It then selects the next evaluation by maximizing mutual information with that distribution, using a combination of analytic entropy calculations and Monte-Carlo sampling of descent sequences. Empirical results on high-complexity synthetic objectives and benchmark problems show that LES achieves strong sample efficiency compared to existing local and global Bayesian optimization methods.", "date": "2025-11-24", "categories": []}
{"id": "2207.09154", "title": "Investigating Bayesian optimization for expensive-to-evaluate black box functions: Application in fluid dynamics", "abstract": "Bayesian optimization provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g. in machine learning to optimize hyperparameters of neural networks, and in engineering, e.g. in fluid dynamics to optimize control strategies that maximize drag reduction. This paper empirically studies and compares the performance and the robustness of common Bayesian optimization algorithms on a range of synthetic test functions to provide general guidance on the design of Bayesian optimization algorithms for specific problems. It investigates the choice of acquisition function, the effect of different numbers of training samples, the exact and Monte Carlo based calculation of acquisition functions, and both single-point and multi-point optimization. The test functions considered cover a wide selection of challenges and therefore serve as an ideal test bed to understand the performance of Bayesian optimization to specific challenges, and in general. To illustrate how these findings can be used to inform a Bayesian optimization setup tailored to a specific problem, two simulations in the area of computational fluid dynamics are optimized, giving evidence that suitable solutions can be found in a small number of evaluations of the objective function for complex, real problems. The results of our investigation can similarly be applied to other areas, such as machine learning and physical experiments, where objective functions are expensive to evaluate and their mathematical expressions are unknown.", "date": "2022-07-19", "categories": []}
{"id": "2402.03006", "title": "On the development of a practical Bayesian optimisation algorithm for expensive experiments and simulations with changing environmental conditions", "abstract": "Experiments in engineering are typically conducted in controlled environments where parameters can be set to any desired value. This assumes that the same applies in a real-world setting -- an assumption that is often incorrect as many experiments are influenced by uncontrollable environmental conditions such as temperature, humidity and wind speed. When optimising such experiments, the focus should lie on finding optimal values conditionally on these uncontrollable variables. This article extends Bayesian optimisation to the optimisation of systems in changing environments that include controllable and uncontrollable parameters. The extension fits a global surrogate model over all controllable and environmental variables but optimises only the controllable parameters conditional on measurements of the uncontrollable variables. The method is validated on two synthetic test functions and the effects of the noise level, the number of the environmental parameters, the parameter fluctuation, the variability of the uncontrollable parameters, and the effective domain size are investigated. ENVBO, the proposed algorithm resulting from this investigation, is applied to a wind farm simulator with eight controllable and one environmental parameter. ENVBO finds solutions for the full domain of the environmental variable that outperforms results from optimisation algorithms that only focus on a fixed environmental value in all but one case while using a fraction of their evaluation budget. This makes the proposed approach very sample-efficient and cost-effective. An off-the-shelf open-source version of ENVBO is available via the NUBO Python package.", "date": "2024-02-05", "categories": []}
{"id": "2412.02423", "title": "Time-Series-Informed Closed-loop Learning for Sequential Decision Making and Control", "abstract": "Closed-loop performance of sequential decision making algorithms, such as model predictive control, depends strongly on the choice of controller parameters. Bayesian optimization allows learning of parameters from closed-loop experiments, but standard Bayesian optimization treats this as a black-box problem and ignores the temporal structure of closed-loop trajectories, leading to slow convergence and inefficient use of experimental resources. We propose a time-series-informed multi-fidelity Bayesian optimization framework that aligns the fidelity dimension with closed-loop time, enabling intermediate performance evaluations within a closed-loop experiment to be incorporated as lower-fidelity observations. Additionally, we derive probabilistic early stopping criteria to terminate unpromising closed-loop experiments based on the surrogate model's posterior belief, avoiding full episodes for poor parameterizations and thereby reducing resource usage. Simulation results on a nonlinear control benchmark demonstrate that, compared to standard black-box Bayesian optimization approaches, the proposed method achieves comparable closed-loop performance with roughly half the experimental resources, and yields better final performance when using the same resource budget, highlighting the value of exploiting temporal structure for sample-efficient closed-loop controller tuning.", "date": "2024-12-03", "categories": []}
{"id": "2511.11739", "title": "Noise-Aware Optimization in Nominally Identical Manufacturing and Measuring Systems for High-Throughput Parallel Workflows", "abstract": "Device-to-device variability in experimental noise critically impacts reproducibility, especially in automated, high-throughput systems like additive manufacturing farms. While manageable in small labs, such variability can escalate into serious risks at larger scales, such as architectural 3D printing, where noise may cause structural or economic failures. This contribution presents a noise-aware decision-making algorithm that quantifies and models device-specific noise profiles to manage variability adaptively. It uses distributional analysis and pairwise divergence metrics with clustering to choose between single-device and robust multi-device Bayesian optimization strategies. Unlike conventional methods that assume homogeneous devices or generic robustness, this framework explicitly leverages inter-device differences to enhance performance, reproducibility, and efficiency. An experimental case study involving three nominally identical 3D printers (same brand, model, and close serial numbers) demonstrates reduced redundancy, lower resource usage, and improved reliability. Overall, this framework establishes a paradigm for precision- and resource-aware optimization in scalable, automated experimental platforms.", "date": "2025-11-13", "categories": []}
{"id": "2511.11983", "title": "Bayesian--AI Fusion for Epidemiological Decision Making: Calibrated Risk, Honest Uncertainty, and Hyperparameter Intelligence", "abstract": "Modern epidemiological analytics increasingly use machine learning models that offer strong prediction but often lack calibrated uncertainty. Bayesian methods provide principled uncertainty quantification, yet are viewed as difficult to integrate with contemporary AI workflows. This paper proposes a unified Bayesian and AI framework that combines Bayesian prediction with Bayesian hyperparameter optimization.\n  We use Bayesian logistic regression to obtain calibrated individual-level disease risk and credible intervals on the Pima Indians Diabetes dataset. In parallel, we use Gaussian-process Bayesian optimization to tune penalized Cox survival models on the GBSG2 breast cancer cohort. This yields a two-layer system: a Bayesian predictive layer that represents risk as a posterior distribution, and a Bayesian optimization layer that treats model selection as inference over a black-box objective.\n  Simulation studies in low- and high-dimensional regimes show that the Bayesian layer provides reliable coverage and improved calibration, while Bayesian shrinkage improves AUC, Brier score, and log-loss. Bayesian optimization consistently pushes survival models toward near-oracle concordance. Overall, Bayesian reasoning enhances both what we infer and how we search, enabling calibrated risk and principled hyperparameter intelligence for epidemiological decision making.", "date": "2025-11-15", "categories": []}
{"id": "2511.10590", "title": "Pretrained Joint Predictions for Scalable Batch Bayesian Optimization of Molecular Designs", "abstract": "Batched synthesis and testing of molecular designs is the key bottleneck of drug development. There has been great interest in leveraging biomolecular foundation models as surrogates to accelerate this process. In this work, we show how to obtain scalable probabilistic surrogates of binding affinity for use in Batch Bayesian Optimization (Batch BO). This demands parallel acquisition functions that hedge between designs and the ability to rapidly sample from a joint predictive density to approximate them. Through the framework of Epistemic Neural Networks (ENNs), we obtain scalable joint predictive distributions of binding affinity on top of representations taken from large structure-informed models. Key to this work is an investigation into the importance of prior networks in ENNs and how to pretrain them on synthetic data to improve downstream performance in Batch BO. Their utility is demonstrated by rediscovering known potent EGFR inhibitors on a semi-synthetic benchmark in up to 5x fewer iterations, as well as potent inhibitors from a real-world small-molecule library in up to 10x fewer iterations, offering a promising solution for large-scale drug discovery applications.", "date": "2025-11-13", "categories": []}
{"id": "2511.07734", "title": "Global Optimization on Graph-Structured Data via Gaussian Processes with Spectral Representations", "abstract": "Bayesian optimization (BO) is a powerful framework for optimizing expensive black-box objectives, yet extending it to graph-structured domains remains challenging due to the discrete and combinatorial nature of graphs. Existing approaches often rely on either full graph topology-impractical for large or partially observed graphs-or incremental exploration, which can lead to slow convergence. We introduce a scalable framework for global optimization over graphs that employs low-rank spectral representations to build Gaussian process (GP) surrogates from sparse structural observations. The method jointly infers graph structure and node representations through learnable embeddings, enabling efficient global search and principled uncertainty estimation even with limited data. We also provide theoretical analysis establishing conditions for accurate recovery of underlying graph structure under different sampling regimes. Experiments on synthetic and real-world datasets demonstrate that our approach achieves faster convergence and improved optimization performance compared to prior methods.", "date": "2025-11-11", "categories": []}
{"id": "2509.08736", "title": "ChemBOMAS: Accelerated BO in Chemistry with LLM-Enhanced Multi-Agent System", "abstract": "Bayesian optimization (BO) is a powerful tool for scientific discovery in chemistry, yet its efficiency is often hampered by the sparse experimental data and vast search space. Here, we introduce ChemBOMAS: a large language model (LLM)-enhanced multi-agent system that accelerates BO through synergistic data- and knowledge-driven strategies. Firstly, the data-driven strategy involves an 8B-scale LLM regressor fine-tuned on a mere 1% labeled samples for pseudo-data generation, robustly initializing the optimization process. Secondly, the knowledge-driven strategy employs a hybrid Retrieval-Augmented Generation approach to guide LLM in dividing the search space while mitigating LLM hallucinations. An Upper Confidence Bound algorithm then identifies high-potential subspaces within this established partition. Across the LLM-refined subspaces and supported by LLM-generated data, BO achieves the improvement of effectiveness and efficiency. Comprehensive evaluations across multiple scientific benchmarks demonstrate that ChemBOMAS set a new state-of-the-art, accelerating optimization efficiency by up to 5-fold compared to baseline methods.", "date": "2025-09-10", "categories": []}
{"id": "2409.00979", "title": "Regret Analysis for Randomized Gaussian Process Upper Confidence Bound", "abstract": "Gaussian process upper confidence bound (GP-UCB) is a theoretically established algorithm for Bayesian optimization (BO), where we assume the objective function $f$ follows a GP. One notable drawback of GP-UCB is that the theoretical confidence parameter $\\beta$ increases along with the iterations and is too large. To alleviate this drawback, this paper analyzes the randomized variant of GP-UCB called improved randomized GP-UCB (IRGP-UCB), which uses the confidence parameter generated from the shifted exponential distribution. We analyze the expected regret and conditional expected regret, where the expectation and the probability are taken respectively with $f$ and noise and with the randomness of the BO algorithm. In both regret analyses, IRGP-UCB achieves a sub-linear regret upper bound without increasing the confidence parameter if the input domain is finite. Furthermore, we show that randomization plays a key role in avoiding an increase in confidence parameter by showing that GP-UCB using a constant confidence parameter can incur linearly growing expected cumulative regret. Finally, we show numerical experiments using synthetic and benchmark functions and real-world emulators.", "date": "2024-09-02", "categories": []}
{"id": "2511.05163", "title": "Consecutive Preferential Bayesian Optimization", "abstract": "Preferential Bayesian optimization allows optimization of objectives that are either expensive or difficult to measure directly, by relying on a minimal number of comparative evaluations done by a human expert. Generating candidate solutions for evaluation is also often expensive, but this cost is ignored by existing methods. We generalize preference-based optimization to explicitly account for production and evaluation costs with Consecutive Preferential Bayesian Optimization, reducing production cost by constraining comparisons to involve previously generated candidates. We also account for the perceptual ambiguity of the oracle providing the feedback by incorporating a Just-Noticeable Difference threshold into a probabilistic preference model to capture indifference to small utility differences. We adapt an information-theoretic acquisition strategy to this setting, selecting new configurations that are most informative about the unknown optimum under a preference model accounting for the perceptual ambiguity. We empirically demonstrate a notable increase in accuracy in setups with high production costs or with indifference feedback.", "date": "2025-11-07", "categories": []}
{"id": "2411.06184", "title": "Alleviating Hyperparameter-Tuning Burden in SVM Classifiers for Pulmonary Nodules Diagnosis with Multi-Task Bayesian Optimization", "abstract": "In the field of non-invasive medical imaging, radiomic features are utilized to measure tumor characteristics. However, these features can be affected by the techniques used to discretize the images, ultimately impacting the accuracy of diagnosis. To investigate the influence of various image discretization methods on diagnosis, it is common practice to evaluate multiple discretization strategies individually. This approach often leads to redundant and time-consuming tasks such as training predictive models and fine-tuning hyperparameters separately. This study examines the feasibility of employing multi-task Bayesian optimization to accelerate the hyperparameters search for classifying benign and malignant pulmonary nodules using RBF SVM. Our findings suggest that multi-task Bayesian optimization significantly accelerates the search for hyperparameters in comparison to a single-task approach. To the best of our knowledge, this is the first investigation to utilize multi-task Bayesian optimization in a critical medical context.", "date": "2024-11-09", "categories": []}
{"id": "2511.00750", "title": "Trust Region-Based Bayesian Optimisation to Discover Diverse Solutions", "abstract": "Bayesian optimisation (BO) is a surrogate-based optimisation technique that efficiently solves expensive black-box functions with small evaluation budgets. Recent studies consider trust regions to improve the scalability of BO approaches when the problem space scales to more dimensions. Motivated by this research, we explore the effectiveness of trust region-based BO algorithms for diversity optimisation in different dimensional black box problems. We propose diversity optimisation approaches extending TuRBO1, which is the first BO method that uses a trust region-based approach for scalability. We extend TuRBO1 as divTuRBO1, which finds an optimal solution while maintaining a given distance threshold relative to a reference solution set. We propose two approaches to find diverse solutions for black-box functions by combining divTuRBO1 runs in a sequential and an interleaving fashion. We conduct experimental investigations on the proposed algorithms and compare their performance with that of the baseline method, ROBOT (rank-ordered Bayesian optimisation with trust regions). We evaluate proposed algorithms on benchmark functions with dimensions 2 to 20. Experimental investigations demonstrate that the proposed methods perform well, particularly in larger dimensions, even with a limited evaluation budget.", "date": "2025-11-02", "categories": []}
{"id": "2511.01006", "title": "None To Optima in Few Shots: Bayesian Optimization with MDP Priors", "abstract": "Bayesian Optimization (BO) is an efficient tool for optimizing black-box functions, but its theoretical guarantees typically hold in the asymptotic regime. In many critical real-world applications such as drug discovery or materials design, where each evaluation can be very costly and time-consuming, BO becomes impractical for many evaluations. In this paper, we introduce the Procedure-inFormed BO (ProfBO) algorithm, which solves black-box optimization with remarkably few function evaluations. At the heart of our algorithmic design are Markov Decision Process (MDP) priors that model optimization trajectories from related source tasks, thereby capturing procedural knowledge on efficient optimization. We embed these MDP priors into a prior-fitted neural network and employ model-agnostic meta-learning for fast adaptation to new target tasks. Experiments on real-world Covid and Cancer benchmarks and hyperparameter tuning tasks demonstrate that ProfBO consistently outperforms state-of-the-art methods by achieving high-quality solutions with significantly fewer evaluations, making it ready for practical deployment.", "date": "2025-11-02", "categories": []}
{"id": "2510.26633", "title": "Omnipresent Yet Overlooked: Heat Kernels in Combinatorial Bayesian Optimization", "abstract": "Bayesian Optimization (BO) has the potential to solve various combinatorial tasks, ranging from materials science to neural architecture search. However, BO requires specialized kernels to effectively model combinatorial domains. Recent efforts have introduced several combinatorial kernels, but the relationships among them are not well understood. To bridge this gap, we develop a unifying framework based on heat kernels, which we derive in a systematic way and express as simple closed-form expressions. Using this framework, we prove that many successful combinatorial kernels are either related or equivalent to heat kernels, and validate this theoretical claim in our experiments. Moreover, our analysis confirms and extends the results presented in Bounce: certain algorithms' performance decreases substantially when the unknown optima of the function do not have a certain structure. In contrast, heat kernels are not sensitive to the location of the optima. Lastly, we show that a fast and simple pipeline, relying on heat kernels, is able to achieve state-of-the-art results, matching or even outperforming certain slow or complex algorithms.", "date": "2025-10-30", "categories": []}
{"id": "2510.22734", "title": "Centrum: Model-based Database Auto-tuning with Minimal Distributional Assumptions", "abstract": "Gaussian-Process-based Bayesian optimization (GP-BO), is a prevailing model-based framework for DBMS auto-tuning. However, recent work shows GP-BO-based DBMS auto-tuners significantly outperformed auto-tuners based on SMAC, which features random forest surrogate models; such results motivate us to rethink and investigate the limitations of GP-BO in auto-tuner design. We find the fundamental assumptions of GP-BO are widely violated when modeling and optimizing DBMS performance, while tree-ensemble-BOs (e.g., SMAC) can avoid the assumption pitfalls and deliver improved tuning efficiency and effectiveness. Moreover, we argue that existing tree-ensemble-BOs restrict further advancement in DBMS auto-tuning. First, existing tree-ensemble-BOs can only achieve distribution-free point estimates, but still impose unrealistic distributional assumptions on uncertainty estimates, compromising surrogate modeling and distort the acquisition function. Second, recent advances in gradient boosting, which can further enhance surrogate modeling against vanilla GP and random forest counterparts, have rarely been applied in optimizing DBMS auto-tuners. To address these issues, we propose a novel model-based DBMS auto-tuner, Centrum. Centrum improves distribution-free point and interval estimation in surrogate modeling with a two-phase learning procedure of stochastic gradient boosting ensembles. Moreover, Centrum adopts a generalized SGBE-estimated locally-adaptive conformal prediction to facilitate a distribution-free uncertainty estimation and acquisition function. To our knowledge, Centrum is the first auto-tuner to realize distribution-freeness, enhancing BO's practicality in DBMS auto-tuning, and the first to seamlessly fuse gradient boosting ensembles and conformal inference in BO. Extensive physical and simulation experiments on two DBMSs and three workloads show Centrum outperforms 21 SOTA methods.", "date": "2025-10-26", "categories": []}
{"id": "2510.20872", "title": "MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directions", "abstract": "Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains challenging. In this paper, we propose MOBO-OSD, a multi-objective Bayesian Optimization algorithm designed to generate a diverse set of Pareto optimal solutions by solving multiple constrained optimization problems, referred to as MOBO-OSD subproblems, along orthogonal search directions (OSDs) defined with respect to an approximated convex hull of individual objective minima. By employing a well-distributed set of OSDs, MOBO-OSD ensures broad coverage of the objective space, enhancing both solution diversity and hypervolume performance. To further improve the density of the set of Pareto optimal candidate solutions without requiring an excessive number of subproblems, we leverage a Pareto Front Estimation technique to generate additional solutions in the neighborhood of existing solutions. Additionally, MOBO-OSD supports batch optimization, enabling parallel function evaluations to accelerate the optimization process when resources are available. Through extensive experiments and analysis on a variety of synthetic and real-world benchmark functions with two to six objectives, we demonstrate that MOBO-OSD consistently outperforms the state-of-the-art algorithms. Our code implementation can be found at https://github.com/LamNgo1/mobo-osd.", "date": "2025-10-23", "categories": []}
{"id": "2507.22766", "title": "Bayesian Optimization of Process Parameters of a Sensor-Based Sorting System using Gaussian Processes as Surrogate Models", "abstract": "Sensor-based sorting systems enable the physical separation of a material stream into two fractions. The sorting decision is based on the image data evaluation of the sensors used and is carried out using actuators. Various process parameters must be set depending on the properties of the material stream, the dimensioning of the system, and the required sorting accuracy. However, continuous verification and re-adjustment are necessary due to changing requirements and material stream compositions. In this paper, we introduce an approach for optimizing, recurrently monitoring and adjusting the process parameters of a sensor-based sorting system. Based on Bayesian Optimization, Gaussian process regression models are used as surrogate models to achieve specific requirements for system behavior with the uncertainties contained therein. This method minimizes the number of necessary experiments while simultaneously considering two possible optimization targets based on the requirements for both material output streams. In addition, uncertainties are considered during determining sorting accuracies in the model calculation. We evaluated the method with three example process parameters.", "date": "2025-07-30", "categories": []}
{"id": "2510.19530", "title": "Optimizing the Unknown: Black Box Bayesian Optimization with Energy-Based Model and Reinforcement Learning", "abstract": "Existing Bayesian Optimization (BO) methods typically balance exploration and exploitation to optimize costly objective functions. However, these methods often suffer from a significant one-step bias, which may lead to convergence towards local optima and poor performance in complex or high-dimensional tasks. Recently, Black-Box Optimization (BBO) has achieved success across various scientific and engineering domains, particularly when function evaluations are costly and gradients are unavailable. Motivated by this, we propose the Reinforced Energy-Based Model for Bayesian Optimization (REBMBO), which integrates Gaussian Processes (GP) for local guidance with an Energy-Based Model (EBM) to capture global structural information. Notably, we define each Bayesian Optimization iteration as a Markov Decision Process (MDP) and use Proximal Policy Optimization (PPO) for adaptive multi-step lookahead, dynamically adjusting the depth and direction of exploration to effectively overcome the limitations of traditional BO methods. We conduct extensive experiments on synthetic and real-world benchmarks, confirming the superior performance of REBMBO. Additional analyses across various GP configurations further highlight its adaptability and robustness.", "date": "2025-10-22", "categories": []}
{"id": "2409.01163", "title": "PACSBO: Probably approximately correct safe Bayesian optimization", "abstract": "Safe Bayesian optimization (BO) algorithms promise to find optimal control policies without knowing the system dynamics while at the same time guaranteeing safety with high probability. In exchange for those guarantees, popular algorithms require a smoothness assumption: a known upper bound on a norm in a reproducing kernel Hilbert space (RKHS). The RKHS is a potentially infinite-dimensional space, and it is unclear how to, in practice, obtain an upper bound of an unknown function in its corresponding RKHS. In response, we propose an algorithm that estimates an upper bound on the RKHS norm of an unknown function from data and investigate its theoretical properties. Moreover, akin to Lipschitz-based methods, we treat the RKHS norm as a local rather than a global object, and thus reduce conservatism. Integrating the RKHS norm estimation and the local interpretation of the RKHS norm into a safe BO algorithm yields PACSBO, an algorithm for probably approximately correct safe Bayesian optimization, for which we provide numerical and hardware experiments that demonstrate its applicability and benefits over popular safe BO algorithms.", "date": "2024-09-02", "categories": []}
{"id": "2510.18824", "title": "BO4Mob: Bayesian Optimization Benchmarks for High-Dimensional Urban Mobility Problem", "abstract": "We introduce \\textbf{BO4Mob}, a new benchmark framework for high-dimensional Bayesian Optimization (BO), driven by the challenge of origin-destination (OD) travel demand estimation in large urban road networks. Estimating OD travel demand from limited traffic sensor data is a difficult inverse optimization problem, particularly in real-world, large-scale transportation networks. This problem involves optimizing over high-dimensional continuous spaces where each objective evaluation is computationally expensive, stochastic, and non-differentiable. BO4Mob comprises five scenarios based on real-world San Jose, CA road networks, with input dimensions scaling up to 10,100. These scenarios utilize high-resolution, open-source traffic simulations that incorporate realistic nonlinear and stochastic dynamics. We demonstrate the benchmark's utility by evaluating five optimization methods: three state-of-the-art BO algorithms and two non-BO baselines. This benchmark is designed to support both the development of scalable optimization algorithms and their application for the design of data-driven urban mobility models, including high-resolution digital twins of metropolitan road networks. Code and documentation are available at https://github.com/UMN-Choi-Lab/BO4Mob.", "date": "2025-10-21", "categories": []}
{"id": "2501.18963", "title": "Time-Varying Bayesian Optimization Without a Metronome", "abstract": "Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying, expensive, noisy black-box function $f$. However, most of the asymptotic guarantees offered by TVBO algorithms rely on the assumption that observations are acquired at a constant frequency. As the GP inference complexity scales with the cube of its dataset size, this assumption is unrealistic in the long run. In this paper, we relax this assumption and derive the first upper regret bound that explicitly accounts for changes in the observations sampling frequency. Based on this analysis, we formulate practical recommendations about dataset sizes and stale data policies of TVBO algorithms. We illustrate how an algorithm (BOLT) that follows these recommendations performs better than the state-of-the-art of TVBO through experiments on synthetic and real-world problems.", "date": "2025-01-31", "categories": []}
{"id": "2505.13012", "title": "Asymptotic Performance of Time-Varying Bayesian Optimization", "abstract": "Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying black-box objective function that may be noisy and expensive to evaluate, but its excellent empirical performance remains to be understood theoretically. Is it possible for the instantaneous regret of a TVBO algorithm to vanish asymptotically, and if so, when? We answer this question of great importance by providing upper bounds and algorithm-independent lower bounds for the cumulative regret of TVBO algorithms. In doing so, we provide important insights about the TVBO framework and derive sufficient conditions for a TVBO algorithm to have the no-regret property. To the best of our knowledge, our analysis is the first to cover all major classes of stationary kernel functions used in practice.", "date": "2025-05-19", "categories": []}
{"id": "2510.16652", "title": "ARCO-BO: Adaptive Resource-aware COllaborative Bayesian Optimization for Heterogeneous Multi-Agent Design", "abstract": "Modern scientific and engineering design increasingly involves distributed optimization, where agents such as laboratories, simulations, or industrial partners pursue related goals under differing conditions. These agents often face heterogeneities in objectives, evaluation budgets, and accessible design variables, which complicates coordination and can lead to redundancy, poor resource use, and ineffective information sharing. Bayesian Optimization (BO) is a widely used decision-making framework for expensive black box functions, but its single-agent formulation assumes centralized control and full data sharing. Recent collaborative BO methods relax these assumptions, yet they often require uniform resources, fully shared input spaces, and fixed task alignment, conditions rarely satisfied in practice. To address these challenges, we introduce Adaptive Resource Aware Collaborative Bayesian Optimization (ARCO-BO), a framework that explicitly accounts for heterogeneity in multi-agent optimization. ARCO-BO combines three components: a similarity and optima-aware consensus mechanism for adaptive information sharing, a budget-aware asynchronous sampling strategy for resource coordination, and a partial input space sharing for heterogeneous design spaces. Experiments on synthetic and high-dimensional engineering problems show that ARCO-BO consistently outperforms independent BO and existing collaborative BO via consensus approach, achieving robust and efficient performance in complex multi-agent settings.", "date": "2025-10-18", "categories": []}
{"id": "2510.15260", "title": "DRO-InstructZero: Distributionally Robust Prompt Optimization for Large Language Models", "abstract": "Large language models are highly sensitive to prompt wording. However, popular automatic prompt search methods, including InstructZero, often degrade under distribution shift and adversarial evaluation because they optimize expected performance under a single evaluation distribution. Consequently, prompts that work in one setting frequently fail to transfer. To address this, DRO-InstructZero formulates zero-shot prompt optimization as robust Bayesian optimization. Specifically, an f-divergence ball defines an ambiguity set around the evaluation distribution, and a robust acquisition rule maximizes worst-case expected utility while retaining the query efficiency of Bayesian search. Therefore, the search explicitly targets reliability under distribution shift rather than average behavior alone. Experiments follow the instruction-induction protocol with matched query budgets across formality rewriting, code debugging, and translation. For example, on BIG-Bench informative-to-formal rewriting, accuracy improves from 61.3 +/- 0.7% to approximately 85-90%, yielding an absolute gain of about 25-30 points. Moreover, auto-debugging shows about +25-point gains under domain shift. Meanwhile, stable tasks such as cause-and-effect remain above 96%, indicating no loss on in-distribution cases. Furthermore, improvements are consistent across divergence choices and decoding temperatures. Overall, DRO-InstructZero connects distributionally robust optimization with prompt learning, offering a plug-and-play and general approach for reliable, transferable prompt alignment under real-world uncertainty.", "date": "2025-10-17", "categories": []}
{"id": "2510.15435", "title": "Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization", "abstract": "Bayesian optimisation (BO) is a standard approach for sample-efficient global optimisation of expensive black-box functions, yet its scalability to high dimensions remains challenging. Here, we investigate nonlinear dimensionality reduction techniques that reduce the problem to a sequence of low-dimensional Latent-Space BO (LSBO). While early LSBO methods used (linear) random projections (Wang et al., 2013), building on Grosnit et al. (2021), we employ Variational Autoencoders (VAEs) for LSBO, focusing on deep metric loss for structured latent manifolds and VAE retraining to adapt the encoder-decoder to newly sampled regions. We propose some changes in their implementation, originally designed for tasks such as molecule generation, and reformulate the algorithm for broader optimisation purposes. We then couple LSBO with Sequential Domain Reduction (SDR) directly in the latent space (SDR-LSBO), yielding an algorithm that narrows the latent search domains as evidence accumulates. Implemented in a GPU-accelerated BoTorch stack with Matern-5/2 Gaussian process surrogates, our numerical results show improved optimisation quality across benchmark tasks and that structured latent manifolds improve BO performance. Additionally, we compare random embeddings and VAEs as two mechanisms for dimensionality reduction, showing that the latter outperforms the former. To the best of our knowledge, this is the first study to combine SDR with VAE-based LSBO, and our analysis clarifies design choices for metric shaping and retraining that are critical for scalable latent space BO. For reproducibility, our source code is available at https://github.com/L-Lok/Nonlinear-Dimensionality-Reduction-Techniques-for-Bayesian-Optimization.git.", "date": "2025-10-17", "categories": []}
{"id": "2510.04384", "title": "LLM Based Bayesian Optimization for Prompt Search", "abstract": "Bayesian Optimization (BO) has been widely used to efficiently optimize expensive black-box functions with limited evaluations. In this paper, we investigate the use of BO for prompt engineering to enhance text classification with Large Language Models (LLMs). We employ an LLM-powered Gaussian Process (GP) as the surrogate model to estimate the performance of different prompt candidates. These candidates are generated by an LLM through the expansion of a set of seed prompts and are subsequently evaluated using an Upper Confidence Bound (UCB) acquisition function in conjunction with the GP posterior. The optimization process iteratively refines the prompts based on a subset of the data, aiming to improve classification accuracy while reducing the number of API calls by leveraging the prediction uncertainty of the LLM-based GP. The proposed BO-LLM algorithm is evaluated on two datasets, and its advantages are discussed in detail in this paper.", "date": "2025-10-05", "categories": []}
{"id": "2510.11792", "title": "On Thompson Sampling and Bilateral Uncertainty in Additive Bayesian Optimization", "abstract": "In Bayesian Optimization (BO), additive assumptions can mitigate the twin difficulties of modeling and searching a complex function in high dimension. However, common acquisition functions, like the Additive Lower Confidence Bound, ignore pairwise covariances between dimensions, which we'll call \\textit{bilateral uncertainty} (BU), imposing a second layer of approximations. While theoretical results indicate that asymptotically not much is lost in doing so, little is known about the practical effects of this assumption in small budgets. In this article, we show that by exploiting conditional independence, Thompson Sampling respecting BU can be efficiently conducted. We use this fact to execute an empirical investigation into the loss incurred by ignoring BU, finding that the additive approximation to Thompson Sampling does indeed have, on balance, worse performance than the exact method, but that this difference is of little practical significance. This buttresses the theoretical understanding and suggests that the BU-ignoring approximation is sufficient for BO in practice, even in the non-asymptotic regime.", "date": "2025-10-13", "categories": []}
{"id": "2510.12447", "title": "Bayesian Optimization for Dynamic Pricing and Learning", "abstract": "Dynamic pricing is the practice of adjusting the selling price of a product to maximize a firm's revenue by responding to market demand. The literature typically distinguishes between two settings: infinite inventory, where the firm has unlimited stock and time to sell, and finite inventory, where both inventory and selling horizon are limited. In both cases, the central challenge lies in the fact that the demand function -- how sales respond to price -- is unknown and must be learned from data. Traditional approaches often assume a specific parametric form for the demand function, enabling the use of reinforcement learning (RL) to identify near-optimal pricing strategies. However, such assumptions may not hold in real-world scenarios, limiting the applicability of these methods. In this work, we propose a Gaussian Process (GP) based nonparametric approach to dynamic pricing that avoids restrictive modeling assumptions. We treat the demand function as a black-box function of the price and develop pricing algorithms based on Bayesian Optimization (BO) -- a sample-efficient method for optimizing unknown functions. We present BO-based algorithms tailored for both infinite and finite inventory settings and provide regret guarantees for both regimes, thereby quantifying the learning efficiency of our methods. Through extensive experiments, we demonstrate that our BO-based methods outperform several state-of-the-art RL algorithms in terms of revenue, while requiring fewer assumptions and offering greater robustness. This highlights Bayesian Optimization as a powerful and practical tool for dynamic pricing in complex, uncertain environments.", "date": "2025-10-14", "categories": []}
{"id": "2504.07742", "title": "Gradient-based Sample Selection for Faster Bayesian Optimization", "abstract": "Bayesian optimization (BO) is an effective technique for black-box optimization. However, its applicability is typically limited to moderate-budget problems due to the cubic complexity of fitting the Gaussian process (GP) surrogate model. In large-budget scenarios, directly employing the standard GP model faces significant challenges in computational time and resource requirements. In this paper, we propose a novel approach, gradient-based sample selection Bayesian Optimization (GSSBO), to enhance the computational efficiency of BO. The GP model is constructed on a selected set of samples instead of the whole dataset. These samples are selected by leveraging gradient information to remove redundancy while preserving diversity and representativeness. We provide a theoretical analysis of the gradient-based sample selection strategy and obtain explicit sublinear regret bounds for our proposed framework. Extensive experiments on synthetic and real-world tasks demonstrate that our approach significantly reduces the computational cost of GP fitting in BO while maintaining optimization performance comparable to baseline methods.", "date": "2025-04-10", "categories": []}
{"id": "2510.08965", "title": "HiBBO: HiPPO-based Space Consistency for High-dimensional Bayesian Optimisation", "abstract": "Bayesian Optimisation (BO) is a powerful tool for optimising expensive blackbox functions but its effectiveness diminishes in highdimensional spaces due to sparse data and poor surrogate model scalability While Variational Autoencoder (VAE) based approaches address this by learning low-dimensional latent representations the reconstructionbased objective function often brings the functional distribution mismatch between the latent space and original space leading to suboptimal optimisation performance In this paper we first analyse the reason why reconstructiononly loss may lead to distribution mismatch and then propose HiBBO a novel BO framework that introduces the space consistency into the latent space construction in VAE using HiPPO - a method for longterm sequence modelling - to reduce the functional distribution mismatch between the latent space and original space Experiments on highdimensional benchmark tasks demonstrate that HiBBO outperforms existing VAEBO methods in convergence speed and solution quality Our work bridges the gap between high-dimensional sequence representation learning and efficient Bayesian Optimisation enabling broader applications in neural architecture search materials science and beyond.", "date": "2025-10-10", "categories": []}
{"id": "2410.10190", "title": "Language Model Embeddings Can Be Sufficient for Bayesian Optimization", "abstract": "Bayesian Optimization is ubiquitous in experimental design and black-box optimization for improving search efficiency. However, most existing approaches rely on regression models which are limited to fixed search spaces and structured, tabular input features. This paper explores the use of LLM embeddings over string inputs for in-context regression in Bayesian Optimization. Our results show that representing inputs as strings enables general-purpose regression across diverse domains, including synthetic, combinatorial, and hyperparameter optimization. Furthermore, our approach achieves optimization performance comparable to state-of-the-art Gaussian Process-based methods such as Google Vizier, and demonstrates potential for broader and more flexible applications.", "date": "2024-10-14", "categories": []}
{"id": "2505.14756", "title": "LLINBO: Trustworthy LLM-in-the-Loop Bayesian Optimization", "abstract": "Bayesian optimization (BO) is a sequential decision-making tool widely used for optimizing expensive black-box functions. Recently, Large Language Models (LLMs) have shown remarkable adaptability in low-data regimes, making them promising tools for black-box optimization by leveraging contextual knowledge to propose high-quality query points. However, relying solely on LLMs as optimization agents introduces risks due to their lack of explicit surrogate modeling and calibrated uncertainty, as well as their inherently opaque internal mechanisms. This structural opacity makes it difficult to characterize or control the exploration-exploitation trade-off, ultimately undermining theoretical tractability and reliability. To address this, we propose LLINBO: LLM-in-the-Loop BO, a hybrid framework for BO that combines LLMs with statistical surrogate experts (e.g., Gaussian Processes (GP)). The core philosophy is to leverage contextual reasoning strengths of LLMs for early exploration, while relying on principled statistical models to guide efficient exploitation. Specifically, we introduce three mechanisms that enable this collaboration and establish their theoretical guarantees. We end the paper with a real-life proof-of-concept in the context of 3D printing. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/LLM-in-the-Loop-BO.", "date": "2025-05-20", "categories": []}
{"id": "2506.11898", "title": "Martingale Posterior Neural Networks for Fast Sequential Decision Making", "abstract": "We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model parameters, our methods adopt a predictive-first perspective based on martingale posteriors. In particular, we work directly with the one-step-ahead posterior predictive, which we parameterize with a neural network and update sequentially with incoming observations. This decouples Bayesian decision-making from parameter-space inference: we sample from the posterior predictive for decision making, and update the parameters of the posterior predictive via fast, frequentist Kalman-filter-like recursions. Our algorithms operate in a fully online, replay-free setting, providing principled uncertainty quantification without costly posterior sampling. Empirically, they achieve competitive performance-speed trade-offs in non-stationary contextual bandits and Bayesian optimization, offering 10-100 times faster inference than classical Thompson sampling while maintaining comparable or superior decision performance.", "date": "2025-06-13", "categories": []}
{"id": "2509.07030", "title": "A Minimalist Bayesian Framework for Stochastic Optimization", "abstract": "The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the component of interest, such as the location of the optimum. Nuisance parameters are eliminated via profile likelihood, which naturally handles constraints. As a direct instantiation, we develop a MINimalist Thompson Sampling (MINTS) algorithm. Our framework accommodates structured problems, including continuum-armed Lipschitz bandits and dynamic pricing. It also provides a probabilistic lens on classical convex optimization algorithms such as the center of gravity and ellipsoid methods. We further analyze MINTS for multi-armed bandits and establish near-optimal regret guarantees.", "date": "2025-09-07", "categories": []}
{"id": "2510.06439", "title": "Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models", "abstract": "Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel Bayesian optimization framework tailored for hyperparameter tuning under uncertainty, with a focus on optimizing a scale- or precision-type parameter in stochastic models. The proposed method employs a statistical surrogate for the underlying random variable, enabling analytical evaluation of the expectation operator. Moreover, we derive a closed-form expression for the optimizer of the random acquisition function, which significantly reduces computational cost per iteration. Compared with a conventional one-dimensional Monte Carlo-based optimization scheme, the proposed approach requires 40 times fewer data points, resulting in up to a 40-fold reduction in computational cost. We demonstrate the effectiveness of the proposed method through two numerical examples in computational engineering.", "date": "2025-10-07", "categories": []}
{"id": "2510.03277", "title": "Quantile-Scaled Bayesian Optimization Using Rank-Only Feedback", "abstract": "Bayesian Optimization (BO) is widely used for optimizing expensive black-box functions, particularly in hyperparameter tuning. However, standard BO assumes access to precise objective values, which may be unavailable, noisy, or unreliable in real-world settings where only relative or rank-based feedback can be obtained. In this study, we propose Quantile-Scaled Bayesian Optimization (QS-BO), a principled rank-based optimization framework. QS-BO converts ranks into heteroscedastic Gaussian targets through a quantile-scaling pipeline, enabling the use of Gaussian process surrogates and standard acquisition functions without requiring explicit metric scores. We evaluate QS-BO on synthetic benchmark functions, including one- and two-dimensional nonlinear functions and the Branin function, and compare its performance against Random Search. Results demonstrate that QS-BO consistently achieves lower objective values and exhibits greater stability across runs. Statistical tests further confirm that QS-BO significantly outperforms Random Search at the 1\\% significance level. These findings establish QS-BO as a practical and effective extension of Bayesian Optimization for rank-only feedback, with promising applications in preference learning, recommendation, and human-in-the-loop optimization where absolute metric values are unavailable or unreliable.", "date": "2025-09-28", "categories": []}
{"id": "2510.03893", "title": "BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty", "abstract": "Optimal design under uncertainty remains a fundamental challenge in advancing reliable, next-generation process systems. Robust optimization (RO) offers a principled approach by safeguarding against worst-case scenarios across a range of uncertain parameters. However, traditional RO methods typically require known problem structure, which limits their applicability to high-fidelity simulation environments. To overcome these limitations, recent work has explored robust Bayesian optimization (RBO) as a flexible alternative that can accommodate expensive, black-box objectives. Existing RBO methods, however, generally ignore available structural information and struggle to scale to high-dimensional settings. In this work, we introduce BONSAI (Bayesian Optimization of Network Systems under uncertAInty), a new RBO framework that leverages partial structural knowledge commonly available in simulation-based models. Instead of treating the objective as a monolithic black box, BONSAI represents it as a directed graph of interconnected white- and black-box components, allowing the algorithm to utilize intermediate information within the optimization process. We further propose a scalable Thompson sampling-based acquisition function tailored to the structured RO setting, which can be efficiently optimized using gradient-based methods. We evaluate BONSAI across a diverse set of synthetic and real-world case studies, including applications in process systems engineering. Compared to existing simulation-based RO algorithms, BONSAI consistently delivers more sample-efficient and higher-quality robust solutions, highlighting its practical advantages for uncertainty-aware design in complex engineering systems.", "date": "2025-10-04", "categories": []}
{"id": "2510.01471", "title": "Fine-tuning LLMs with variational Bayesian last layer for high-dimensional Bayesian optimization", "abstract": "A plethora of applications entail solving black-box optimization problems with high evaluation costs, including drug discovery, material design, as well as hyperparameter tuning. Toward finding the global optimum of such black-box optimization problems with sample efficiency, Bayesian optimization (BO) is a theoretically elegant framework that relies on a probabilistic surrogate model so as to iteratively select the query point with well-balanced exploration-exploitation tradeoffs. The Gaussian process (GP), as the de-facto choice for surrogate modeling, has achieved compelling performances for vanilla BO with low-dimensional continuous variables. However, GPs fall short in coping with high-dimensional counterparts with {\\it irregular} variables (e.g., categorical, ordinal, etc.). To alleviate this, neural network-based surrogates have been explored. Inspired by the powerful capabilities of LLMs, we adopt the LLM as the surrogate to model the mapping from the high-dimensional input variables to the objective function. To adapt to the current problem, we leverage the low-rank adaptation (LoRA) to fine-tune the LLM parameters together with the posterior of a linear regression head via the variational Bayesian last layer (VBLL) framework. The resulting LoRA-VBLL is not only computationally light compared to existing alternatives, but also admits recursive updates. To automate the critical selection of the LoRA rank as well as other hyperparameters, a weighted ensemble (ENS) of LoRA-VBLL surrogates has been devised, which further accommodates continual update of the per-model weight and individual LoRA-VBLL parameters via recursive Bayes. Extensive experimental results demonstrate the compelling performance of the proposed (ENS-)LoRA-VBLL approaches on various high-dimensional benchmarks and the real-world molecular optimization tasks.", "date": "2025-10-01", "categories": []}
{"id": "2208.10300", "title": "Efficient Contextual Preferential Bayesian Optimization with Historical Examples", "abstract": "State-of-the-art multi-objective optimization often assumes a known utility function, learns it interactively, or computes the full Pareto front-each requiring costly expert input.~Real-world problems, however, involve implicit preferences that are hard to formalize. To reduce expert involvement, we propose an offline, interpretable utility learning method that uses expert knowledge, historical examples, and coarse information about the utility space to reduce sample requirements. We model uncertainty via a full Bayesian posterior and propagate it throughout the optimization process. Our method outperforms standard Gaussian processes and BOPE across four domains, showing strong performance even with biased samples, as encountered in the real-world, and limited expert input.", "date": "2022-08-22", "categories": []}
{"id": "2507.09828", "title": "Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimization", "abstract": "Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical analyses of EI are limited compared with other theoretically established algorithms. This paper analyzes a randomized variant of EI, which evaluates the EI from the maximum of the posterior sample path. We show that this posterior sampling-based random EI achieves the sublinear Bayesian cumulative regret bounds under the assumption that the black-box function follows a Gaussian process. Finally, we demonstrate the effectiveness of the proposed method through numerical experiments.", "date": "2025-07-13", "categories": []}
{"id": "2509.22677", "title": "Profit over Proxies: A Scalable Bayesian Decision Framework for Optimizing Multi-Variant Online Experiments", "abstract": "Online controlled experiments (A/B tests) are fundamental to data-driven decision-making in the digital economy. However, their real-world application is frequently compromised by two critical shortcomings: the use of statistically flawed heuristics like \"p-value peeking\", which inflates false positive rates, and an over-reliance on proxy metrics like conversion rates, which can lead to decisions that inadvertently harm core business profitability. This paper addresses these challenges by introducing a comprehensive and scalable Bayesian decision framework designed for profit optimization in multi-variant (A/B/n) experiments.\n  We propose a hierarchical Bayesian model that simultaneously estimates the probability of conversion (using a Beta-Bernoulli model) and the monetary value of that conversion (using a robust Bayesian model for the mean transaction value). Building on this, we employ a decision-theoretic stopping rule based on Expected Loss, enabling experiments to be concluded not only when a superior variant is identified but also when it becomes clear that no variant offers a practically significant improvement (stopping for futility). The framework successfully navigates \"revenue traps\" where a variant with a higher conversion rate would have resulted in a net financial loss, correctly terminates futile experiments early to conserve resources, and maintains strict statistical integrity throughout the monitoring process.\n  Ultimately, this work provides a practical and principled methodology for organizations to move beyond simple A/B testing towards a mature, profit-driven experimentation culture, ensuring that statistical conclusions translate directly to strategic business value.", "date": "2025-09-16", "categories": []}
{"id": "2509.25051", "title": "Symmetry-Aware Bayesian Optimization via Max Kernels", "abstract": "Bayesian Optimization (BO) is a powerful framework for optimizing noisy, expensive-to-evaluate black-box functions. When the objective exhibits invariances under a group action, exploiting these symmetries can substantially improve BO efficiency. While using maximum similarity across group orbits has long been considered in other domains, the fact that the max kernel is not positive semidefinite (PSD) has prevented its use in BO. In this work, we revisit this idea by considering a PSD projection of the max kernel. Compared to existing invariant (and non-invariant) kernels, we show it achieves significantly lower regret on both synthetic and real-world BO benchmarks, without increasing computational complexity.", "date": "2025-09-29", "categories": []}
{"id": "2411.01423", "title": "Conditional Latent Space Molecular Scaffold Optimization for Accelerated Molecular Design", "abstract": "The rapid discovery of new chemical compounds is essential for advancing global health and developing treatments. While generative models show promise in creating novel molecules, challenges remain in ensuring the real-world applicability of these molecules and finding such molecules efficiently. To address this challenge, we introduce Conditional Latent Space Molecular Scaffold Optimization (CLaSMO), which integrates a Conditional Variational Autoencoder (CVAE) with Latent Space Bayesian Optimization (LSBO) to strategically modify molecules while preserving similarity to the original input, effectively framing the task as constrained optimization. Our LSBO setting improves the sample-efficiency of the molecular optimization, and our modification approach helps us to obtain molecules with higher chances of real-world applicability. CLaSMO explores substructures of molecules in a sample-efficient manner by performing BO in the latent space of a CVAE conditioned on the atomic environment of the molecule to be optimized. Our extensive evaluations across diverse optimization tasks, including rediscovery, docking score, and multi-property optimization, show that CLaSMO efficiently enhances target properties, delivers remarkable sample-efficiency crucial for resource-limited applications while considering molecular similarity constraints, achieves state of the art performance, and maintains practical synthetic accessibility. We also provide an open-source web application that enables chemical experts to apply CLaSMO in a Human-in-the-Loop setting.", "date": "2024-11-03", "categories": []}
{"id": "2505.12833", "title": "Reasoning BO: Enhancing Bayesian Optimization with Long-Context Reasoning Power of LLMs", "abstract": "Many real-world scientific and industrial applications require the optimization of expensive black-box functions. Bayesian Optimization (BO) provides an effective framework for such problems. However, traditional BO methods are prone to get trapped in local optima and often lack interpretable insights. To address this issue, this paper designs Reasoning BO, a novel framework that leverages reasoning models to guide the sampling process in BO while incorporating multi-agent systems and knowledge graphs for online knowledge accumulation. By integrating the reasoning and contextual understanding capabilities of Large Language Models (LLMs), we can provide strong guidance to enhance the BO process. As the optimization progresses, Reasoning BO provides real-time sampling recommendations along with critical insights grounded in plausible scientific theories, aiding in the discovery of superior solutions within the search space. We systematically evaluate our approach across 10 diverse tasks encompassing synthetic mathematical functions and complex real-world applications. The framework demonstrates its capability to progressively refine sampling strategies through real-time insights and hypothesis evolution, effectively identifying higher-performing regions of the search space for focused exploration. This process highlights the powerful reasoning and context-learning abilities of LLMs in optimization scenarios. For example, in the Direct Arylation task, our method increased the yield to 60.7%, whereas traditional BO achieved only a 25.2% yield. Furthermore, our investigation reveals that smaller LLMs, when fine-tuned through reinforcement learning, can attain comparable performance to their larger counterparts.", "date": "2025-05-19", "categories": []}
{"id": "2509.21403", "title": "LLMs for Bayesian Optimization in Scientific Domains: Are We There Yet?", "abstract": "Large language models (LLMs) have recently been proposed as general-purpose agents for experimental design, with claims that they can perform in-context experimental design. We evaluate this hypothesis using both open- and closed-source instruction-tuned LLMs applied to genetic perturbation and molecular property discovery tasks. We find that LLM-based agents show no sensitivity to experimental feedback: replacing true outcomes with randomly permuted labels has no impact on performance. Across benchmarks, classical methods such as linear bandits and Gaussian process optimization consistently outperform LLM agents. We further propose a simple hybrid method, LLM-guided Nearest Neighbour (LLMNN) sampling, that combines LLM prior knowledge with nearest-neighbor sampling to guide the design of experiments. LLMNN achieves competitive or superior performance across domains without requiring significant in-context adaptation. These results suggest that current open- and closed-source LLMs do not perform in-context experimental design in practice and highlight the need for hybrid frameworks that decouple prior-based reasoning from batch acquisition with updated posteriors.", "date": "2025-09-24", "categories": []}
{"id": "2411.04744", "title": "Respecting the limit:Bayesian optimization with a bound on the optimal value", "abstract": "In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact, lower bound on its value. We propose bound-aware Bayesian optimization (BABO), a Bayesian optimization method that uses a new surrogate model and acquisition function to utilize such prior information. We present SlogGP, a new surrogate model that incorporates bound information and adapts the Expected Improvement (EI) acquisition function accordingly. Empirical results on a variety of benchmarks demonstrate the benefit of taking prior information about the optimal value into account, and that the proposed approach significantly outperforms existing techniques. Furthermore, we notice that even in the absence of prior information on the bound, the proposed SlogGP surrogate model still performs better than the standard GP model in most cases, which we explain by its larger expressiveness.", "date": "2024-11-07", "categories": []}
{"id": "2509.17998", "title": "Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMs", "abstract": "The efficiency of Bayesian optimization (BO) relies heavily on the choice of the Gaussian process (GP) kernel, which plays a central role in balancing exploration and exploitation under limited evaluation budgets. Traditional BO methods often rely on fixed or heuristic kernel selection strategies, which can result in slow convergence or suboptimal solutions when the chosen kernel is poorly suited to the underlying objective function. To address this limitation, we propose a freshly-baked Context-Aware Kernel Evolution (CAKE) to enhance BO with large language models (LLMs). Concretely, CAKE leverages LLMs as the crossover and mutation operators to adaptively generate and refine GP kernels based on the observed data throughout the optimization process. To maximize the power of CAKE, we further propose BIC-Acquisition Kernel Ranking (BAKER) to select the most effective kernel through balancing the model fit measured by the Bayesian information criterion (BIC) with the expected improvement at each iteration of BO. Extensive experiments demonstrate that our fresh CAKE-based BO method consistently outperforms established baselines across a range of real-world tasks, including hyperparameter optimization, controller tuning, and photonic chip design. Our code is publicly available at https://github.com/richardcsuwandi/cake.", "date": "2025-09-22", "categories": []}
{"id": "2308.11787", "title": "HypBO: Accelerating Black-Box Scientific Experiments Using Experts' Hypotheses", "abstract": "Robotics and automation offer massive accelerations for solving intractable, multivariate scientific problems such as materials discovery, but the available search spaces can be dauntingly large. Bayesian optimization (BO) has emerged as a popular sample-efficient optimization engine, thriving in tasks where no analytic form of the target function/property is known. Here, we exploit expert human knowledge in the form of hypotheses to direct Bayesian searches more quickly to promising regions of chemical space. Previous methods have used underlying distributions derived from existing experimental measurements, which is unfeasible for new, unexplored scientific tasks. Also, such distributions cannot capture intricate hypotheses. Our proposed method, which we call HypBO, uses expert human hypotheses to generate improved seed samples. Unpromising seeds are automatically discounted, while promising seeds are used to augment the surrogate model data, thus achieving better-informed sampling. This process continues in a global versus local search fashion, organized in a bilevel optimization framework. We validate the performance of our method on a range of synthetic functions and demonstrate its practical utility on a real chemical design task where the use of expert hypotheses accelerates the search performance significantly.", "date": "2023-08-22", "categories": []}
{"id": "2501.16224", "title": "Language-Based Bayesian Optimization Research Assistant (BORA)", "abstract": "Many important scientific problems involve multivariate optimization coupled with slow and laborious experimental measurements. These complex, high-dimensional searches can be defined by non-convex optimization landscapes that resemble needle-in-a-haystack surfaces, leading to entrapment in local minima. Contextualizing optimizers with human domain knowledge is a powerful approach to guide searches to localized fruitful regions. However, this approach is susceptible to human confirmation bias and it is also challenging for domain experts to keep track of the rapidly expanding scientific literature. Here, we propose the use of Large Language Models (LLMs) for contextualizing Bayesian optimization (BO) via a hybrid optimization framework that intelligently and economically blends stochastic inference with domain knowledge-based insights from the LLM, which is used to suggest new, better-performing areas of the search space for exploration. Our method fosters user engagement by offering real-time commentary on the optimization progress, explaining the reasoning behind the search strategies. We validate the effectiveness of our approach on synthetic benchmarks with up to 15 independent variables and demonstrate the ability of LLMs to reason in four real-world experimental tasks where context-aware suggestions boost optimization performance substantially.", "date": "2025-01-27", "categories": []}
{"id": "2504.13320", "title": "Gradient-Free Sequential Bayesian Experimental Design via Interacting Particle Systems", "abstract": "We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling-both of which are derivative-free and ensemble-based. To address the computational challenges posed by nested expectations in BOED, we propose variational Gaussian and parametrized Laplace approximations that provide tractable upper and lower bounds on the Expected Information Gain (EIG). These approximations enable scalable utility estimation in high-dimensional spaces and PDE-constrained inverse problems. We demonstrate the performance of our framework through numerical experiments ranging from linear Gaussian models to PDE-based inference tasks, highlighting the method's robustness, accuracy, and efficiency in information-driven experimental design.", "date": "2025-04-17", "categories": []}
{"id": "2509.14408", "title": "Deep Gaussian Process-based Cost-Aware Batch Bayesian Optimization for Complex Materials Design Campaigns", "abstract": "The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast, nonlinear design spaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surrogates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations across multiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost into an upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes small batches of candidates in parallel, balancing exploration of under-characterized regions with exploitation of high-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.", "date": "2025-09-17", "categories": []}
{"id": "2503.02749", "title": "Improving Oil Slick Trajectory Simulations with Bayesian Optimization", "abstract": "Accurate simulations of oil spill trajectories are essential for supporting practitioners' response and mitigating environmental and socioeconomic impacts. Numerical models, such as MEDSLIK-II, simulate advection, dispersion, and transformation processes of oil particles. However, simulations heavily rely on accurate parameter tuning, still based on expert knowledge and manual calibration. To overcome these limitations, we integrate the MEDSLIK-II numerical oil spill model with a Bayesian optimization framework to iteratively estimate the best physical parameter configuration that yields simulation closer to satellite observations of the slick. We focus on key parameters, such as horizontal diffusivity and drift factor, maximizing the Fraction Skill Score (FSS) as a measure of spatio-temporal overlap between simulated and observed oil distributions. We validate the framework for the Baniyas oil incident that occurred in Syria between August 23 and September 4, 2021, which released over 12,000 $m^3$ of oil. We show that, on average, the proposed approach systematically improves the FSS from 5.82% to 11.07% compared to control simulations initialized with default parameters. The optimization results in consistent improvement across multiple time steps, particularly during periods of increased drift variability, demonstrating the robustness of our method in dynamic environmental conditions.", "date": "2025-03-04", "categories": []}
{"id": "2206.09022", "title": "Designing MacPherson Suspension Architectures using Bayesian Optimization", "abstract": "Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed first by computer simulation using what is called a discipline model. Such a model can be implemented by a finite element analysis, multibody systems approach, etc. Designs passing this simulation are then considered for physical prototyping. The overall process may take months, and is a significant cost in practice. We have developed a Bayesian optimization system for partially automating this process by directly optimizing compliance with the target specification with respect to the design parameters. The proposed method is a general framework for computing a generalized inverse of a high-dimensional non-linear function that does not require e.g. gradient information, which is often unavailable from discipline models. We furthermore develop a two-tier convergence criterion based on (i) convergence to a solution optimally satisfying all specified design criteria, or (ii) convergence to a minimum-norm solution. We demonstrate the proposed approach on a vehicle chassis design problem motivated by an industry setting using a state-of-the-art commercial discipline model. We show that the proposed approach is general, scalable, and efficient, and that the novel convergence criteria can be implemented straightforwardly based on existing concepts and subroutines in popular Bayesian optimization software packages.", "date": "2022-06-17", "categories": []}
{"id": "2509.09238", "title": "Global Optimization of Stochastic Black-Box Functions with Arbitrary Noise Distributions using Wilson Score Kernel Density Estimation", "abstract": "Many optimization problems in robotics involve the optimization of time-expensive black-box functions, such as those involving complex simulations or evaluation of real-world experiments. Furthermore, these functions are often stochastic as repeated experiments are subject to unmeasurable disturbances. Bayesian optimization can be used to optimize such methods in an efficient manner by deploying a probabilistic function estimator to estimate with a given confidence so that regions of the search space can be pruned away. Consequently, the success of the Bayesian optimization depends on the function estimator's ability to provide informative confidence bounds. Existing function estimators require many function evaluations to infer the underlying confidence or depend on modeling of the disturbances. In this paper, it is shown that the confidence bounds provided by the Wilson Score Kernel Density Estimator (WS-KDE) are applicable as excellent bounds to any stochastic function with an output confined to the closed interval [0;1] regardless of the distribution of the output. This finding opens up the use of WS-KDE for stable global optimization on a wider range of cost functions. The properties of WS-KDE in the context of Bayesian optimization are demonstrated in simulation and applied to the problem of automated trap design for vibrational part feeders.", "date": "2025-09-11", "categories": []}
{"id": "2501.19073", "title": "Pareto-frontier Entropy Search with Variational Lower Bound Maximization", "abstract": "This study considers multi-objective Bayesian optimization (MOBO) through the information gain of the Pareto-frontier. To calculate the information gain, a predictive distribution conditioned on the Pareto-frontier plays a key role, which is defined as a distribution truncated by the Pareto-frontier. However, it is usually impossible to obtain the entire Pareto-frontier in a continuous domain, and therefore, the complete truncation cannot be known. We consider an approximation of the truncate distribution by using a mixture distribution consisting of two possible approximate truncation obtainable from a subset of the Pareto-frontier, which we call over- and under-truncation. Since the optimal balance of the mixture is unknown beforehand, we propose optimizing the balancing coefficient through the variational lower bound maximization framework, by which the approximation error of the information gain can be minimized. Our empirical evaluation demonstrates the effectiveness of the proposed method particularly when the number of objective functions is large.", "date": "2025-01-31", "categories": []}
{"id": "2411.10471", "title": "Constrained composite Bayesian optimization for rational synthesis of polymeric particles", "abstract": "Polymeric nano- and micro-scale particles have critical roles in tackling critical healthcare and energy challenges with their miniature characteristics. However, tailoring their synthesis process to meet specific design targets has traditionally depended on domain expertise and costly trial-and-errors. Recently, modeling strategies, particularly Bayesian optimization (BO), have been proposed to aid materials discovery for maximized/minimized properties. Coming from practical demands, this study for the first time integrates constrained and composite Bayesian optimization (CCBO) to perform efficient target value optimization under black-box feasibility constraints and limited data for laboratory experimentation. Using a synthetic problem that simulates electrospraying, a model nanomanufacturing process, CCBO strategically avoided infeasible conditions and efficiently optimized particle production towards predefined size targets, surpassing standard BO pipelines and providing decisions comparable to human experts. Further laboratory experiments validated CCBO capability to guide the rational synthesis of poly(lactic-co-glycolic acid) (PLGA) particles with diameters of 300 nm and 3.0 $\\mu$m via electrospraying. With minimal initial data and unknown experiment constraints, CCBO reached the design targets within 4 iterations. Overall, the CCBO approach presents a versatile and holistic optimization paradigm for next-generation target-driven particle synthesis empowered by artificial intelligence (AI).", "date": "2024-11-06", "categories": []}
{"id": "2508.18423", "title": "Enhancing Trust-Region Bayesian Optimization via Newton Methods", "abstract": "Bayesian Optimization (BO) has been widely applied to optimize expensive black-box functions while retaining sample efficiency. However, scaling BO to high-dimensional spaces remains challenging. Existing literature proposes performing standard BO in multiple local trust regions (TuRBO) for heterogeneous modeling of the objective function and avoiding over-exploration. Despite its advantages, using local Gaussian Processes (GPs) reduces sampling efficiency compared to a global GP. To enhance sampling efficiency while preserving heterogeneous modeling, we propose to construct multiple local quadratic models using gradients and Hessians from a global GP, and select new sample points by solving the bound-constrained quadratic program. Additionally, we address the issue of vanishing gradients of GPs in high-dimensional spaces. We provide a convergence analysis and demonstrate through experimental results that our method enhances the efficacy of TuRBO and outperforms a wide range of high-dimensional BO techniques on synthetic functions and real-world applications.", "date": "2025-08-25", "categories": []}
{"id": "2401.10811", "title": "Simulation Based Bayesian Optimization", "abstract": "Bayesian Optimization (BO) is a powerful method for optimizing black-box functions by combining prior knowledge with ongoing function evaluations. BO constructs a probabilistic surrogate model of the objective function given the covariates, which is in turn used to inform the selection of future evaluation points through an acquisition function. For smooth continuous search spaces, Gaussian Processes (GPs) are commonly used as the surrogate model as they offer analytical access to posterior predictive distributions, thus facilitating the computation and optimization of acquisition functions. However, in complex scenarios involving optimization over categorical or mixed covariate spaces, GPs may not be ideal. This paper introduces Simulation Based Bayesian Optimization (SBBO) as a novel approach to optimizing acquisition functions that only requires sampling-based access to posterior predictive distributions. SBBO allows the use of surrogate probabilistic models tailored for combinatorial spaces with discrete variables. Any Bayesian model in which posterior inference is carried out through Markov chain Monte Carlo can be selected as the surrogate model in SBBO. We demonstrate empirically the effectiveness of SBBO using various choices of surrogate models in applications involving combinatorial optimization.", "date": "2024-01-19", "categories": []}
{"id": "2508.06847", "title": "MOCA-HESP: Meta High-dimensional Bayesian Optimization for Combinatorial and Mixed Spaces via Hyper-ellipsoid Partitioning", "abstract": "High-dimensional Bayesian Optimization (BO) has attracted significant attention in recent research. However, existing methods have mainly focused on optimizing in continuous domains, while combinatorial (ordinal and categorical) and mixed domains still remain challenging. In this paper, we first propose MOCA-HESP, a novel high-dimensional BO method for combinatorial and mixed variables. The key idea is to leverage the hyper-ellipsoid space partitioning (HESP) technique with different categorical encoders to work with high-dimensional, combinatorial and mixed spaces, while adaptively selecting the optimal encoders for HESP using a multi-armed bandit technique. Our method, MOCA-HESP, is designed as a \\textit{meta-algorithm} such that it can incorporate other combinatorial and mixed BO optimizers to further enhance the optimizers' performance. Finally, we develop three practical BO methods by integrating MOCA-HESP with state-of-the-art BO optimizers for combinatorial and mixed variables: standard BO, CASMOPOLITAN, and Bounce. Our experimental results on various synthetic and real-world benchmarks show that our methods outperform existing baselines. Our code implementation can be found at https://github.com/LamNgo1/moca-hesp", "date": "2025-08-09", "categories": []}
{"id": "2504.03744", "title": "Comparative Explanations: Explanation Guided Decision Making for Human-in-the-Loop Preference Selection", "abstract": "This paper introduces Multi-Output LOcal Narrative Explanation (MOLONE), a novel comparative explanation method designed to enhance preference selection in human-in-the-loop Preference Bayesian optimization (PBO). The preference elicitation in PBO is a non-trivial task because it involves navigating implicit trade-offs between vector-valued outcomes, subjective priorities of decision-makers, and decision-makers' uncertainty in preference selection. Existing explainable AI (XAI) methods for BO primarily focus on input feature importance, neglecting the crucial role of outputs (objectives) in human preference elicitation. MOLONE addresses this gap by providing explanations that highlight both input and output importance, enabling decision-makers to understand the trade-offs between competing objectives and make more informed preference selections. MOLONE focuses on local explanations, comparing the importance of input features and outcomes across candidate samples within a local neighborhood of the search space, thus capturing nuanced differences relevant to preference-based decision-making. We evaluate MOLONE within a PBO framework using benchmark multi-objective optimization functions, demonstrating its effectiveness in improving convergence compared to noisy preference selections. Furthermore, a user study confirms that MOLONE significantly accelerates convergence in human-in-the-loop scenarios by facilitating more efficient identification of preferred options.", "date": "2025-04-01", "categories": []}
{"id": "2410.09290", "title": "Ranking over Regression for Bayesian Optimization and Molecule Selection", "abstract": "Bayesian optimization (BO) has become an indispensable tool for autonomous decision-making across diverse applications from autonomous vehicle control to accelerated drug and materials discovery. With the growing interest in self-driving laboratories, BO of chemical systems is crucial for machine learning (ML) guided experimental planning. Typically, BO employs a regression surrogate model to predict the distribution of unseen parts of the search space. However, for the selection of molecules, picking the top candidates with respect to a distribution, the relative ordering of their properties may be more important than their exact values. In this paper, we introduce Rank-based Bayesian Optimization (RBO), which utilizes a ranking model as the surrogate. We present a comprehensive investigation of RBO's optimization performance compared to conventional BO on various chemical datasets. Our results demonstrate similar or improved optimization performance using ranking models, particularly for datasets with rough structure-property landscapes and activity cliffs. Furthermore, we observe a high correlation between the surrogate ranking ability and BO performance, and this ability is maintained even at early iterations of BO optimization when using ranking surrogate models. We conclude that RBO is an effective alternative to regression-based BO, especially for optimizing novel chemical compounds.", "date": "2024-10-11", "categories": []}
{"id": "2508.15674", "title": "Bayesian Optimization with Expected Improvement: No Regret and the Choice of Incumbent", "abstract": "Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven empirical success in applications, the cumulative regret upper bound of EI remains an open question. In this paper, we analyze the classic noisy Gaussian process expected improvement (GP-EI) algorithm. We consider the Bayesian setting, where the objective is a sample from a GP. Three commonly used incumbents, namely the best posterior mean incumbent (BPMI), the best sampled posterior mean incumbent (BSPMI), and the best observation incumbent (BOI) are considered as the choices of the current best value in GP-EI. We present for the first time the cumulative regret upper bounds of GP-EI with BPMI and BSPMI. Importantly, we show that in both cases, GP-EI is a no-regret algorithm for both squared exponential (SE) and Mat\\'ern kernels. Further, we present for the first time that GP-EI with BOI either achieves a sublinear cumulative regret upper bound or has a fast converging noisy simple regret bound for SE and Mat\\'ern kernels. Our results provide theoretical guidance to the choice of incumbent when practitioners apply GP-EI in the noisy setting. Numerical experiments are conducted to validate our findings.", "date": "2025-08-21", "categories": []}
{"id": "2505.11294", "title": "Bidirectional Information Flow (BIF) -- A Sample Efficient Hierarchical Gaussian Process for Bayesian Optimization", "abstract": "Hierarchical Gaussian Process (H-GP) models divide problems into different subtasks, allowing for different models to address each part, making them well-suited for problems with inherent hierarchical structure. However, typical H-GP models do not fully take advantage of this structure, only sending information up or down the hierarchy. This one-way coupling limits sample efficiency and slows convergence. We propose Bidirectional Information Flow (BIF), an efficient H-GP framework that establishes bidirectional information exchange between parent and child models in H-GPs for online training. BIF retains the modular structure of hierarchical models - the parent combines subtask knowledge from children GPs - while introducing top-down feedback to continually refine children models during online learning. This mutual exchange improves sample efficiency, enables robust training, and allows modular reuse of learned subtask models. BIF outperforms conventional H-GP Bayesian Optimization methods, achieving up to 4x and 3x higher $R^2$ scores for the parent and children respectively, on synthetic and real-world neurostimulation optimization tasks.", "date": "2025-05-16", "categories": []}
{"id": "2503.06381", "title": "Adaptive Bayesian Optimization for Robust Identification of Stochastic Dynamical Systems", "abstract": "This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require nontrivial gradient computations and are prone to local optima. To overcome these limitations, a sample-efficient global optimization method based on Bayesian optimization (BO) is proposed, using an ensemble Gaussian process (EGP) surrogate with weighted kernels from a predefined dictionary. This ensemble enables a richer function space and improves robustness over single-kernel BO. Each objective evaluation is efficiently performed via Kalman filter recursion. Extensive experiments across parameter settings and sampling intervals show that the EGP-based BO consistently outperforms MLE via steady-state filtering and expectation-maximization (whose derivation is a side contribution) in terms of RMSE and statistical consistency. Unlike the ensemble variant, single-kernel BO does not always yield such gains, underscoring the benefits of model averaging. Notably, the BO-based estimator achieves RMSE below the classical Cramer-Rao bound, particularly for the inverse time constant, long considered difficult to estimate. This counterintuitive outcome is attributed to a data-driven prior implicitly induced by the GP surrogate in BO.", "date": "2025-03-09", "categories": []}
{"id": "2412.13559", "title": "Indirect Query Bayesian Optimization with Integrated Feedback", "abstract": "We develop the framework of Indirect Query Bayesian Optimization (IQBO), a new class of Bayesian optimization problems where the integrated feedback is given via a conditional expectation of the unknown function $f$ to be optimized. The underlying conditional distribution can be unknown and learned from data. The goal is to find the global optimum of $f$ by adaptively querying and observing in the space transformed by the conditional distribution. This is motivated by real-world applications where one cannot access direct feedback due to privacy, hardware or computational constraints. We propose the Conditional Max-Value Entropy Search (CMES) acquisition function to address this novel setting, and propose a hierarchical search algorithm with multi-resolution feedback to improve computational efficiency. We show regret bounds for our proposed methods and demonstrate the effectiveness of our approaches on simulated optimization tasks.", "date": "2024-12-18", "categories": []}
{"id": "2502.05372", "title": "Active Learning of Model Discrepancy with Bayesian Experimental Design", "abstract": "Digital twins have been actively explored in many engineering applications, such as manufacturing and autonomous systems. However, model discrepancy is ubiquitous in most digital twin models and has significant impacts on the performance of using those models. In recent years, data-driven modeling techniques have been demonstrated promising in characterizing the model discrepancy in existing models, while the training data for the learning of model discrepancy is often obtained in an empirical way and an active approach of gathering informative data can potentially benefit the learning of model discrepancy. On the other hand, Bayesian experimental design (BED) provides a systematic approach to gathering the most informative data, but its performance is often negatively impacted by the model discrepancy. In this work, we build on sequential BED and propose an efficient approach to iteratively learn the model discrepancy based on the data from the BED. The performance of the proposed method is validated by a classical numerical example governed by a convection-diffusion equation, for which full BED is still feasible. The proposed method is then further studied in the same numerical example with a high-dimensional model discrepancy, which serves as a demonstration for the scenarios where full BED is not practical anymore. An ensemble-based approximation of information gain is further utilized to assess the data informativeness and to enhance learning model discrepancy. The results show that the proposed method is efficient and robust to the active learning of high-dimensional model discrepancy, using data suggested by the sequential BED. We also demonstrate that the proposed method is compatible with both classical numerical solvers and modern auto-differentiable solvers.", "date": "2025-02-07", "categories": []}
{"id": "2504.10076", "title": "Towards Scalable Bayesian Optimization via Gradient-Informed Bayesian Neural Networks", "abstract": "Bayesian optimization (BO) is a widely used method for data-driven optimization that generally relies on zeroth-order data of objective function to construct probabilistic surrogate models. These surrogates guide the exploration-exploitation process toward finding global optimum. While Gaussian processes (GPs) are commonly employed as surrogates of the unknown objective function, recent studies have highlighted the potential of Bayesian neural networks (BNNs) as scalable and flexible alternatives. Moreover, incorporating gradient observations into GPs, when available, has been shown to improve BO performance. However, the use of gradients within BNN surrogates remains unexplored. By leveraging automatic differentiation, gradient information can be seamlessly integrated into BNN training, resulting in more informative surrogates for BO. We propose a gradient-informed loss function for BNN training, effectively augmenting function observations with local gradient information. The effectiveness of this approach is demonstrated on well-known benchmarks in terms of improved BNN predictions and faster BO convergence as the number of decision variables increases.", "date": "2025-04-14", "categories": []}
{"id": "2508.01834", "title": "Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design", "abstract": "With advances in scientific computing, computer experiments are increasingly used for optimizing complex systems. However, for modern applications, e.g., the optimization of nuclear physics detectors, each experiment run can require hundreds of CPU hours, making the optimization of its black-box simulator over a high-dimensional space a challenging task. Given limited runs at inputs $\\mathbf{x}_1, \\cdots, \\mathbf{x}_n$, the best solution from these evaluated inputs can be far from optimal, particularly as dimensionality increases. Existing black-box methods, however, largely employ this ''pick-the-winner'' (PW) solution, which leads to mediocre optimization performance. To address this, we propose a new Black-box Optimization via Marginal Means (BOMM) approach. The key idea is a new estimator of a global optimizer $\\mathbf{x}^*$ that leverages the so-called marginal mean functions, which can be efficiently inferred with limited runs in high dimensions. Unlike PW, this estimator can select solutions beyond evaluated inputs for improved optimization performance. Assuming the objective function follows a generalized additive model with unknown link function and under mild conditions, we prove that the BOMM estimator not only is consistent for optimization, but also has an optimization rate that tempers the ''curse-of-dimensionality'' faced by existing methods, thus enabling better performance as dimensionality increases. We present a practical framework for implementing BOMM using the transformed additive Gaussian process surrogate model. Finally, we demonstrate the effectiveness of BOMM in numerical experiments and an application on neutrino detector optimization in nuclear physics.", "date": "2025-08-03", "categories": []}
{"id": "2508.00833", "title": "Deep Kernel Bayesian Optimisation for Closed-Loop Electrode Microstructure Design with User-Defined Properties based on GANs", "abstract": "The generation of multiphase porous electrode microstructures with optimum morphological and transport properties is essential in the design of improved electrochemical energy storage devices, such as lithium-ion batteries. Electrode characteristics directly influence battery performance by acting as the main sites where the electrochemical reactions coupled with transport processes occur. This work presents a generation-optimisation closed-loop algorithm for the design of microstructures with tailored properties. A deep convolutional Generative Adversarial Network is used as a deep kernel and employed to generate synthetic three-phase three-dimensional images of a porous lithium-ion battery cathode material. A Gaussian Process Regression uses the latent space of the generator and serves as a surrogate model to correlate the morphological and transport properties of the synthetic microstructures. This surrogate model is integrated into a deep kernel Bayesian optimisation framework, which optimises cathode properties as a function of the latent space of the generator. A set of objective functions were defined to perform the maximisation of morphological properties (e.g., volume fraction, specific surface area) and transport properties (relative diffusivity). We demonstrate the ability to perform simultaneous maximisation of correlated properties (specific surface area and relative diffusivity), as well as constrained optimisation of these properties. This is the maximisation of morphological or transport properties constrained by constant values of the volume fraction of the phase of interest. Visualising the optimised latent space reveals its correlation with morphological properties, enabling the fast generation of visually realistic microstructures with customised properties.", "date": "2025-06-07", "categories": []}
{"id": "2508.01013", "title": "On Some Tunable Multi-fidelity Bayesian Optimization Frameworks", "abstract": "Multi-fidelity optimization employs surrogate models that integrate information from varying levels of fidelity to guide efficient exploration of complex design spaces while minimizing the reliance on (expensive) high-fidelity objective function evaluations. To advance Gaussian Process (GP)-based multi-fidelity optimization, we implement a proximity-based acquisition strategy that simplifies fidelity selection by eliminating the need for separate acquisition functions at each fidelity level. We also enable multi-fidelity Upper Confidence Bound (UCB) strategies by combining them with multi-fidelity GPs rather than the standard GPs typically used. We benchmark these approaches alongside other multi-fidelity acquisition strategies (including fidelity-weighted approaches) comparing their performance, reliance on high-fidelity evaluations, and hyperparameter tunability in representative optimization tasks. The results highlight the capability of the proximity-based multi-fidelity acquisition function to deliver consistent control over high-fidelity usage while maintaining convergence efficiency. Our illustrative examples include multi-fidelity chemical kinetic models, both homogeneous and heterogeneous (dynamic catalysis for ammonia production).", "date": "2025-08-01", "categories": []}
{"id": "2406.03616", "title": "BEACON: A Bayesian Optimization Strategy for Novelty Search in Expensive Black-Box Systems", "abstract": "Novelty search (NS) refers to a class of exploration algorithms that seek to uncover diverse system behaviors through simulations or experiments. Such diversity is central to many AI-driven discovery and design tasks, including material and drug development, neural architecture search, and reinforcement learning. However, existing NS methods typically rely on evolutionary strategies and other meta-heuristics that require dense sampling of the input space, making them impractical for expensive black-box systems. In this work, we introduce BEACON, a sample-efficient, Bayesian optimization-inspired approach to NS that is tailored for settings where the input-to-behavior relationship is opaque and costly to evaluate. BEACON models this mapping using multi-output Gaussian processes (MOGPs) and selects new inputs by maximizing a novelty metric computed from posterior samples of the MOGP, effectively balancing the exploration-exploitation trade-off. By leveraging recent advances in posterior sampling and high-dimensional GP modeling, our method remains scalable to large input spaces and datasets. We evaluate BEACON across ten synthetic benchmarks and eight real-world tasks, including the design of diverse materials for clean energy applications. Our results show that BEACON significantly outperforms existing NS baselines, consistently discovering a broader set of behaviors under tight evaluation budgets.", "date": "2024-06-05", "categories": []}
{"id": "2507.21449", "title": "From Global to Local: A Scalable Benchmark for Local Posterior Sampling", "abstract": "Degeneracy is an inherent feature of the loss landscape of neural networks, but it is not well understood how stochastic gradient MCMC (SGMCMC) algorithms interact with this degeneracy. In particular, current global convergence guarantees for common SGMCMC algorithms rely on assumptions which are likely incompatible with degenerate loss landscapes. In this paper, we argue that this gap requires a shift in focus from global to local posterior sampling, and, as a first step, we introduce a novel scalable benchmark for evaluating the local sampling performance of SGMCMC algorithms. We evaluate a number of common algorithms, and find that RMSProp-preconditioned SGLD is most effective at faithfully representing the local geometry of the posterior distribution. Although we lack theoretical guarantees about global sampler convergence, our empirical results show that we are able to extract non-trivial local information in models with up to O(100M) parameters.", "date": "2025-07-29", "categories": []}
{"id": "2305.15612", "title": "Density Ratio Estimation-based Bayesian Optimization with Semi-Supervised Learning", "abstract": "Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of efficiently finding a global optimum of an expensive-to-evaluate black-box function. In general, a probabilistic regression model is widely used as a surrogate function to model an explicit distribution over function evaluations given an input to estimate and a training dataset. Beyond the probabilistic regression-based methods, density ratio estimation-based Bayesian optimization has been suggested in order to estimate a density ratio of the groups relatively close and relatively far to a global optimum. Developing this line of research further, supervised classifiers are employed to estimate a class probability for the two groups instead of a density ratio. However, the supervised classifiers used in this strategy are prone to be overconfident for known knowledge on global solution candidates. Supposing that we have access to unlabeled points, e.g., predefined fixed-size pools, we propose density ratio estimation-based Bayesian optimization with semi-supervised learning to solve this challenge. Finally, we show the empirical results of our methods and several baseline methods in two distinct scenarios with unlabeled point sampling and a fixed-size pool, and analyze the validity of our methods in diverse experiments.", "date": "2023-05-24", "categories": []}
{"id": "2507.19663", "title": "Adaptive Bayesian Data-Driven Design of Reliable Solder Joints for Micro-electronic Devices", "abstract": "Solder joint reliability related to failures due to thermomechanical loading is a critically important yet physically complex engineering problem. As a result, simulated behavior is oftentimes computationally expensive. In an increasingly data-driven world, the usage of efficient data-driven design schemes is a popular choice. Among them, Bayesian optimization (BO) with Gaussian process regression is one of the most important representatives. The authors argue that computational savings can be obtained from exploiting thorough surrogate modeling and selecting a design candidate based on multiple acquisition functions. This is feasible due to the relatively low computational cost, compared to the expensive simulation objective. This paper addresses the shortcomings in the adjacent literature by providing and implementing a novel heuristic framework to perform BO with adaptive hyperparameters across the various optimization iterations. Adaptive BO is subsequently compared to regular BO when faced with synthetic objective minimization problems. The results show the efficiency of adaptive BO when compared any worst-performing regular Bayesian schemes. As an engineering use case, the solder joint reliability problem is tackled by minimizing the accumulated non-linear creep strain under a cyclic thermal load. Results show that adaptive BO outperforms regular BO by 3% on average at any given computational budget threshold, critically saving half of the computational expense budget. This practical result underlines the methodological potential of the adaptive Bayesian data-driven methodology to achieve better results and cut optimization-related expenses. Lastly, in order to promote the reproducibility of the results, the data-driven implementations are made available on an open-source basis.", "date": "2025-07-25", "categories": []}
{"id": "2507.20533", "title": "Kernel Learning for Sample Constrained Black-Box Optimization", "abstract": "Black box optimization (BBO) focuses on optimizing unknown functions in high-dimensional spaces. In many applications, sampling the unknown function is expensive, imposing a tight sample budget. Ongoing work is making progress on reducing the sample budget by learning the shape/structure of the function, known as kernel learning. We propose a new method to learn the kernel of a Gaussian Process. Our idea is to create a continuous kernel space in the latent space of a variational autoencoder, and run an auxiliary optimization to identify the best kernel. Results show that the proposed method, Kernel Optimized Blackbox Optimization (KOBO), outperforms state of the art by estimating the optimal at considerably lower sample budgets. Results hold not only across synthetic benchmark functions but also in real applications. We show that a hearing aid may be personalized with fewer audio queries to the user, or a generative model could converge to desirable images from limited user ratings.", "date": "2025-07-28", "categories": []}
{"id": "2402.04711", "title": "High-dimensional multidisciplinary design optimization for aircraft eco-design / Optimisation multi-disciplinaire en grande dimension pour l'\\'eco-conception avion en avant-projet", "abstract": "The objective of this Philosophiae Doctor (Ph.D) thesis is to propose an efficient approach for optimizing a multidisciplinary black-box model when the optimization problem is constrained and involves a large number of mixed integer design variables (typically 100 variables). The targeted optimization approach, called EGO, is based on a sequential enrichment of an adaptive surrogate model and, in this context, GP surrogate models are one of the most widely used in engineering problems to approximate time-consuming high fidelity models. EGO is a heuristic BO method that performs well in terms of solution quality. However, like any other global optimization method, EGO suffers from the curse of dimensionality, meaning that its performance is satisfactory on lower dimensional problems, but deteriorates as the dimensionality of the optimization search space increases. For realistic aircraft design problems, the typical size of the design variables can even exceed 100 and, thus, trying to solve directly the problems using EGO is ruled out. The latter is especially true when the problems involve both continuous and categorical variables increasing even more the size of the search space. In this Ph.D thesis, effective parameterization tools are investigated, including techniques like partial least squares regression, to significantly reduce the number of design variables. Additionally, Bayesian optimization is adapted to handle discrete variables and high-dimensional spaces in order to reduce the number of evaluations when optimizing innovative aircraft concepts such as the \"DRAGON\" hybrid airplane to reduce their climate impact.", "date": "2024-02-07", "categories": []}
{"id": "2504.03172", "title": "Bayesian Optimization of Robustness Measures under Input Uncertainty: A Randomized Gaussian Process Upper Confidence Bound Approach", "abstract": "Bayesian optimization based on the Gaussian process upper confidence bound (GP-UCB) offers a theoretical guarantee for optimizing black-box functions. In practice, however, black-box functions often involve input uncertainty. To handle such cases, GP-UCB can be extended to optimize evaluation criteria known as robustness measures. However, GP-UCB-based methods for robustness measures require a trade-off parameter, $\\beta$, which, as in the original GP-UCB, must be set sufficiently large to ensure theoretical validity. In this study, we propose randomized robustness measure GP-UCB (RRGP-UCB), a novel method that samples $\\beta$ from a chi-squared-based probability distribution. This approach eliminates the need to explicitly specify $\\beta$. Notably, the expected value of $\\beta$ under this distribution is not excessively large. Furthermore, we show that RRGP-UCB provides tight bounds on the expected regret between the optimal and estimated solutions. Numerical experiments demonstrate the effectiveness of the proposed method.", "date": "2025-04-04", "categories": []}
{"id": "2507.15235", "title": "Accelerated Bayesian Optimal Experimental Design via Conditional Density Estimation and Informative Data", "abstract": "The Design of Experiments (DOEs) is a fundamental scientific methodology that provides researchers with systematic principles and techniques to enhance the validity, reliability, and efficiency of experimental outcomes. In this study, we explore optimal experimental design within a Bayesian framework, utilizing Bayes' theorem to reformulate the utility expectation--originally expressed as a nested double integral--into an independent double integral form, significantly improving numerical efficiency. To further accelerate the computation of the proposed utility expectation, conditional density estimation is employed to approximate the ratio of two Gaussian random fields, while covariance serves as a selection criterion to identify informative datasets during model fitting and integral evaluation. In scenarios characterized by low simulation efficiency and high costs of raw data acquisition, key challenges such as surrogate modeling, failure probability estimation, and parameter inference are systematically restructured within the Bayesian experimental design framework. The effectiveness of the proposed methodology is validated through both theoretical analysis and practical applications, demonstrating its potential for enhancing experimental efficiency and decision-making under uncertainty.", "date": "2025-07-21", "categories": []}
{"id": "2507.12773", "title": "Sample-Constrained Black Box Optimization for Audio Personalization", "abstract": "We consider the problem of personalizing audio to maximize user experience. Briefly, we aim to find a filter $h^*$, which applied to any music or speech, will maximize the user's satisfaction. This is a black-box optimization problem since the user's satisfaction function is unknown. Substantive work has been done on this topic where the key idea is to play audio samples to the user, each shaped by a different filter $h_i$, and query the user for their satisfaction scores $f(h_i)$. A family of ``surrogate\" functions is then designed to fit these scores and the optimization method gradually refines these functions to arrive at the filter $\\hat{h}^*$ that maximizes satisfaction. In certain applications, we observe that a second type of querying is possible where users can tell us the individual elements $h^*[j]$ of the optimal filter $h^*$. Consider an analogy from cooking where the goal is to cook a recipe that maximizes user satisfaction. A user can be asked to score various cooked recipes (e.g., tofu fried rice) or to score individual ingredients (say, salt, sugar, rice, chicken, etc.). Given a budget of $B$ queries, where a query can be of either type, our goal is to find the recipe that will maximize this user's satisfaction. Our proposal builds on Sparse Gaussian Process Regression (GPR) and shows how a hybrid approach can outperform any one type of querying. Our results are validated through simulations and real world experiments, where volunteers gave feedback on music/speech audio and were able to achieve high satisfaction levels. We believe this idea of hybrid querying opens new problems in black-box optimization and solutions can benefit other applications beyond audio personalization.", "date": "2025-07-17", "categories": []}
{"id": "2501.13535", "title": "LITE: Efficiently Estimating Gaussian Probability of Maximality", "abstract": "We consider the problem of computing the probability of maximality (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to reinforcement learning, where the PoM not only helps with finding an optimal action, but yields a fine-grained analysis of the action domain, crucial in tasks such as drug discovery. Existing techniques are costly, scaling polynomially in computation and memory with the vector size. We introduce LITE, the first approach for estimating Gaussian PoM with almost-linear time and memory complexity. LITE achieves SOTA accuracy on a number of tasks, while being in practice several orders of magnitude faster than the baselines. This also translates to a better performance on downstream tasks such as entropy estimation and optimal control of bandits. Theoretically, we cast LITE as entropy-regularized UCB and connect it to prior PoM estimators.", "date": "2025-01-23", "categories": []}
{"id": "2507.06529", "title": "Direct Regret Optimization in Bayesian Optimization", "abstract": "Bayesian optimization (BO) is a powerful paradigm for optimizing expensive black-box functions. Traditional BO methods typically rely on separate hand-crafted acquisition functions and surrogate models for the underlying function, and often operate in a myopic manner. In this paper, we propose a novel direct regret optimization approach that jointly learns the optimal model and non-myopic acquisition by distilling from a set of candidate models and acquisitions, and explicitly targets minimizing the multi-step regret. Our framework leverages an ensemble of Gaussian Processes (GPs) with varying hyperparameters to generate simulated BO trajectories, each guided by an acquisition function chosen from a pool of conventional choices, until a Bayesian early stop criterion is met. These simulated trajectories, capturing multi-step exploration strategies, are used to train an end-to-end decision transformer that directly learns to select next query points aimed at improving the ultimate objective. We further adopt a dense training--sparse learning paradigm: The decision transformer is trained offline with abundant simulated data sampled from ensemble GPs and acquisitions, while a limited number of real evaluations refine the GPs online. Experimental results on synthetic and real-world benchmarks suggest that our method consistently outperforms BO baselines, achieving lower simple regret and demonstrating more robust exploration in high-dimensional or noisy settings.", "date": "2025-07-09", "categories": []}
{"id": "2502.16824", "title": "Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization", "abstract": "Optimizing high-dimensional and complex black-box functions is crucial in numerous scientific applications. While Bayesian optimization (BO) is a powerful method for sample-efficient optimization, it struggles with the curse of dimensionality and scaling to thousands of evaluations. Recently, leveraging generative models to solve black-box optimization problems has emerged as a promising framework. However, those methods often underperform compared to BO methods due to limited expressivity and difficulty of uncertainty estimation in high-dimensional spaces. To overcome these issues, we introduce \\textbf{DiBO}, a novel framework for solving high-dimensional black-box optimization problems. Our method iterates two stages. First, we train a diffusion model to capture the data distribution and deep ensembles to predict function values with uncertainty quantification. Second, we cast the candidate selection as a posterior inference problem to balance exploration and exploitation in high-dimensional spaces. Concretely, we fine-tune diffusion models to amortize posterior inference. Extensive experiments demonstrate that our method outperforms state-of-the-art baselines across synthetic and real-world tasks. Our code is publicly available \\href{https://github.com/umkiyoung/DiBO}{here}.", "date": "2025-02-24", "categories": []}
{"id": "2507.03910", "title": "Return of the Latent Space COWBOYS: Re-thinking the use of VAEs for Bayesian Optimisation of Structured Spaces", "abstract": "Bayesian optimisation in the latent space of a Variational AutoEncoder (VAE) is a powerful framework for optimisation tasks over complex structured domains, such as the space of scientifically interesting molecules. However, existing approaches tightly couple the surrogate and generative models, which can lead to suboptimal performance when the latent space is not tailored to specific tasks, which in turn has led to the proposal of increasingly sophisticated algorithms. In this work, we explore a new direction, instead proposing a decoupled approach that trains a generative model and a Gaussian Process (GP) surrogate separately, then combines them via a simple yet principled Bayesian update rule. This separation allows each component to focus on its strengths -- structure generation from the VAE and predictive modelling by the GP. We show that our decoupled approach improves our ability to identify high-potential candidates in molecular optimisation problems under constrained evaluation budgets.", "date": "2025-07-05", "categories": []}
{"id": "2507.05175", "title": "Blind Targeting: Personalization under Third-Party Privacy Constraints", "abstract": "Major advertising platforms recently increased privacy protections by limiting advertisers' access to individual-level data. Instead of providing access to granular raw data, the platforms only allow a limited number of aggregate queries to a dataset, which is further protected by adding differentially private noise. This paper studies whether and how advertisers can design effective targeting policies within these restrictive privacy preserving data environments. To achieve this, I develop a probabilistic machine learning method based on Bayesian optimization, which facilitates dynamic data exploration. Since Bayesian optimization was designed to sample points from a function to find its maximum, it is not applicable to aggregate queries and to targeting. Therefore, I introduce two innovations: (i) integral updating of posteriors which allows to select the best regions of the data to query rather than individual points and (ii) a targeting-aware acquisition function that dynamically selects the most informative regions for the targeting task. I identify the conditions of the dataset and privacy environment that necessitate the use of such a \"smart\" querying strategy. I apply the strategic querying method to the Criteo AI Labs dataset for uplift modeling (Diemert et al., 2018) that contains visit and conversion data from 14M users. I show that an intuitive benchmark strategy only achieves 33% of the non-privacy-preserving targeting potential in some cases, while my strategic querying method achieves 97-101% of that potential, and is statistically indistinguishable from Causal Forest (Athey et al., 2019): a state-of-the-art non-privacy-preserving machine learning targeting method.", "date": "2025-07-07", "categories": []}
{"id": "2504.06469", "title": "AI-Assisted Transport of Radioactive Ion Beams", "abstract": "Beams of radioactive heavy ions allow researchers to study rare and unstable atomic nuclei, shedding light into the internal structure of exotic nuclei and on how chemical elements are formed in stars. However, the extraction and transport of radioactive beams rely on time-consuming expert-driven tuning methods, where hundreds of parameters are manually optimized. Here, we introduce a system that employs Artificial Intelligence (AI), specifically utilizing Bayesian Optimization, to assist in the transport process of radioactive beams. We apply our methodology to real-life scenarios showing advantages when compared with standard tuning methods. This AI-assisted approach can be extended to other radioactive beam facilities around the world to improve operational efficiency and enhance scientific output.", "date": "2025-04-08", "categories": []}
{"id": "2506.11456", "title": "Fast Bayesian Optimization of Function Networks with Partial Evaluations", "abstract": "Bayesian optimization of function networks (BOFN) is a framework for optimizing expensive-to-evaluate objective functions structured as networks, where some nodes' outputs serve as inputs for others. Many real-world applications, such as manufacturing and drug discovery, involve function networks with additional properties - nodes that can be evaluated independently and incur varying costs. A recent BOFN variant, p-KGFN, leverages this structure and enables cost-aware partial evaluations, selectively querying only a subset of nodes at each iteration. p-KGFN reduces the number of expensive objective function evaluations needed but has a large computational overhead: choosing where to evaluate requires optimizing a nested Monte Carlo-based acquisition function for each node in the network. To address this, we propose an accelerated p-KGFN algorithm that reduces computational overhead with only a modest loss in query efficiency. Key to our approach is generation of node-specific candidate inputs for each node in the network via one inexpensive global Monte Carlo simulation. Numerical experiments show that our method maintains competitive query efficiency while achieving up to a 16x speedup over the original p-KGFN algorithm.", "date": "2025-06-13", "categories": []}
{"id": "2410.18973", "title": "Tuning-Free Coreset Markov Chain Monte Carlo via Hot DoG", "abstract": "A Bayesian coreset is a small, weighted subset of a data set that replaces the full data during inference to reduce computational cost. The state-of-the-art coreset construction algorithm, Coreset Markov chain Monte Carlo (Coreset MCMC), uses draws from an adaptive Markov chain targeting the coreset posterior to train the coreset weights via stochastic gradient optimization. However, the quality of the constructed coreset, and thus the quality of its posterior approximation, is sensitive to the stochastic optimization learning rate. In this work, we propose a learning-rate-free stochastic gradient optimization procedure, Hot-start Distance over Gradient (Hot DoG), for training coreset weights in Coreset MCMC without user tuning effort. We provide a theoretical analysis of the convergence of the coreset weights produced by Hot DoG. We also provide empirical results demonstrate that Hot DoG provides higher quality posterior approximations than other learning-rate-free stochastic gradient methods, and performs competitively to optimally-tuned ADAM.", "date": "2024-10-24", "categories": []}
{"id": "2506.16316", "title": "Bayesian Optimization over Bounded Domains with the Beta Product Kernel", "abstract": "Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Mat\\'ern and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the domain of the function, which may limit their applicability in bounded domains. To address the limitation, we introduce the Beta kernel, a non-stationary kernel induced by a product of Beta distribution density functions. Such a formulation allows our kernel to naturally model functions on bounded domains. We present statistical evidence supporting the hypothesis that the kernel exhibits an exponential eigendecay rate, based on empirical analyses of its spectral properties across different settings. Our experimental results demonstrate the robustness of the Beta kernel in modeling functions with optima located near the faces or vertices of the unit hypercube. The experiments show that our kernel consistently outperforms a wide range of kernels, including the well-known Mat\\'ern and RBF, in different problems, including synthetic function optimization and the compression of vision and language models.", "date": "2025-06-19", "categories": []}
{"id": "2506.14619", "title": "Feasibility-Driven Trust Region Bayesian Optimization", "abstract": "Bayesian optimization is a powerful tool for solving real-world optimization tasks under tight evaluation budgets, making it well-suited for applications involving costly simulations or experiments. However, many of these tasks are also characterized by the presence of expensive constraints whose analytical formulation is unknown and often defined in high-dimensional spaces where feasible regions are small, irregular, and difficult to identify. In such cases, a substantial portion of the optimization budget may be spent just trying to locate the first feasible solution, limiting the effectiveness of existing methods. In this work, we present a Feasibility-Driven Trust Region Bayesian Optimization (FuRBO) algorithm. FuRBO iteratively defines a trust region from which the next candidate solution is selected, using information from both the objective and constraint surrogate models. Our adaptive strategy allows the trust region to shift and resize significantly between iterations, enabling the optimizer to rapidly refocus its search and consistently accelerate the discovery of feasible and good-quality solutions. We empirically demonstrate the effectiveness of FuRBO through extensive testing on the full BBOB-constrained COCO benchmark suite and other physics-inspired benchmarks, comparing it against state-of-the-art baselines for constrained black-box optimization across varying levels of constraint severity and problem dimensionalities ranging from 2 to 60.", "date": "2025-06-17", "categories": []}
{"id": "2506.11831", "title": "Bayesian Optimization with Inexact Acquisition: Is Random Grid Search Sufficient?", "abstract": "Bayesian optimization (BO) is a widely used iterative algorithm for optimizing black-box functions. Each iteration requires maximizing an acquisition function, such as the upper confidence bound (UCB) or a sample path from the Gaussian process (GP) posterior, as in Thompson sampling (TS). However, finding an exact solution to these maximization problems is often intractable and computationally expensive. Reflecting such realistic situations, in this paper, we delve into the effect of inexact maximizers of the acquisition functions. Defining a measure of inaccuracy in acquisition solutions, we establish cumulative regret bounds for both GP-UCB and GP-TS without requiring exact solutions of acquisition function maximization. Our results show that under appropriate conditions on accumulated inaccuracy, inexact BO algorithms can still achieve sublinear cumulative regret. Motivated by such findings, we provide both theoretical justification and numerical validation for random grid search as an effective and computationally efficient acquisition function solver.", "date": "2025-06-13", "categories": []}
{"id": "2503.08131", "title": "Large Scale Multi-Task Bayesian Optimization with Large Language Models", "abstract": "In multi-task Bayesian optimization, the goal is to leverage experience from optimizing existing tasks to improve the efficiency of optimizing new ones. While approaches using multi-task Gaussian processes or deep kernel transfer exist, the performance improvement is marginal when scaling beyond a moderate number of tasks. We introduce a novel approach leveraging large language models (LLMs) to learn from, and improve upon, previous optimization trajectories, scaling to approximately 1500 distinct tasks. Specifically, we propose a feedback loop in which an LLM is fine-tuned on the high quality solutions to specific tasks found by Bayesian optimization (BO). This LLM is then used to generate initialization points for future BO searches for new tasks. The trajectories of these new searches provide additional training data for fine-tuning the LLM, completing the loop. We evaluate our method on two distinct domains: database query optimization and antimicrobial peptide design. Results demonstrate that our approach creates a positive feedback loop, where the LLM's generated initializations gradually improve, leading to better optimization performance. As this feedback loop continues, we find that the LLM is eventually able to generate solutions to new tasks in just a few shots that are better than the solutions produced by \"from scratch\" by Bayesian optimization while simultaneously requiring significantly fewer oracle calls.", "date": "2025-03-11", "categories": []}
{"id": "2406.04308", "title": "Approximation-Aware Bayesian Optimization", "abstract": "High-dimensional Bayesian optimization (BO) tasks such as molecular design often require 10,000 function evaluations before obtaining meaningful results. While methods like sparse variational Gaussian processes (SVGPs) reduce computational requirements in these settings, the underlying approximations result in suboptimal data acquisitions that slow the progress of optimization. In this paper we modify SVGPs to better align with the goals of BO: targeting informed data acquisition rather than global posterior fidelity. Using the framework of utility-calibrated variational inference, we unify GP approximation and data acquisition into a joint optimization problem, thereby ensuring optimal decisions under a limited computational budget. Our approach can be used with any decision-theoretic acquisition function and is compatible with trust region methods like TuRBO. We derive efficient joint objectives for the expected improvement and knowledge gradient acquisition functions in both the standard and batch BO settings. Our approach outperforms standard SVGPs on high-dimensional benchmark tasks in control and molecular design.", "date": "2024-06-06", "categories": []}
{"id": "2403.04764", "title": "TS-RSR: A provably efficient approach for batch Bayesian Optimization", "abstract": "This paper presents a new approach for batch Bayesian Optimization (BO) called Thompson Sampling-Regret to Sigma Ratio directed sampling (TS-RSR), where we sample a new batch of actions by minimizing a Thompson Sampling approximation of a regret to uncertainty ratio. Our sampling objective is able to coordinate the actions chosen in each batch in a way that minimizes redundancy between points whilst focusing on points with high predictive means or high uncertainty. Theoretically, we provide rigorous convergence guarantees on our algorithm's regret, and numerically, we demonstrate that our method attains state-of-the-art performance on a range of challenging synthetic and realistic test functions, where it outperforms several competitive benchmark batch BO algorithms.", "date": "2024-03-07", "categories": []}
{"id": "2506.07247", "title": "Promoting Ensemble Diversity with Interactive Bayesian Distributional Robustness for Fine-tuning Foundation Models", "abstract": "We introduce Interactive Bayesian Distributional Robustness (IBDR), a novel Bayesian inference framework that allows modeling the interactions between particles, thereby enhancing ensemble quality through increased particle diversity. IBDR is grounded in a generalized theoretical framework that connects the distributional population loss with the approximate posterior, motivating a practical dual optimization procedure that enforces distributional robustness while fostering particle diversity. We evaluate IBDR's performance against various baseline methods using the VTAB-1K benchmark and the common reasoning language task. The results consistently show that IBDR outperforms these baselines, underscoring its effectiveness in real-world applications.", "date": "2025-06-08", "categories": []}
{"id": "2410.03085", "title": "Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach", "abstract": "Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data is scarce and training times are limited. We propose a semi-supervised Bayesian Neural Networks (BNNs) based optimization proxy for this complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step for minimizing cost, and an unsupervised learning step for enforcing constraint feasibility. We show that the proposed semi-supervised BNN outperforms DNN architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the inequality gaps. Further, the BNN's ability to provide posterior samples is leveraged to construct practically meaningful probabilistic confidence bounds on performance using a limited validation data, unlike prior methods. The implementation code for this study is available at: https://github.com/kaarthiksundar/BNN-OPF/.", "date": "2024-10-04", "categories": []}
{"id": "2503.05574", "title": "BARK: A Fully Bayesian Tree Kernel for Black-box Optimization", "abstract": "We perform Bayesian optimization using a Gaussian process perspective on Bayesian Additive Regression Trees (BART). Our BART Kernel (BARK) uses tree agreement to define a posterior over piecewise-constant functions, and we explore the space of tree kernels using a Markov chain Monte Carlo approach. Where BART only samples functions, the resulting BARK model obtains samples of Gaussian processes defining distributions over functions, which allow us to build acquisition functions for Bayesian optimization. Our tree-based approach enables global optimization over the surrogate, even for mixed-feature spaces. Moreover, where many previous tree-based kernels provide uncertainty quantification over function values, our sampling scheme captures uncertainty over the tree structure itself. Our experiments show the strong performance of BARK on both synthetic and applied benchmarks, due to the combination of our fully Bayesian surrogate and the optimization procedure.", "date": "2025-03-07", "categories": []}
{"id": "2410.00544", "title": "Best Practices for Multi-Fidelity Bayesian Optimization in Materials and Molecular Research", "abstract": "Multi-fidelity Bayesian Optimization (MFBO) is a promising framework to speed up materials and molecular discovery as sources of information of different accuracies are at hand at increasing cost. Despite its potential use in chemical tasks, there is a lack of systematic evaluation of the many parameters playing a role in MFBO. In this work, we provide guidelines and recommendations to decide when to use MFBO in experimental settings. We investigate MFBO methods applied to molecules and materials problems. First, we test two different families of acquisition functions in two synthetic problems and study the effect of the informativeness and cost of the approximate function. We use our implementation and guidelines to benchmark three real discovery problems and compare them against their single-fidelity counterparts. Our results may help guide future efforts to implement MFBO as a routine tool in the chemical sciences.", "date": "2024-10-01", "categories": []}
{"id": "2506.00754", "title": "EcoLens: Leveraging Multi-Objective Bayesian Optimization for Energy-Efficient Video Processing on Edge Devices", "abstract": "Video processing for real-time analytics in resource-constrained environments presents a significant challenge in balancing energy consumption and video semantics. This paper addresses the problem of energy-efficient video processing by proposing a system that dynamically optimizes processing configurations to minimize energy usage on the edge, while preserving essential video features for deep learning inference. We first gather an extensive offline profile of various configurations consisting of device CPU frequencies, frame filtering features, difference thresholds, and video bitrates, to establish apriori knowledge of their impact on energy consumption and inference accuracy. Leveraging this insight, we introduce an online system that employs multi-objective Bayesian optimization to intelligently explore and adapt configurations in real time. Our approach continuously refines processing settings to meet a target inference accuracy with minimal edge device energy expenditure. Experimental results demonstrate the system's effectiveness in reducing video processing energy use while maintaining high analytical performance, offering a practical solution for smart devices and edge computing applications.", "date": "2025-05-31", "categories": []}
{"id": "2505.23913", "title": "Simplifying Bayesian Optimization Via In-Context Direct Optimum Sampling", "abstract": "The optimization of expensive black-box functions is ubiquitous in science and engineering. A common solution to this problem is Bayesian optimization (BO), which is generally comprised of two components: (i) a surrogate model and (ii) an acquisition function, which generally require expensive re-training and optimization steps at each iteration, respectively. Although recent work enabled in-context surrogate models that do not require re-training, virtually all existing BO methods still require acquisition function maximization to select the next observation, which introduces many knobs to tune, such as Monte Carlo samplers and multi-start optimizers. In this work, we propose a completely in-context, zero-shot solution for BO that does not require surrogate fitting or acquisition function optimization. This is done by using a pre-trained deep generative model to directly sample from the posterior over the optimum point. We show that this process is equivalent to Thompson sampling and demonstrate the capabilities and cost-effectiveness of our foundation model on a suite of real-world benchmarks. We achieve an efficiency gain of more than 35x in terms of wall-clock time when compared with Gaussian process-based BO, enabling efficient parallel and distributed BO, e.g., for high-throughput optimization.", "date": "2025-05-29", "categories": []}
{"id": "2505.21974", "title": "BOFormer: Learning to Solve Multi-Objective Bayesian Optimization via Non-Markovian RL", "abstract": "Bayesian optimization (BO) offers an efficient pipeline for optimizing black-box functions with the help of a Gaussian process prior and an acquisition function (AF). Recently, in the context of single-objective BO, learning-based AFs witnessed promising empirical results given its favorable non-myopic nature. Despite this, the direct extension of these approaches to multi-objective Bayesian optimization (MOBO) suffer from the \\textit{hypervolume identifiability issue}, which results from the non-Markovian nature of MOBO problems. To tackle this, inspired by the non-Markovian RL literature and the success of Transformers in language modeling, we present a generalized deep Q-learning framework and propose \\textit{BOFormer}, which substantiates this framework for MOBO via sequence modeling. Through extensive evaluation, we demonstrate that BOFormer constantly outperforms the benchmark rule-based and learning-based algorithms in various synthetic MOBO and real-world multi-objective hyperparameter optimization problems. We have made the source code publicly available to encourage further research in this direction.", "date": "2025-05-28", "categories": []}
{"id": "2505.23673", "title": "Bayesian Optimization from Human Feedback: Near-Optimal Regret Bounds", "abstract": "Bayesian optimization (BO) with preference-based feedback has recently garnered significant attention due to its emerging applications. We refer to this problem as Bayesian Optimization from Human Feedback (BOHF), which differs from conventional BO by learning the best actions from a reduced feedback model, where only the preference between two actions is revealed to the learner at each time step. The objective is to identify the best action using a limited number of preference queries, typically obtained through costly human feedback. Existing work, which adopts the Bradley-Terry-Luce (BTL) feedback model, provides regret bounds for the performance of several algorithms. In this work, within the same framework we develop tighter performance guarantees. Specifically, we derive regret bounds of $\\tilde{\\mathcal{O}}(\\sqrt{\\Gamma(T)T})$, where $\\Gamma(T)$ represents the maximum information gain$\\unicode{x2014}$a kernel-specific complexity term$\\unicode{x2014}$and $T$ is the number of queries. Our results significantly improve upon existing bounds. Notably, for common kernels, we show that the order-optimal sample complexities of conventional BO$\\unicode{x2014}$achieved with richer feedback models$\\unicode{x2014}$are recovered. In other words, the same number of preferential samples as scalar-valued samples is sufficient to find a nearly optimal solution.", "date": "2025-05-29", "categories": []}
{"id": "2502.02121", "title": "BILBO: BILevel Bayesian Optimization", "abstract": "Bilevel optimization is characterized by a two-level optimization structure, where the upper-level problem is constrained by optimal lower-level solutions, and such structures are prevalent in real-world problems. The constraint by optimal lower-level solutions poses significant challenges, especially in noisy, constrained, and derivative-free settings, as repeating lower-level optimizations is sample inefficient and predicted lower-level solutions may be suboptimal. We present BILevel Bayesian Optimization (BILBO), a novel Bayesian optimization algorithm for general bilevel problems with blackbox functions, which optimizes both upper- and lower-level problems simultaneously, without the repeated lower-level optimization required by existing methods. BILBO samples from confidence-bounds based trusted sets, which bounds the suboptimality on the lower level. Moreover, BILBO selects only one function query per iteration, where the function query selection strategy incorporates the uncertainty of estimated lower-level solutions and includes a conditional reassignment of the query to encourage exploration of the lower-level objective. The performance of BILBO is theoretically guaranteed with a sublinear regret bound for commonly used kernels and is empirically evaluated on several synthetic and real-world problems.", "date": "2025-02-04", "categories": []}
{"id": "2306.04343", "title": "Bayesian Optimisation Against Climate Change: Applications and Benchmarks", "abstract": "Bayesian optimisation is a powerful method for optimising black-box functions, popular in settings where the true function is expensive to evaluate and no gradient information is available. Bayesian optimisation can improve responses to many optimisation problems within climate change for which simulator models are unavailable or expensive to sample from. While there have been several demonstrations of climate-related applications, there has been no unifying review of applications and benchmarks. We provide such a review here, to encourage the use of Bayesian optimisation for important and well-suited applications. We identify four main application domains: material discovery, wind farm layout, optimal renewable control and environmental monitoring. For each domain we identify a public benchmark or data set that is easy to use and evaluate systems against, while being representative of real-world problems. Due to the lack of a suitable benchmark for environmental monitoring, we propose LAQN-BO, based on air pollution data. Our contributions are: a) summarising Bayesian optimisation applications related to climate change; b) identifying a representative range of benchmarks, providing example code where necessary; and c) introducing a new benchmark, LAQN-BO.", "date": "2023-06-07", "categories": []}
{"id": "2405.07760", "title": "CAGES: Cost-Aware Gradient Entropy Search for Efficient Local Multi-Fidelity Bayesian Optimization", "abstract": "Bayesian optimization (BO) is a popular approach for optimizing expensive-to-evaluate black-box objective functions. An important challenge in BO is its application to high-dimensional search spaces due in large part to the curse of dimensionality. One way to overcome this challenge is to focus on local BO methods that aim to efficiently learn gradients, which have shown strong empirical performance on high-dimensional problems including policy search in reinforcement learning (RL). Current local BO methods assume access to only a single high-fidelity information source whereas, in many problems, one has access to multiple cheaper approximations of the objective. We propose a novel algorithm, Cost-Aware Gradient Entropy Search (CAGES), for local BO of multi-fidelity black-box functions. CAGES makes no assumption about the relationship between different information sources, making it more flexible than other multi-fidelity methods. It also employs a new information-theoretic acquisition function, which enables systematic identification of samples that maximize the information gain about the unknown gradient per evaluation cost. We demonstrate CAGES can achieve significant performance improvements compared to other state-of-the-art methods on synthetic and benchmark RL problems.", "date": "2024-05-13", "categories": []}
{"id": "2505.17151", "title": "Bayesian Optimization for Enhanced Language Models: Optimizing Acquisition Functions", "abstract": "With the rise of different language model architecture, fine-tuning is becoming even more important for down stream tasks Model gets messy, finding proper hyperparameters for fine-tuning. Although BO has been tried for hyperparameter tuning, most of the existing methods are oblivious to the fact that BO relies on careful choices of acquisition functions, which are essential components of BO that guide how much to explore versus exploit during the optimization process; Different acquisition functions have different levels of sensitivity towards training loss and validation performance; existing methods often just apply an acquisition function no matter if the training and validation performance are sensitive to the acquisition function or not. This work introduces{Bilevel - BO - SWA}, a model fusion approach coupled with a bilevel BO strategy to improve the fine - tunning of large language models. Our work on mixture of acquisition functions like EI and UCB into nested opt loops, where inner loop perform minimization of training loss while outer loops optimized w.r.t. val metric. Experiments on GLUE tasks using RoBERTA - base show that when using EI and UCB, there is an improvement in generalization, and fine - tuning can be improved by up to 2.7%.", "date": "2025-05-22", "categories": []}
{"id": "2505.17804", "title": "Hyperparameter Optimization via Interacting with Probabilistic Circuits", "abstract": "Despite the growing interest in designing truly interactive hyperparameter optimization (HPO) methods, to date, only a few allow to include human feedback. Existing interactive Bayesian optimization (BO) methods incorporate human beliefs by weighting the acquisition function with a user-defined prior distribution. However, in light of the non-trivial inner optimization of the acquisition function prevalent in BO, such weighting schemes do not always accurately reflect given user beliefs. We introduce a novel BO approach leveraging tractable probabilistic models named probabilistic circuits (PCs) as a surrogate model. PCs encode a tractable joint distribution over the hybrid hyperparameter space and evaluation scores. They enable exact conditional inference and sampling. Based on conditional sampling, we construct a novel selection policy that enables an acquisition function-free generation of candidate points (thereby eliminating the need for an additional inner-loop optimization) and ensures that user beliefs are reflected accurately in the selection policy. We provide a theoretical analysis and an extensive empirical evaluation, demonstrating that our method achieves state-of-the-art performance in standard HPO and outperforms interactive BO baselines in interactive HPO.", "date": "2025-05-23", "categories": []}
{"id": "2505.12471", "title": "Wasserstein Barycenter Gaussian Process based Bayesian Optimization", "abstract": "Gaussian Process based Bayesian Optimization is a widely applied algorithm to learn and optimize under uncertainty, well-known for its sample efficiency. However, recently -- and more frequently -- research studies have empirically demonstrated that the Gaussian Process fitting procedure at its core could be its most relevant weakness. Fitting a Gaussian Process means tuning its kernel's hyperparameters to a set of observations, but the common Maximum Likelihood Estimation technique, usually appropriate for learning tasks, has shown different criticalities in Bayesian Optimization, making theoretical analysis of this algorithm an open challenge. Exploiting the analogy between Gaussian Processes and Gaussian Distributions, we present a new approach which uses a prefixed set of hyperparameters values to fit as many Gaussian Processes and then combines them into a unique model as a Wasserstein Barycenter of Gaussian Processes. We considered both \"easy\" test problems and others known to undermine the \\textit{vanilla} Bayesian Optimization algorithm. The new method, namely Wasserstein Barycenter Gausssian Process based Bayesian Optimization (WBGP-BO), resulted promising and able to converge to the optimum, contrary to vanilla Bayesian Optimization, also on the most \"tricky\" test problems.", "date": "2025-05-18", "categories": []}
{"id": "2505.10954", "title": "Constrained Preferential Bayesian Optimization and Its Application in Banner Ad Design", "abstract": "Preferential Bayesian optimization (PBO) is a variant of Bayesian optimization that observes relative preferences (e.g., pairwise comparisons) instead of direct objective values, making it especially suitable for human-in-the-loop scenarios. However, real-world optimization tasks often involve inequality constraints, which existing PBO methods have not yet addressed. To fill this gap, we propose constrained preferential Bayesian optimization (CPBO), an extension of PBO that incorporates inequality constraints for the first time. Specifically, we present a novel acquisition function for this purpose. Our technical evaluation shows that our CPBO method successfully identifies optimal solutions by focusing on exploring feasible regions. As a practical application, we also present a designer-in-the-loop system for banner ad design using CPBO, where the objective is the designer's subjective preference, and the constraint ensures a target predicted click-through rate. We conducted a user study with professional ad designers, demonstrating the potential benefits of our approach in guiding creative design under real-world constraints.", "date": "2025-05-16", "categories": []}
{"id": "2505.11281", "title": "Adaptive Linear Embedding for Nonstationary High-Dimensional Optimization", "abstract": "Bayesian Optimization (BO) in high-dimensional spaces remains fundamentally limited by the curse of dimensionality and the rigidity of global low-dimensional assumptions. While Random EMbedding Bayesian Optimization (REMBO) mitigates this via linear projections into low-dimensional subspaces, it typically assumes a single global embedding and a stationary objective. In this work, we introduce Self-Adaptive embedding REMBO (SA-REMBO), a novel framework that generalizes REMBO to support multiple random Gaussian embeddings, each capturing a different local subspace structure of the high-dimensional objective. An index variable governs the embedding choice and is jointly modeled with the latent optimization variable via a product kernel in a Gaussian Process surrogate. This enables the optimizer to adaptively select embeddings conditioned on location, effectively capturing locally varying effective dimensionality, nonstationarity, and heteroscedasticity in the objective landscape. We theoretically analyze the expressiveness and stability of the index-conditioned product kernel and empirically demonstrate the advantage of our method across synthetic and real-world high-dimensional benchmarks, where traditional REMBO and other low-rank BO methods fail. Our results establish SA-REMBO as a powerful and flexible extension for scalable BO in complex, structured design spaces.", "date": "2025-05-16", "categories": []}
{"id": "2304.05341", "title": "Bayesian Optimization of Catalysis With In-Context Learning", "abstract": "Large language models (LLMs) can perform accurate classification with zero or few examples through in-context learning. We extend this capability to regression with uncertainty estimation using frozen LLMs (e.g., GPT-3.5, Gemini), enabling Bayesian optimization (BO) in natural language without explicit model training or feature engineering. We apply this to materials discovery by representing experimental catalyst synthesis and testing procedures as natural language prompts. A key challenge in materials discovery is the need to characterize suboptimal candidates, which slows progress. While BO is effective for navigating large design spaces, standard surrogate models like Gaussian processes assume smoothness and continuity, an assumption that fails in highly non-linear domains such as heterogeneous catalysis. Our task-agnostic BO workflow overcomes this by operating directly in language space, producing interpretable and actionable predictions without requiring structural or electronic descriptors. On benchmarks like aqueous solubility and oxidative coupling of methane (OCM), BO-ICL matches or outperforms Gaussian processes. In live experiments on the reverse water-gas shift (RWGS) reaction, BO-ICL identifies near-optimal multi-metallic catalysts within six iterations from a pool of 3,700 candidates. Our method redefines materials representation and accelerates discovery, with broad applications across catalysis, materials science, and AI. Code: https://github.com/ur-whitelab/BO-ICL.", "date": "2023-04-11", "categories": []}
{"id": "2505.06519", "title": "Interpretable SHAP-bounded Bayesian Optimization for Underwater Acoustic Metamaterial Coating Design", "abstract": "We developed an interpretability informed Bayesian optimization framework to optimize underwater acoustic coatings based on polyurethane elastomers with embedded metamaterial features. A data driven model was employed to analyze the relationship between acoustic performance, specifically sound absorption and the corresponding design variables. By leveraging SHapley Additive exPlanations (SHAP), a machine learning interpretability tool, we identified the key parameters influencing the objective function and gained insights into how these parameters affect sound absorption. The insights derived from the SHAP analysis were subsequently used to automatically refine the bounds of the optimization problem automatically, enabling a more targeted and efficient exploration of the design space.\n  The proposed approach was applied to two polyurethane materials with distinct hardness levels, resulting in improved optimal solutions compared to those obtained without SHAP-informed guidance. Notably, these enhancements were achieved without increasing the number of simulation iterations. Our findings demonstrate the potential of SHAP to streamline optimization processes by uncovering hidden parameter relationships and guiding the search toward promising regions of the design space. This work underscores the effectiveness of combining interpretability techniques with Bayesian optimization for the efficient and cost-effective design of underwater acoustic metamaterials under strict computational constraints and can be generalized towards other materials and engineering optimization problems.", "date": "2025-05-10", "categories": []}
{"id": "2305.11774", "title": "Multi-objective optimisation via the R2 utilities", "abstract": "  The goal of multi-objective optimisation is to identify a collection of\npoints which describe the best possible trade-offs between the multiple\nobjectives. In order to solve this vector-valued optimisation problem,\npractitioners often appeal to the use of scalarisation functions in order to\ntransform the multi-objective problem into a collection of single-objective\nproblems. This set of scalarised problems can then be solved using traditional\nsingle-objective optimisation techniques. In this work, we formalise this\nconvention into a general mathematical framework. We show how this strategy\neffectively recasts the original multi-objective optimisation problem into a\nsingle-objective optimisation problem defined over sets. An appropriate class\nof objective functions for this new problem are the R2 utilities, which are\nutility functions that are defined as a weighted integral over the scalarised\noptimisation problems. As part of our work, we show that these utilities are\nmonotone and submodular set functions which can be optimised effectively using\ngreedy optimisation algorithms. We then analyse the performance of these greedy\nalgorithms both theoretically and empirically. Our analysis largely focusses on\nBayesian optimisation, which is a popular probabilistic framework for black-box\noptimisation.\n", "date": "2023-05-19", "categories": []}
{"id": "2410.06333", "title": "Batched Bayesian optimization by maximizing the probability of including\n  the optimum", "abstract": "  Batched Bayesian optimization (BO) can accelerate molecular design by\nefficiently identifying top-performing compounds from a large chemical library.\nExisting acquisition strategies for batch design in BO aim to balance\nexploration and exploitation. This often involves optimizing non-additive batch\nacquisition functions, necessitating approximation via myopic construction\nand/or diversity heuristics. In this work, we propose an acquisition strategy\nfor discrete optimization that is motivated by pure exploitation, qPO\n(multipoint Probability of Optimality). qPO maximizes the probability that the\nbatch includes the true optimum, which is expressible as the sum over\nindividual acquisition scores and thereby circumvents the combinatorial\nchallenge of optimizing a batch acquisition function. We differentiate the\nproposed strategy from parallel Thompson sampling and discuss how it implicitly\ncaptures diversity. Finally, we apply our method to the model-guided\nexploration of large chemical libraries and provide empirical evidence that it\nis competitive with and complements other state-of-the-art methods in batched\nBayesian optimization.\n", "date": "2024-10-08", "categories": []}
{"id": "2312.02012", "title": "Optimal Data Generation in Multi-Dimensional Parameter Spaces, using\n  Bayesian Optimization", "abstract": "  Acquiring a substantial number of data points for training accurate machine\nlearning (ML) models is a big challenge in scientific fields where data\ncollection is resource-intensive. Here, we propose a novel approach for\nconstructing a minimal yet highly informative database for training ML models\nin complex multi-dimensional parameter spaces. To achieve this, we mimic the\nunderlying relation between the output and input parameters using Gaussian\nprocess regression (GPR). Using a set of known data, GPR provides predictive\nmeans and standard deviation for the unknown data. Given the predicted standard\ndeviation by GPR, we select data points using Bayesian optimization to obtain\nan efficient database for training ML models. We compare the performance of ML\nmodels trained on databases obtained through this method, with databases\nobtained using traditional approaches. Our results demonstrate that the ML\nmodels trained on the database obtained using Bayesian optimization approach\nconsistently outperform the other two databases, achieving high accuracy with a\nsignificantly smaller number of data points. Our work contributes to the\nresource-efficient collection of data in high-dimensional complex parameter\nspaces, to achieve high precision machine learning predictions.\n", "date": "2023-12-04", "categories": []}
{"id": "2503.08555", "title": "An Analysis of Safety Guarantees in Multi-Task Bayesian Optimization", "abstract": "  This paper addresses the integration of additional information sources into a\nBayesian optimization framework while ensuring that safety constraints are\nsatisfied. The interdependencies between these information sources are modeled\nusing an unknown correlation matrix. We explore how uniform error bounds must\nbe adjusted to maintain constraint satisfaction throughout the optimization\nprocess, considering both Bayesian and frequentist statistical perspectives.\nThis is achieved by appropriately scaling the error bounds based on a\nconfidence interval that can be estimated from the data. Furthermore, the\nefficacy of the proposed approach is demonstrated through experiments on two\nbenchmark functions and a controller parameter optimization problem. Our\nresults highlight a significant improvement in sample efficiency, demonstrating\nthe methods suitability for optimizing expensive-to-evaluate functions.\n", "date": "2025-03-11", "categories": []}
{"id": "2412.08085", "title": "Non-Myopic Multi-Objective Bayesian Optimization", "abstract": "  We consider the problem of finite-horizon sequential experimental design to\nsolve multi-objective optimization (MOO) of expensive black-box objective\nfunctions. This problem arises in many real-world applications, including\nmaterials design, where we have a small resource budget to make and evaluate\ncandidate materials in the lab. We solve this problem using the framework of\nBayesian optimization (BO) and propose the first set of non-myopic methods for\nMOO problems. Prior work on non-myopic BO for single-objective problems relies\non the Bellman optimality principle to handle the lookahead reasoning process.\nHowever, this principle does not hold for most MOO problems because the reward\nfunction needs to satisfy some conditions: scalar variable, monotonicity, and\nadditivity. We address this challenge by using hypervolume improvement (HVI) as\nour scalarization approach, which allows us to use a lower-bound on the Bellman\nequation to approximate the finite-horizon using a batch expected hypervolume\nimprovement (EHVI) acquisition function (AF) for MOO. Our formulation naturally\nallows us to use other improvement-based scalarizations and compare their\nefficacy to HVI. We derive three non-myopic AFs for MOBO: 1) the Nested AF,\nwhich is based on the exact computation of the lower bound, 2) the Joint AF,\nwhich is a lower bound on the nested AF, and 3) the BINOM AF, which is a fast\nand approximate variant based on batch multi-objective acquisition functions.\nOur experiments on multiple diverse real-world MO problems demonstrate that our\nnon-myopic AFs substantially improve performance over the existing myopic AFs\nfor MOBO.\n", "date": "2024-12-11", "categories": []}
{"id": "2411.09694", "title": "A Bayesian Optimization Approach to Machine Translation Reranking", "abstract": "  Reranking a list of candidates from a machine translation system with an\nexternal scoring model and returning the highest-scoring candidate remains a\nsimple and effective method for improving the overall output quality.\nTranslation scoring models continue to grow in size, with the best models being\ncomparable to generation models. Thus, reranking can add substantial\ncomputational cost to the translation pipeline. In this work, we pose reranking\nas a Bayesian optimization (BayesOpt) problem. By strategically selecting\ncandidates to score based on a balance of exploration and exploitation, we show\nthat it is possible to find top-scoring candidates when scoring only a fraction\nof the candidate list. For instance, our method achieves the same CometKiwi\nscore using only 70 scoring evaluations compared a baseline system using 180.\nWe present a multi-fidelity setting for BayesOpt, where the candidates are\nfirst scored with a cheaper but noisier proxy scoring model, which further\nimproves the cost-performance tradeoff when using smaller but well-trained\ndistilled proxy scorers.\n", "date": "2024-11-14", "categories": []}
{"id": "2504.20307", "title": "FigBO: A Generalized Acquisition Function Framework with Look-Ahead\n  Capability for Bayesian Optimization", "abstract": "  Bayesian optimization is a powerful technique for optimizing\nexpensive-to-evaluate black-box functions, consisting of two main components: a\nsurrogate model and an acquisition function. In recent years, myopic\nacquisition functions have been widely adopted for their simplicity and\neffectiveness. However, their lack of look-ahead capability limits their\nperformance. To address this limitation, we propose FigBO, a generalized\nacquisition function that incorporates the future impact of candidate points on\nglobal information gain. FigBO is a plug-and-play method that can integrate\nseamlessly with most existing myopic acquisition functions. Theoretically, we\nanalyze the regret bound and convergence rate of FigBO when combined with the\nmyopic base acquisition function expected improvement (EI), comparing them to\nthose of standard EI. Empirically, extensive experimental results across\ndiverse tasks demonstrate that FigBO achieves state-of-the-art performance and\nsignificantly faster convergence compared to existing methods.\n", "date": "2025-04-28", "categories": []}
{"id": "2504.17124", "title": "Demonstration of an AI-driven workflow for dynamic x-ray spectroscopy", "abstract": "  X-ray absorption near edge structure (XANES) spectroscopy is a powerful\ntechnique for characterizing the chemical state and symmetry of individual\nelements within materials, but requires collecting data at many energy points\nwhich can be time-consuming. While adaptive sampling methods exist for\nefficiently collecting spectroscopic data, they often lack domain-specific\nknowledge about XANES spectra structure. Here we demonstrate a\nknowledge-injected Bayesian optimization approach for adaptive XANES data\ncollection that incorporates understanding of spectral features like absorption\nedges and pre-edge peaks. We show this method accurately reconstructs the\nabsorption edge of XANES spectra using only 15-20% of the measurement points\ntypically needed for conventional sampling, while maintaining the ability to\ndetermine the x-ray energy of the sharp peak after absorption edge with errors\nless than 0.03 eV, the absorption edge with errors less than 0.1 eV; and\noverall root-mean-square errors less than 0.005 compared to compared to\ntraditionally sampled spectra. Our experiments on battery materials and\ncatalysts demonstrate the method's effectiveness for both static and dynamic\nXANES measurements, improving data collection efficiency and enabling better\ntime resolution for tracking chemical changes. This approach advances the\ndegree of automation in XANES experiments reducing the common errors of under-\nor over-sampling points in near the absorption edge and enabling dynamic\nexperiments that require high temporal resolution or limited measurement time.\n", "date": "2025-04-23", "categories": []}
{"id": "2411.03641", "title": "Constrained Multi-objective Bayesian Optimization through Optimistic\n  Constraints Estimation", "abstract": "  Multi-objective Bayesian optimization has been widely adopted in scientific\nexperiment design, including drug discovery and hyperparameter optimization. In\npractice, regulatory or safety concerns often impose additional thresholds on\ncertain attributes of the experimental outcomes. Previous work has primarily\nfocused on constrained single-objective optimization tasks or active search\nunder constraints. The existing constrained multi-objective algorithms address\nthe issue with heuristics and approximations, posing challenges to the analysis\nof the sample efficiency. We propose a novel constrained multi-objective\nBayesian optimization algorithm COMBOO that balances active learning of the\nlevel-set defined on multiple unknowns with multi-objective optimization within\nthe feasible region. We provide both theoretical analysis and empirical\nevidence, demonstrating the efficacy of our approach on various synthetic\nbenchmarks and real-world applications.\n", "date": "2024-11-06", "categories": []}
{"id": "2504.14889", "title": "Latent Bayesian Optimization via Autoregressive Normalizing Flows", "abstract": "  Bayesian Optimization (BO) has been recognized for its effectiveness in\noptimizing expensive and complex objective functions. Recent advancements in\nLatent Bayesian Optimization (LBO) have shown promise by integrating generative\nmodels such as variational autoencoders (VAEs) to manage the complexity of\nhigh-dimensional and structured data spaces. However, existing LBO approaches\noften suffer from the value discrepancy problem, which arises from the\nreconstruction gap between input and latent spaces. This value discrepancy\nproblem propagates errors throughout the optimization process, leading to\nsuboptimal outcomes. To address this issue, we propose a Normalizing Flow-based\nBayesian Optimization (NF-BO), which utilizes normalizing flow as a generative\nmodel to establish one-to-one encoding function from the input space to the\nlatent space, along with its left-inverse decoding function, eliminating the\nreconstruction gap. Specifically, we introduce SeqFlow, an autoregressive\nnormalizing flow for sequence data. In addition, we develop a new candidate\nsampling strategy that dynamically adjusts the exploration probability for each\ntoken based on its importance. Through extensive experiments, our NF-BO method\ndemonstrates superior performance in molecule generation tasks, significantly\noutperforming both traditional and recent LBO approaches.\n", "date": "2025-04-21", "categories": []}
{"id": "2504.10770", "title": "Collaborative Bayesian Optimization via Wasserstein Barycenters", "abstract": "  Motivated by the growing need for black-box optimization and data privacy, we\nintroduce a collaborative Bayesian optimization (BO) framework that addresses\nboth of these challenges. In this framework agents work collaboratively to\noptimize a function they only have oracle access to. In order to mitigate\nagainst communication and privacy constraints, agents are not allowed to share\ntheir data but can share their Gaussian process (GP) surrogate models. To\nenable collaboration under these constraints, we construct a central model to\napproximate the objective function by leveraging the concept of Wasserstein\nbarycenters of GPs. This central model integrates the shared models without\naccessing the underlying data. A key aspect of our approach is a collaborative\nacquisition function that balances exploration and exploitation, allowing for\nthe optimization of decision variables collaboratively in each iteration. We\nprove that our proposed algorithm is asymptotically consistent and that its\nimplementation via Monte Carlo methods is numerically accurate. Through\nnumerical experiments, we demonstrate that our approach outperforms other\nbaseline collaborative frameworks and is competitive with centralized\napproaches that do not consider data privacy.\n", "date": "2025-04-15", "categories": []}
{"id": "2504.11353", "title": "An Adaptive Dropout Approach for High-Dimensional Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is a widely used algorithm for solving expensive\nblack-box optimization problems. However, its performance decreases\nsignificantly on high-dimensional problems due to the inherent\nhigh-dimensionality of the acquisition function. In the proposed algorithm, we\nadaptively dropout the variables of the acquisition function along the\niterations. By gradually reducing the dimension of the acquisition function,\nthe proposed approach has less and less difficulty to optimize the acquisition\nfunction. Numerical experiments demonstrate that AdaDropout effectively tackle\nhigh-dimensional challenges and improve solution quality where standard\nBayesian optimization methods often struggle. Moreover, it achieves superior\nresults when compared with state-of-the-art high-dimensional Bayesian\noptimization approaches. This work provides a simple yet efficient solution for\nhigh-dimensional expensive optimization.\n", "date": "2025-04-15", "categories": []}
{"id": "2411.02253", "title": "Towards safe Bayesian optimization with Wiener kernel regression", "abstract": "  Bayesian Optimization (BO) is a data-driven strategy for\nminimizing/maximizing black-box functions based on probabilistic surrogate\nmodels. In the presence of safety constraints, the performance of BO crucially\nrelies on tight probabilistic error bounds related to the uncertainty\nsurrounding the surrogate model. For the case of Gaussian Process surrogates\nand Gaussian measurement noise, we present a novel error bound based on the\nrecently proposed Wiener kernel regression. We prove that under rather mild\nassumptions, the proposed error bound is tighter than bounds previously\ndocumented in the literature, leading to enlarged safety regions. We draw upon\na numerical example to demonstrate the efficacy of the proposed error bound in\nsafe BO.\n", "date": "2024-11-04", "categories": []}
{"id": "2504.08874", "title": "Distilling and exploiting quantitative insights from Large Language\n  Models for enhanced Bayesian optimization of chemical reactions", "abstract": "  Machine learning and Bayesian optimization (BO) algorithms can significantly\naccelerate the optimization of chemical reactions. Transfer learning can\nbolster the effectiveness of BO algorithms in low-data regimes by leveraging\npre-existing chemical information or data outside the direct optimization task\n(i.e., source data). Large language models (LLMs) have demonstrated that\nchemical information present in foundation training data can give them utility\nfor processing chemical data. Furthermore, they can be augmented with and help\nsynthesize potentially multiple modalities of source chemical data germane to\nthe optimization task. In this work, we examine how chemical information from\nLLMs can be elicited and used for transfer learning to accelerate the BO of\nreaction conditions to maximize yield. Specifically, we show that a survey-like\nprompting scheme and preference learning can be used to infer a utility\nfunction which models prior chemical information embedded in LLMs over a\nchemical parameter space; we find that the utility function shows modest\ncorrelation to true experimental measurements (yield) over the parameter space\ndespite operating in a zero-shot setting. Furthermore, we show that the utility\nfunction can be leveraged to focus BO efforts in promising regions of the\nparameter space, improving the yield of the initial BO query and enhancing\noptimization in 4 of the 6 datasets studied. Overall, we view this work as a\nstep towards bridging the gap between the chemistry knowledge embedded in LLMs\nand the capabilities of principled BO methods to accelerate reaction\noptimization.\n", "date": "2025-04-11", "categories": []}
{"id": "2504.09930", "title": "Multi-objective Bayesian Optimization With Mixed-categorical Design\n  Variables for Expensive-to-evaluate Aeronautical Applications", "abstract": "  This work aims at developing new methodologies to optimize computational\ncostly complex systems (e.g., aeronautical engineering systems). The proposed\nsurrogate-based method (often called Bayesian optimization) uses adaptive\nsampling to promote a trade-off between exploration and exploitation. Our\nin-house implementation, called SEGOMOE, handles a high number of design\nvariables (continuous, discrete or categorical) and nonlinearities by combining\nmixtures of experts for the objective and/or the constraints. Additionally, the\nmethod handles multi-objective optimization settings, as it allows the\nconstruction of accurate Pareto fronts with a minimal number of function\nevaluations. Different infill criteria have been implemented to handle multiple\nobjectives with or without constraints. The effectiveness of the proposed\nmethod was tested on practical aeronautical applications within the context of\nthe European Project AGILE 4.0 and demonstrated favorable results. A first\nexample concerns a retrofitting problem where a comparison between two\noptimizers have been made. A second example introduces hierarchical variables\nto deal with architecture system in order to design an aircraft family. The\nthird example increases drastically the number of categorical variables as it\ncombines aircraft design, supply chain and manufacturing process. In this\narticle, we show, on three different realistic problems, various aspects of our\noptimization codes thanks to the diversity of the treated aircraft problems.\n", "date": "2025-04-14", "categories": []}
{"id": "2504.08671", "title": "Regularized infill criteria for multi-objective Bayesian optimization\n  with application to aircraft design", "abstract": "  Bayesian optimization is an advanced tool to perform ecient global\noptimization It consists on enriching iteratively surrogate Kriging models of\nthe objective and the constraints both supposed to be computationally expensive\nof the targeted optimization problem Nowadays efficient extensions of Bayesian\noptimization to solve expensive multiobjective problems are of high interest\nThe proposed method in this paper extends the super efficient global\noptimization with mixture of experts SEGOMOE to solve constrained\nmultiobjective problems To cope with the illposedness of the multiobjective\ninll criteria different enrichment procedures using regularization techniques\nare proposed The merit of the proposed approaches are shown on known\nmultiobjective benchmark problems with and without constraints The proposed\nmethods are then used to solve a biobjective application related to conceptual\naircraft design with ve unknown design variables and three nonlinear inequality\nconstraints The preliminary results show a reduction of the total cost in terms\nof function evaluations by a factor of 20 compared to the evolutionary\nalgorithm NSGA-II.\n", "date": "2025-04-11", "categories": []}
{"id": "2504.08682", "title": "Bayesian optimization for mixed variables using an adaptive dimension\n  reduction process: applications to aircraft design", "abstract": "  Multidisciplinary design optimization methods aim at adapting numerical\noptimization techniques to the design of engineering systems involving multiple\ndisciplines. In this context, a large number of mixed continuous, integer and\ncategorical variables might arise during the optimization process and practical\napplications involve a large number of design variables. Recently, there has\nbeen a growing interest in mixed variables constrained Bayesian optimization\nbut most existing approaches severely increase the number of the\nhyperparameters related to the surrogate model. In this paper, we address this\nissue by constructing surrogate models using less hyperparameters. The\nreduction process is based on the partial least squares method. An adaptive\nprocedure for choosing the number of hyperparameters is proposed. The\nperformance of the proposed approach is confirmed on analytical tests as well\nas two real applications related to aircraft design. A significant improvement\nis obtained compared to genetic algorithms.\n", "date": "2025-04-11", "categories": []}
{"id": "2504.08721", "title": "Surrogate-based optimization of system architectures subject to hidden\n  constraints", "abstract": "  The exploration of novel architectures requires physics-based simulation due\nto a lack of prior experience to start from, which introduces two specific\nchallenges for optimization algorithms: evaluations become more expensive (in\ntime) and evaluations might fail. The former challenge is addressed by\nSurrogate-Based Optimization (SBO) algorithms, in particular Bayesian\nOptimization (BO) using Gaussian Process (GP) models. An overview is provided\nof how BO can deal with challenges specific to architecture optimization, such\nas design variable hierarchy and multiple objectives: specific measures include\nensemble infills and a hierarchical sampling algorithm. Evaluations might fail\ndue to non-convergence of underlying solvers or infeasible geometry in certain\nareas of the design space. Such failed evaluations, also known as hidden\nconstraints, pose a particular challenge to SBO/BO, as the surrogate model\ncannot be trained on empty results. This work investigates various strategies\nfor satisfying hidden constraints in BO algorithms. Three high-level strategies\nare identified: rejection of failed points from the training set, replacing\nfailed points based on viable (non-failed) points, and predicting the failure\nregion. Through investigations on a set of test problems including a jet engine\narchitecture optimization problem, it is shown that best performance is\nachieved with a mixed-discrete GP to predict the Probability of Viability\n(PoV), and by ensuring selected infill points satisfy some minimum PoV\nthreshold. This strategy is demonstrated by solving a jet engine architecture\nproblem that features at 50% failure rate and could not previously be solved by\na BO algorithm. The developed BO algorithm and used test problems are available\nin the open-source Python library SBArchOpt.\n", "date": "2025-04-11", "categories": []}
{"id": "2504.06525", "title": "The Power of the Pareto Front: Balancing Uncertain Rewards for Adaptive\n  Experimentation in scanning probe microscopy", "abstract": "  Automated experimentation has the potential to revolutionize scientific\ndiscovery, but its effectiveness depends on well-defined optimization targets,\nwhich are often uncertain or probabilistic in real-world settings. In this\nwork, we demonstrate the application of Multi-Objective Bayesian Optimization\n(MOBO) to balance multiple, competing rewards in autonomous experimentation.\nUsing scanning probe microscopy (SPM) imaging, one of the most widely used and\nfoundational SPM modes, we show that MOBO can optimize imaging parameters to\nenhance measurement quality, reproducibility, and efficiency. A key advantage\nof this approach is the ability to compute and analyze the Pareto front, which\nnot only guides optimization but also provides physical insights into the\ntrade-offs between different objectives. Additionally, MOBO offers a natural\nframework for human-in-the-loop decision-making, enabling researchers to\nfine-tune experimental trade-offs based on domain expertise. By standardizing\nhigh-quality, reproducible measurements and integrating human input into\nAI-driven optimization, this work highlights MOBO as a powerful tool for\nadvancing autonomous scientific discovery.\n", "date": "2025-04-09", "categories": []}
{"id": "2406.17811", "title": "CATBench: A Compiler Autotuning Benchmarking Suite for Black-box\n  Optimization", "abstract": "  Bayesian optimization is a powerful method for automating tuning of\ncompilers. The complex landscape of autotuning provides a myriad of rarely\nconsidered structural challenges for black-box optimizers, and the lack of\nstandardized benchmarks has limited the study of Bayesian optimization within\nthe domain. To address this, we present CATBench, a comprehensive benchmarking\nsuite that captures the complexities of compiler autotuning, ranging from\ndiscrete, conditional, and permutation parameter types to known and unknown\nbinary constraints, as well as both multi-fidelity and multi-objective\nevaluations. The benchmarks in CATBench span a range of machine\nlearning-oriented computations, from tensor algebra to image processing and\nclustering, and uses state-of-the-art compilers, such as TACO and RISE/ELEVATE.\nCATBench offers a unified interface for evaluating Bayesian optimization\nalgorithms, promoting reproducibility and innovation through an easy-to-use,\nfully containerized setup of both surrogate and real-world compiler\noptimization tasks. We validate CATBench on several state-of-the-art\nalgorithms, revealing their strengths and weaknesses and demonstrating the\nsuite's potential for advancing both Bayesian optimization and compiler\nautotuning research.\n", "date": "2024-06-24", "categories": []}
{"id": "2504.06111", "title": "Leveraging Axis-Aligned Subspaces for High-Dimensional Bayesian\n  Optimization with Group Testing", "abstract": "  Bayesian optimization (BO ) is an effective method for optimizing\nexpensive-to-evaluate black-box functions. While high-dimensional problems can\nbe particularly challenging, due to the multitude of parameter choices and the\npotentially high number of data points required to fit the model, this\nlimitation can be addressed if the problem satisfies simplifying assumptions.\nAxis-aligned subspace approaches, where few dimensions have a significant\nimpact on the objective, motivated several algorithms for high-dimensional BO .\nHowever, the validity of this assumption is rarely verified, and the assumption\nis rarely exploited to its full extent. We propose a group testing ( GT)\napproach to identify active variables to facilitate efficient optimization in\nthese domains. The proposed algorithm, Group Testing Bayesian Optimization\n(GTBO), first runs a testing phase where groups of variables are systematically\nselected and tested on whether they influence the objective, then terminates\nonce active dimensions are identified. To that end, we extend the\nwell-established GT theory to functions over continuous domains. In the second\nphase, GTBO guides optimization by placing more importance on the active\ndimensions. By leveraging the axis-aligned subspace assumption, GTBO\noutperforms state-of-the-art methods on benchmarks satisfying the assumption of\naxis-aligned subspaces, while offering improved interpretability.\n", "date": "2025-04-08", "categories": []}
{"id": "2504.04244", "title": "From Automation to Autonomy in Smart Manufacturing: A Bayesian\n  Optimization Framework for Modeling Multi-Objective Experimentation and\n  Sequential Decision Making", "abstract": "  Discovering novel materials with desired properties is essential for driving\ninnovation. Industry 4.0 and smart manufacturing have promised transformative\nadvances in this area through real-time data integration and automated\nproduction planning and control. However, the reliance on automation alone has\noften fallen short, lacking the flexibility needed for complex processes. To\nfully unlock the potential of smart manufacturing, we must evolve from\nautomation to autonomous systems that go beyond rigid programming and can\ndynamically optimize the search for solutions. Current discovery approaches are\noften slow, requiring numerous trials to find optimal combinations, and costly,\nparticularly when optimizing multiple properties simultaneously. This paper\nproposes a Bayesian multi-objective sequential decision-making (BMSDM)\nframework that can intelligently select experiments as manufacturing\nprogresses, guiding us toward the discovery of optimal design faster and more\nefficiently. The framework leverages sequential learning through Bayesian\nOptimization, which iteratively refines a statistical model representing the\nunderlying manufacturing process. This statistical model acts as a surrogate,\nallowing for efficient exploration and optimization without requiring numerous\nreal-world experiments. This approach can significantly reduce the time and\ncost of data collection required by traditional experimental designs. The\nproposed framework is compared with traditional DoE methods and two other\nmulti-objective optimization methods. Using a manufacturing dataset, we\nevaluate and compare the performance of these approaches across five evaluation\nmetrics. BMSDM comprehensively outperforms the competing methods in\nmulti-objective decision-making scenarios. Our proposed approach represents a\nsignificant leap forward in creating an intelligent autonomous platform capable\nof novel material discovery.\n", "date": "2025-04-05", "categories": []}
{"id": "2410.23148", "title": "Navigating in High-Dimensional Search Space: A Hierarchical Bayesian\n  Optimization Approach", "abstract": "  Optimizing black-box functions in high-dimensional search spaces has been\nknown to be challenging for traditional Bayesian Optimization (BO). In this\npaper, we introduce HiBO, a novel hierarchical algorithm integrating\nglobal-level search space partitioning information into the acquisition\nstrategy of a local BO-based optimizer. HiBO employs a search-tree-based\nglobal-level navigator to adaptively split the search space into partitions\nwith different sampling potential. The local optimizer then utilizes this\nglobal-level information to guide its acquisition strategy towards most\npromising regions within the search space. A comprehensive set of evaluations\ndemonstrates that HiBO outperforms state-of-the-art methods in high-dimensional\nsynthetic benchmarks and presents significant practical effectiveness in the\nreal-world task of tuning configurations of database management systems\n(DBMSs).\n", "date": "2024-10-30", "categories": []}
{"id": "2504.01743", "title": "High Dimensional Bayesian Optimization using Lasso Variable Selection", "abstract": "  Bayesian optimization (BO) is a leading method for optimizing expensive\nblack-box optimization and has been successfully applied across various\nscenarios. However, BO suffers from the curse of dimensionality, making it\nchallenging to scale to high-dimensional problems. Existing work has adopted a\nvariable selection strategy to select and optimize only a subset of variables\niteratively. Although this approach can mitigate the high-dimensional challenge\nin BO, it still leads to sample inefficiency. To address this issue, we\nintroduce a novel method that identifies important variables by estimating the\nlength scales of Gaussian process kernels. Next, we construct an effective\nsearch region consisting of multiple subspaces and optimize the acquisition\nfunction within this region, focusing on only the important variables. We\ndemonstrate that our proposed method achieves cumulative regret with a\nsublinear growth rate in the worst case while maintaining computational\nefficiency. Experiments on high-dimensional synthetic functions and real-world\nproblems show that our method achieves state-of-the-art performance.\n", "date": "2025-04-02", "categories": []}
{"id": "2410.22322", "title": "Optimizing Posterior Samples for Bayesian Optimization via Rootfinding", "abstract": "  Bayesian optimization devolves the global optimization of a costly objective\nfunction to the global optimization of a sequence of acquisition functions.\nThis inner-loop optimization can be catastrophically difficult if it involves\nposterior sample paths, especially in higher dimensions. We introduce an\nefficient global optimization strategy for posterior samples based on global\nrootfinding. It provides gradient-based optimizers with two sets of judiciously\nselected starting points, designed to combine exploration and exploitation. The\nnumber of starting points can be kept small without sacrificing optimization\nquality. Remarkably, even with just one point from each set, the global optimum\nis discovered most of the time. The algorithm scales practically linearly to\nhigh dimensions, breaking the curse of dimensionality. For Gaussian process\nThompson sampling (GP-TS), we demonstrate remarkable improvement in both inner-\nand outer-loop optimization, surprisingly outperforming alternatives like EI\nand GP-UCB in most cases. Our approach also improves the performance of other\nposterior sample-based acquisition functions, such as variants of entropy\nsearch. Furthermore, we propose a sample-average formulation of GP-TS, which\nhas a parameter to explicitly control exploitation and can be computed at the\ncost of one posterior sample. Our implementation is available at\nhttps://github.com/UQUH/TSRoots .\n", "date": "2024-10-29", "categories": []}
{"id": "2411.17387", "title": "Robust Bayesian Optimization via Localized Online Conformal Prediction", "abstract": "  Bayesian optimization (BO) is a sequential approach for optimizing black-box\nobjective functions using zeroth-order noisy observations. In BO, Gaussian\nprocesses (GPs) are employed as probabilistic surrogate models to estimate the\nobjective function based on past observations, guiding the selection of future\nqueries to maximize utility. However, the performance of BO heavily relies on\nthe quality of these probabilistic estimates, which can deteriorate\nsignificantly under model misspecification. To address this issue, we introduce\nlocalized online conformal prediction-based Bayesian optimization (LOCBO), a BO\nalgorithm that calibrates the GP model through localized online conformal\nprediction (CP). LOCBO corrects the GP likelihood based on predictive sets\nproduced by LOCBO, and the corrected GP likelihood is then denoised to obtain a\ncalibrated posterior distribution on the objective function. The likelihood\ncalibration step leverages an input-dependent calibration threshold to tailor\ncoverage guarantees to different regions of the input space. Under minimal\nnoise assumptions, we provide theoretical performance guarantees for LOCBO's\niterates that hold for the unobserved objective function. These theoretical\nfindings are validated through experiments on synthetic and real-world\noptimization tasks, demonstrating that LOCBO consistently outperforms\nstate-of-the-art BO algorithms in the presence of model misspecification.\n", "date": "2024-11-26", "categories": []}
{"id": "2406.13425", "title": "Coupled Input-Output Dimension Reduction: Application to Goal-oriented\n  Bayesian Experimental Design and Global Sensitivity Analysis", "abstract": "  We introduce a new method to jointly reduce the dimension of the input and\noutput space of a function between high-dimensional spaces. Choosing a reduced\ninput subspace influences which output subspace is relevant and vice versa.\nConventional methods focus on reducing either the input or output space, even\nthough both are often reduced simultaneously in practice. Our coupled approach\nnaturally supports goal-oriented dimension reduction, where either an input or\noutput quantity of interest is prescribed. We consider, in particular,\ngoal-oriented sensor placement and goal-oriented sensitivity analysis, which\ncan be viewed as dimension reduction where the most important output or,\nrespectively, input components are chosen. Both applications present difficult\ncombinatorial optimization problems with expensive objectives such as the\nexpected information gain and Sobol' indices. By optimizing gradient-based\nbounds, we can determine the most informative sensors and most influential\nparameters as the largest diagonal entries of some diagnostic matrices, thus\nbypassing the combinatorial optimization and objective evaluation.\n", "date": "2024-06-19", "categories": []}
{"id": "2503.20341", "title": "Wasserstein Distributionally Robust Bayesian Optimization with\n  Continuous Context", "abstract": "  We address the challenge of sequential data-driven decision-making under\ncontext distributional uncertainty. This problem arises in numerous real-world\nscenarios where the learner optimizes black-box objective functions in the\npresence of uncontrollable contextual variables. We consider the setting where\nthe context distribution is uncertain but known to lie within an ambiguity set\ndefined as a ball in the Wasserstein distance. We propose a novel algorithm for\nWasserstein Distributionally Robust Bayesian Optimization that can handle\ncontinuous context distributions while maintaining computational tractability.\nOur theoretical analysis combines recent results in self-normalized\nconcentration in Hilbert spaces and finite-sample bounds for distributionally\nrobust optimization to establish sublinear regret bounds that match\nstate-of-the-art results. Through extensive comparisons with existing\napproaches on both synthetic and real-world problems, we demonstrate the\nsimplicity, effectiveness, and practical applicability of our proposed method.\n", "date": "2025-03-26", "categories": []}
{"id": "2503.19479", "title": "Bayesian Optimization of a Lightweight and Accurate Neural Network for\n  Aerodynamic Performance Prediction", "abstract": "  Ensuring high accuracy and efficiency of predictive models is paramount in\nthe aerospace industry, particularly in the context of multidisciplinary design\nand optimization processes. These processes often require numerous evaluations\nof complex objective functions, which can be computationally expensive and\ntime-consuming. To build efficient and accurate predictive models, we propose a\nnew approach that leverages Bayesian Optimization (BO) to optimize the\nhyper-parameters of a lightweight and accurate Neural Network (NN) for\naerodynamic performance prediction. To clearly describe the interplay between\ndesign variables, hierarchical and categorical kernels are used in the BO\nformulation. We demonstrate the efficiency of our approach through two\ncomprehensive case studies, where the optimized NN significantly outperforms\nbaseline models and other publicly available NNs in terms of accuracy and\nparameter efficiency. For the drag coefficient prediction task, the Mean\nAbsolute Percentage Error (MAPE) of our optimized model drops from 0.1433\\% to\n0.0163\\%, which is nearly an order of magnitude improvement over the baseline\nmodel. Additionally, our model achieves a MAPE of 0.82\\% on a benchmark\naircraft self-noise prediction problem, significantly outperforming existing\nmodels (where their MAPE values are around 2 to 3\\%) while requiring less\ncomputational resources. The results highlight the potential of our framework\nto enhance the scalability and performance of NNs in large-scale MDO problems,\noffering a promising solution for the aerospace industry.\n", "date": "2025-03-25", "categories": []}
{"id": "2503.19554", "title": "Causal Bayesian Optimization with Unknown Graphs", "abstract": "  Causal Bayesian Optimization (CBO) is a methodology designed to optimize an\noutcome variable by leveraging known causal relationships through targeted\ninterventions. Traditional CBO methods require a fully and accurately specified\ncausal graph, which is a limitation in many real-world scenarios where such\ngraphs are unknown. To address this, we propose a new method for the CBO\nframework that operates without prior knowledge of the causal graph. Consistent\nwith causal bandit theory, we demonstrate through theoretical analysis and that\nfocusing on the direct causal parents of the target variable is sufficient for\noptimization, and provide empirical validation in the context of CBO.\nFurthermore we introduce a new method that learns a Bayesian posterior over the\ndirect parents of the target variable. This allows us to optimize the outcome\nvariable while simultaneously learning the causal structure. Our contributions\ninclude a derivation of the closed-form posterior distribution for the linear\ncase. In the nonlinear case where the posterior is not tractable, we present a\nGaussian Process (GP) approximation that still enables CBO by inferring the\nparents of the outcome variable. The proposed method performs competitively\nwith existing benchmarks and scales well to larger graphs, making it a\npractical tool for real-world applications where causal information is\nincomplete.\n", "date": "2025-03-25", "categories": []}
{"id": "2306.14348", "title": "Collaborative and Distributed Bayesian Optimization via Consensus:\n  Showcasing the Power of Collaboration for Optimal Design", "abstract": "  Optimal design is a critical yet challenging task within many applications.\nThis challenge arises from the need for extensive trial and error, often done\nthrough simulations or running field experiments. Fortunately, sequential\noptimal design, also referred to as Bayesian optimization when using surrogates\nwith a Bayesian flavor, has played a key role in accelerating the design\nprocess through efficient sequential sampling strategies. However, a key\nopportunity exists nowadays. The increased connectivity of edge devices sets\nforth a new collaborative paradigm for Bayesian optimization. A paradigm\nwhereby different clients collaboratively borrow strength from each other by\neffectively distributing their experimentation efforts to improve and\nfast-track their optimal design process. To this end, we bring the notion of\nconsensus to Bayesian optimization, where clients agree (i.e., reach a\nconsensus) on their next-to-sample designs. Our approach provides a generic and\nflexible framework that can incorporate different collaboration mechanisms. In\nlieu of this, we propose transitional collaborative mechanisms where clients\ninitially rely more on each other to maneuver through the early stages with\nscant data, then, at the late stages, focus on their own objectives to get\nclient-specific solutions. Theoretically, we show the sub-linear growth in\nregret for our proposed framework. Empirically, through simulated datasets and\na real-world collaborative sensor design experiment, we show that our framework\ncan effectively accelerate and improve the optimal design process and benefit\nall participants.\n", "date": "2023-06-25", "categories": []}
{"id": "2503.01126", "title": "Constrained multi-fidelity Bayesian optimization with automatic stop\n  condition", "abstract": "  Bayesian optimization (BO) is increasingly employed in critical applications\nto find the optimal design with minimal cost. While BO is known for its sample\nefficiency, relying solely on costly high-fidelity data can still result in\nhigh costs. This is especially the case in constrained search spaces where BO\nmust not only optimize but also ensure feasibility. A related issue in the BO\nliterature is the lack of a systematic stopping criterion. To solve these\nchallenges, we develop a constrained cost-aware multi-fidelity BO (CMFBO)\nframework whose goal is to minimize overall sampling costs by utilizing\ninexpensive low-fidelity sources while ensuring feasibility. In our case, the\nconstraints can change across the data sources and may be even black-box\nfunctions. We also introduce a systematic stopping criterion that addresses the\nlong-lasting issue associated with BO's convergence assessment. Our framework\nis publicly available on GitHub through the GP+ Python package and herein we\nvalidate it's efficacy on multiple benchmark problems.\n", "date": "2025-03-03", "categories": []}
{"id": "2301.05620", "title": "Optimizing Facial Expressions of an Android Robot Effectively: a\n  Bayesian Optimization Approach", "abstract": "  Expressing various facial emotions is an important social ability for\nefficient communication between humans. A key challenge in human-robot\ninteraction research is providing androids with the ability to make various\nhuman-like facial expressions for efficient communication with humans. The\nandroid Nikola, we have developed, is equipped with many actuators for facial\nmuscle control. While this enables Nikola to simulate various human\nexpressions, it also complicates identification of the optimal parameters for\nproducing desired expressions. Here, we propose a novel method that\nautomatically optimizes the facial expressions of our android. We use a machine\nvision algorithm to evaluate the magnitudes of seven basic emotions, and employ\nthe Bayesian Optimization algorithm to identify the parameters that produce the\nmost convincing facial expressions. Evaluations by naive human participants\ndemonstrate that our method improves the rated strength of the android's facial\nexpressions of anger, disgust, sadness, and surprise compared with the previous\nmethod that relied on Ekman's theory and parameter adjustments by a human\nexpert.\n", "date": "2023-01-13", "categories": []}
{"id": "2503.15928", "title": "Sample-Efficient Bayesian Transfer Learning for Online Machine Parameter\n  Optimization", "abstract": "  Correctly setting the parameters of a production machine is essential to\nimprove product quality, increase efficiency, and reduce production costs while\nalso supporting sustainability goals. Identifying optimal parameters involves\nan iterative process of producing an object and evaluating its quality.\nMinimizing the number of iterations is, therefore, desirable to reduce the\ncosts associated with unsuccessful attempts. This work introduces a method to\noptimize the machine parameters in the system itself using a Bayesian\noptimization algorithm. By leveraging existing machine data, we use a transfer\nlearning approach in order to identify an optimum with minimal iterations,\nresulting in a cost-effective transfer learning algorithm. We validate our\napproach on a laser machine for cutting sheet metal in the real world.\n", "date": "2025-03-20", "categories": []}
{"id": "2503.16841", "title": "Preferential Multi-Objective Bayesian Optimization for Drug Discovery", "abstract": "  Despite decades of advancements in automated ligand screening, large-scale\ndrug discovery remains resource-intensive and requires post-processing hit\nselection, a step where chemists manually select a few promising molecules\nbased on their chemical intuition. This creates a major bottleneck in the\nvirtual screening process for drug discovery, demanding experts to repeatedly\nbalance complex trade-offs among drug properties across a vast pool of\ncandidates. To improve the efficiency and reliability of this process, we\npropose a novel human-centered framework named CheapVS that allows chemists to\nguide the ligand selection process by providing preferences regarding the\ntrade-offs between drug properties via pairwise comparison. Our framework\ncombines preferential multi-objective Bayesian optimization with a docking\nmodel for measuring binding affinity to capture human chemical intuition for\nimproving hit identification. Specifically, on a library of 100K chemical\ncandidates targeting EGFR and DRD2, CheapVS outperforms state-of-the-art\nscreening methods in identifying drugs within a limited computational budget.\nNotably, our method can recover up to 16/37 EGFR and 37/58 DRD2 known drugs\nwhile screening only 6% of the library, showcasing its potential to\nsignificantly advance drug discovery.\n", "date": "2025-03-21", "categories": []}
{"id": "2410.11826", "title": "Bayesian Experimental Design via Contrastive Diffusions", "abstract": "  Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the\ncost of running a sequence of experiments. When based on the Expected\nInformation Gain (EIG), design optimization corresponds to the maximization of\nsome intractable expected contrast between prior and posterior distributions.\nScaling this maximization to high dimensional and complex settings has been an\nissue due to BOED inherent computational complexity. In this work, we introduce\na pooled posterior distribution with cost-effective sampling properties and\nprovide a tractable access to the EIG contrast maximization via a new EIG\ngradient expression. Diffusion-based samplers are used to compute the dynamics\nof the pooled posterior and ideas from bi-level optimization are leveraged to\nderive an efficient joint sampling-optimization loop. The resulting efficiency\ngain allows to extend BOED to the well-tested generative capabilities of\ndiffusion models. By incorporating generative models into the BOED framework,\nwe expand its scope and its use in scenarios that were previously impractical.\nNumerical experiments and comparison with state-of-the-art methods show the\npotential of the approach.\n", "date": "2024-10-15", "categories": []}
{"id": "2503.10352", "title": "Safe exploration in reproducing kernel Hilbert spaces", "abstract": "  Popular safe Bayesian optimization (BO) algorithms learn control policies for\nsafety-critical systems in unknown environments. However, most algorithms make\na smoothness assumption, which is encoded by a known bounded norm in a\nreproducing kernel Hilbert space (RKHS). The RKHS is a potentially\ninfinite-dimensional space, and it remains unclear how to reliably obtain the\nRKHS norm of an unknown function. In this work, we propose a safe BO algorithm\ncapable of estimating the RKHS norm from data. We provide statistical\nguarantees on the RKHS norm estimation, integrate the estimated RKHS norm into\nexisting confidence intervals and show that we retain theoretical guarantees,\nand prove safety of the resulting safe BO algorithm. We apply our algorithm to\nsafely optimize reinforcement learning policies on physics simulators and on a\nreal inverted pendulum, demonstrating improved performance, safety, and\nscalability compared to the state-of-the-art.\n", "date": "2025-03-13", "categories": []}
{"id": "2402.02746", "title": "Standard Gaussian Process is All You Need for High-Dimensional Bayesian\n  Optimization", "abstract": "  A long-standing belief holds that Bayesian Optimization (BO) with standard\nGaussian processes (GP) -- referred to as standard BO -- underperforms in\nhigh-dimensional optimization problems. While this belief seems plausible, it\nlacks both robust empirical evidence and theoretical justification. To address\nthis gap, we present a systematic investigation. First, through a comprehensive\nevaluation across twelve benchmarks, we found that while the popular Square\nExponential (SE) kernel often leads to poor performance, using Mat\\'ern kernels\nenables standard BO to consistently achieve top-tier results, frequently\nsurpassing methods specifically designed for high-dimensional optimization.\nSecond, our theoretical analysis reveals that the SE kernel's failure primarily\nstems from improper initialization of the length-scale parameters, which are\ncommonly used in practice but can cause gradient vanishing in training. We\nprovide a probabilistic bound to characterize this issue, showing that Mat\\'ern\nkernels are less susceptible and can robustly handle much higher dimensions.\nThird, we propose a simple robust initialization strategy that dramatically\nimproves the performance of the SE kernel, bringing it close to\nstate-of-the-art methods, without requiring additional priors or\nregularization. We prove another probabilistic bound that demonstrates how the\ngradient vanishing issue can be effectively mitigated with our method. Our\nfindings advocate for a re-evaluation of standard BO's potential in\nhigh-dimensional settings.\n", "date": "2024-02-05", "categories": []}
{"id": "2402.11345", "title": "Variational Entropy Search for Adjusting Expected Improvement", "abstract": "  Bayesian optimization is a widely used technique for optimizing black-box\nfunctions, with Expected Improvement (EI) being the most commonly utilized\nacquisition function in this domain. While EI is often viewed as distinct from\nother information-theoretic acquisition functions, such as entropy search (ES)\nand max-value entropy search (MES), our work reveals that EI can be considered\na special case of MES when approached through variational inference (VI). In\nthis context, we have developed the Variational Entropy Search (VES)\nmethodology and the VES-Gamma algorithm, which adapts EI by incorporating\nprinciples from information-theoretic concepts. The efficacy of VES-Gamma is\ndemonstrated across a variety of test functions and read datasets, highlighting\nits theoretical and practical utilities in Bayesian optimization scenarios.\n", "date": "2024-02-17", "categories": []}
{"id": "2503.06093", "title": "Clustering-based Meta Bayesian Optimization with Theoretical Guarantee", "abstract": "  Bayesian Optimization (BO) is a well-established method for addressing\nblack-box optimization problems. In many real-world scenarios, optimization\noften involves multiple functions, emphasizing the importance of leveraging\ndata and learned functions from prior tasks to enhance efficiency in the\ncurrent task. To expedite convergence to the global optimum, recent studies\nhave introduced meta-learning strategies, collectively referred to as meta-BO,\nto incorporate knowledge from historical tasks. However, in practical settings,\nthe underlying functions are often heterogeneous, which can adversely affect\noptimization performance for the current task. Additionally, when the number of\nhistorical tasks is large, meta-BO methods face significant scalability\nchallenges. In this work, we propose a scalable and robust meta-BO method\ndesigned to address key challenges in heterogeneous and large-scale meta-tasks.\nOur approach (1) effectively partitions transferred meta-functions into highly\nhomogeneous clusters, (2) learns the geometry-based surrogate prototype that\ncapture the structural patterns within each cluster, and (3) adaptively\nsynthesizes meta-priors during the online phase using statistical\ndistance-based weighting policies. Experimental results on real-world\nhyperparameter optimization (HPO) tasks, combined with theoretical guarantees,\ndemonstrate the robustness and effectiveness of our method in overcoming these\nchallenges.\n", "date": "2025-03-08", "categories": []}
{"id": "2302.01310", "title": "Knowledge Gradient for Multi-Objective Bayesian Optimization with\n  Decoupled Evaluations", "abstract": "  Multi-objective Bayesian optimization aims to find the Pareto front of\ntrade-offs between a set of expensive objectives while collecting as few\nsamples as possible. In some cases, it is possible to evaluate the objectives\nseparately, and a different latency or evaluation cost can be associated with\neach objective. This decoupling of the objectives presents an opportunity to\nlearn the Pareto front faster by avoiding unnecessary, expensive evaluations.\nWe propose a scalarization based knowledge gradient acquisition function which\naccounts for the different evaluation costs of the objectives. We prove\nasymptotic consistency of the estimator of the optimum for an arbitrary,\nD-dimensional, real compact search space and show empirically that the\nalgorithm performs comparably with the state of the art and significantly\noutperforms versions which always evaluate both objectives.\n", "date": "2023-02-02", "categories": []}
{"id": "2503.00420", "title": "A physics-informed Bayesian optimization method for rapid development of\n  electrical machines", "abstract": "  Advanced slot and winding designs are imperative to create future high\nperformance electrical machines (EM). As a result, the development of methods\nto design and improve slot filling factor (SFF) has attracted considerable\nresearch. Recent developments in manufacturing processes, such as additive\nmanufacturing and alternative materials, has also highlighted a need for novel\nhigh-fidelity design techniques to develop high performance complex geometries\nand topologies. This study therefore introduces a novel physics-informed\nmachine learning (PIML) design optimization process for improving SFF in\ntraction electrical machines used in electric vehicles. A maximum entropy\nsampling algorithm (MESA) is used to seed a physics-informed Bayesian\noptimization (PIBO) algorithm, where the target function and its approximations\nare produced by Gaussian processes (GP)s. The proposed PIBO-MESA is coupled\nwith a 2D finite element model (FEM) to perform a GP-based surrogate and\nprovide the first demonstration of the optimal combination of complex design\nvariables for an electrical machine. Significant computational gains were\nachieved using the new PIBO-MESA approach, which is 45% faster than existing\nstochastic methods, such as the non-dominated sorting genetic algorithm II\n(NSGA-II). The FEM results confirm that the new design optimization process and\nkeystone shaped wires lead to a higher SFF (i.e. by 20%) and electromagnetic\nimprovements (e.g. maximum torque by 12%) with similar resistivity. The newly\ndeveloped PIBO-MESA design optimization process therefore presents significant\nbenefits in the design of high-performance electric machines, with reduced\ndevelopment time and costs.\n", "date": "2025-03-01", "categories": []}
{"id": "2503.00924", "title": "PABBO: Preferential Amortized Black-Box Optimization", "abstract": "  Preferential Bayesian Optimization (PBO) is a sample-efficient method to\nlearn latent user utilities from preferential feedback over a pair of designs.\nIt relies on a statistical surrogate model for the latent function, usually a\nGaussian process, and an acquisition strategy to select the next candidate pair\nto get user feedback on. Due to the non-conjugacy of the associated likelihood,\nevery PBO step requires a significant amount of computations with various\napproximate inference techniques. This computational overhead is incompatible\nwith the way humans interact with computers, hindering the use of PBO in\nreal-world cases. Building on the recent advances of amortized BO, we propose\nto circumvent this issue by fully amortizing PBO, meta-learning both the\nsurrogate and the acquisition function. Our method comprises a novel\ntransformer neural process architecture, trained using reinforcement learning\nand tailored auxiliary losses. On a benchmark composed of synthetic and\nreal-world datasets, our method is several orders of magnitude faster than the\nusual Gaussian process-based strategies and often outperforms them in accuracy.\n", "date": "2025-03-02", "categories": []}
{"id": "2301.12822", "title": "Evaluating COVID-19 vaccine allocation policies using Bayesian $m$-top\n  exploration", "abstract": "  Individual-based epidemiological models support the study of fine-grained\npreventive measures, such as tailored vaccine allocation policies, in silico.\nAs individual-based models are computationally intensive, it is pivotal to\nidentify optimal strategies within a reasonable computational budget. Moreover,\ndue to the high societal impact associated with the implementation of\npreventive strategies, uncertainty regarding decisions should be communicated\nto policy makers, which is naturally embedded in a Bayesian approach.\n  We present a novel technique for evaluating vaccine allocation strategies\nusing a multi-armed bandit framework in combination with a Bayesian anytime\n$m$-top exploration algorithm. $m$-top exploration allows the algorithm to\nlearn $m$ policies for which it expects the highest utility, enabling experts\nto inspect this small set of alternative strategies, along with their\nquantified uncertainty. The anytime component provides policy advisors with\nflexibility regarding the computation time and the desired confidence, which is\nimportant as it is difficult to make this trade-off beforehand.\n  We consider the Belgian COVID-19 epidemic using the individual-based model\nSTRIDE, where we learn a set of vaccination policies that minimize the number\nof infections and hospitalisations. Through experiments we show that our method\ncan efficiently identify the $m$-top policies, which is validated in a scenario\nwhere the ground truth is available. Finally, we explore how vaccination\npolicies can best be organised under different contact reduction schemes and we\ninvestigate the impact of vaccine uptake proportions (i.e., the proportion of\nindividuals that will comply with the strategy and take the vaccine).\n", "date": "2023-01-30", "categories": []}
{"id": "2502.18966", "title": "One Set to Rule Them All: How to Obtain General Chemical Conditions via\n  Bayesian Optimization over Curried Functions", "abstract": "  General parameters are highly desirable in the natural sciences - e.g.,\nchemical reaction conditions that enable high yields across a range of related\ntransformations. This has a significant practical impact since those general\nparameters can be transferred to related tasks without the need for laborious\nand time-intensive re-optimization. While Bayesian optimization (BO) is widely\napplied to find optimal parameter sets for specific tasks, it has remained\nunderused in experiment planning towards such general optima. In this work, we\nconsider the real-world problem of condition optimization for chemical\nreactions to study how performing generality-oriented BO can accelerate the\nidentification of general optima, and whether these optima also translate to\nunseen examples. This is achieved through a careful formulation of the problem\nas an optimization over curried functions, as well as systematic evaluations of\ngenerality-oriented strategies for optimization tasks on real-world\nexperimental data. We find that for generality-oriented optimization, simple\nmyopic optimization strategies that decouple parameter and task selection\nperform comparably to more complex ones, and that effective optimization is\nmerely determined by an effective exploration of both parameter and task space.\n", "date": "2025-02-26", "categories": []}
{"id": "2402.01632", "title": "Time-Varying Gaussian Process Bandits with Unknown Prior", "abstract": "  Bayesian optimisation requires fitting a Gaussian process model, which in\nturn requires specifying prior on the unknown black-box function -- most of the\ntheoretical literature assumes this prior is known. However, it is common to\nhave more than one possible prior for a given black-box function, for example\nsuggested by domain experts with differing opinions. In some cases, the type-II\nmaximum likelihood estimator for selecting prior enjoys the consistency\nguarantee, but it does not universally apply to all types of priors. If the\nproblem is stationary, one could rely on the Regret Balancing scheme to conduct\nthe optimisation, but in the case of time-varying problems, such a scheme\ncannot be used. To address this gap in existing research, we propose a novel\nalgorithm, PE-GP-UCB, which is capable of solving time-varying Bayesian\noptimisation problems even without the exact knowledge of the function's prior.\nThe algorithm relies on the fact that either the observed function values are\nconsistent with some of the priors, in which case it is easy to reject the\nwrong priors, or the observations are consistent with all candidate priors, in\nwhich case it does not matter which prior our model relies on. We provide a\nregret bound on the proposed algorithm. Finally, we empirically evaluate our\nalgorithm on toy and real-world time-varying problems and show that it\noutperforms the maximum likelihood estimator, fully Bayesian treatment of\nunknown prior and Regret Balancing.\n", "date": "2024-02-02", "categories": []}
{"id": "2409.18582", "title": "Optimistic Games for Combinatorial Bayesian Optimization with\n  Application to Protein Design", "abstract": "  Bayesian optimization (BO) is a powerful framework to optimize black-box\nexpensive-to-evaluate functions via sequential interactions. In several\nimportant problems (e.g. drug discovery, circuit design, neural architecture\nsearch, etc.), though, such functions are defined over large\n$\\textit{combinatorial and unstructured}$ spaces. This makes existing BO\nalgorithms not feasible due to the intractable maximization of the acquisition\nfunction over these domains. To address this issue, we propose\n$\\textbf{GameOpt}$, a novel game-theoretical approach to combinatorial BO.\n$\\textbf{GameOpt}$ establishes a cooperative game between the different\noptimization variables, and selects points that are game $\\textit{equilibria}$\nof an upper confidence bound acquisition function. These are stable\nconfigurations from which no variable has an incentive to deviate$-$ analog to\nlocal optima in continuous domains. Crucially, this allows us to efficiently\nbreak down the complexity of the combinatorial domain into individual decision\nsets, making $\\textbf{GameOpt}$ scalable to large combinatorial spaces. We\ndemonstrate the application of $\\textbf{GameOpt}$ to the challenging\n$\\textit{protein design}$ problem and validate its performance on four\nreal-world protein datasets. Each protein can take up to $20^{X}$ possible\nconfigurations, where $X$ is the length of a protein, making standard BO\nmethods infeasible. Instead, our approach iteratively selects informative\nprotein configurations and very quickly discovers highly active protein\nvariants compared to other baselines.\n", "date": "2024-09-27", "categories": []}
{"id": "2502.14755", "title": "Multi-Objective Causal Bayesian Optimization", "abstract": "  In decision-making problems, the outcome of an intervention often depends on\nthe causal relationships between system components and is highly costly to\nevaluate. In such settings, causal Bayesian optimization (CBO) can exploit the\ncausal relationships between the system variables and sequentially perform\ninterventions to approach the optimum with minimal data. Extending CBO to the\nmulti-outcome setting, we propose Multi-Objective Causal Bayesian Optimization\n(MO-CBO), a paradigm for identifying Pareto-optimal interventions within a\nknown multi-target causal graph. We first derive a graphical characterization\nfor potentially optimal sets of variables to intervene upon. Showing that any\nMO-CBO problem can be decomposed into several traditional multi-objective\noptimization tasks, we then introduce an algorithm that sequentially balances\nexploration across these tasks using relative hypervolume improvement. The\nproposed method will be validated on both synthetic and real-world causal\ngraphs, demonstrating its superiority over traditional (non-causal)\nmulti-objective Bayesian optimization in settings where causal information is\navailable.\n", "date": "2025-02-20", "categories": []}
{"id": "2408.17387", "title": "Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization\n  Problems", "abstract": "  Bayesian optimization is a sample-efficient method for solving expensive,\nblack-box optimization problems. Stochastic programming concerns optimization\nunder uncertainty where, typically, average performance is the quantity of\ninterest. In the first stage of a two-stage problem, here-and-now decisions\nmust be made in the face of uncertainty, while in the second stage,\nwait-and-see decisions are made after the uncertainty has been resolved. Many\nmethods in stochastic programming assume that the objective is cheap to\nevaluate and linear or convex. We apply Bayesian optimization to solve\nnon-convex, two-stage stochastic programs which are black-box and expensive to\nevaluate as, for example, is often the case with simulation objectives. We\nformulate a knowledge-gradient-based acquisition function to jointly optimize\nthe first- and second-stage variables, establish a guarantee of asymptotic\nconsistency, and provide a computationally efficient approximation. We\ndemonstrate comparable empirical results to an alternative we formulate with\nfewer approximations, which alternates its focus between the two variable\ntypes, and superior empirical results over the state of the art and the\nstandard, na\\\"ive, two-step benchmark.\n", "date": "2024-08-30", "categories": []}
{"id": "2502.06815", "title": "Honegumi: An Interface for Accelerating the Adoption of Bayesian\n  Optimization in the Experimental Sciences", "abstract": "  Bayesian optimization (BO) has emerged as a powerful tool for guiding\nexperimental design and decision-making in various scientific fields, including\nmaterials science, chemistry, and biology. However, despite its growing\npopularity, the complexity of existing BO libraries and the steep learning\ncurve associated with them can deter researchers who are not well-versed in\nmachine learning or programming. To address this barrier, we introduce\nHonegumi, a user-friendly, interactive tool designed to simplify the process of\ncreating advanced Bayesian optimization scripts. Honegumi offers a dynamic\nselection grid that allows users to configure key parameters of their\noptimization tasks, generating ready-to-use, unit-tested Python scripts\ntailored to their specific needs. Accompanying the interface is a comprehensive\nsuite of tutorials that provide both conceptual and practical guidance,\nbridging the gap between theoretical understanding and practical\nimplementation. Built on top of the Ax platform, Honegumi leverages the power\nof existing state-of-the-art libraries while restructuring the user experience\nto make advanced BO techniques more accessible to experimental researchers. By\nlowering the barrier to entry and providing educational resources, Honegumi\naims to accelerate the adoption of advanced Bayesian optimization methods\nacross various domains.\n", "date": "2025-02-04", "categories": []}
{"id": "2502.12315", "title": "Mean-Field Bayesian Optimisation", "abstract": "  We address the problem of optimising the average payoff for a large number of\ncooperating agents, where the payoff function is unknown and treated as a black\nbox. While standard Bayesian Optimisation (BO) methods struggle with the\nscalability required for high-dimensional input spaces, we demonstrate how\nleveraging the mean-field assumption on the black-box function can transform BO\ninto an efficient and scalable solution. Specifically, we introduce MF-GP-UCB,\na novel efficient algorithm designed to optimise agent payoffs in this setting.\nOur theoretical analysis establishes a regret bound for MF-GP-UCB that is\nindependent of the number of agents, contrasting sharply with the exponential\ndependence observed when naive BO methods are applied. We evaluate our\nalgorithm on a diverse set of tasks, including real-world problems, such as\noptimising the location of public bikes for a bike-sharing programme,\ndistributing taxi fleets, and selecting refuelling ports for maritime vessels.\nEmpirical results demonstrate that MF-GP-UCB significantly outperforms existing\nbenchmarks, offering substantial improvements in performance and scalability,\nconstituting a promising solution for mean-field, black-box optimisation. The\ncode is available at https://github.com/petarsteinberg/MF-BO.\n", "date": "2025-02-17", "categories": []}
{"id": "2502.09329", "title": "Bayesian Optimization for Simultaneous Selection of Machine Learning\n  Algorithms and Hyperparameters on Shared Latent Space", "abstract": "  Selecting the optimal combination of a machine learning (ML) algorithm and\nits hyper-parameters is crucial for the development of high-performance ML\nsystems. However, since the combination of ML algorithms and hyper-parameters\nis enormous, the exhaustive validation requires a significant amount of time.\nMany existing studies use Bayesian optimization (BO) for accelerating the\nsearch. On the other hand, a significant difficulty is that, in general, there\nexists a different hyper-parameter space for each one of candidate ML\nalgorithms. BO-based approaches typically build a surrogate model independently\nfor each hyper-parameter space, by which sufficient observations are required\nfor all candidate ML algorithms. In this study, our proposed method embeds\ndifferent hyper-parameter spaces into a shared latent space, in which a\nsurrogate multi-task model for BO is estimated. This approach can share\ninformation of observations from different ML algorithms by which efficient\noptimization is expected with a smaller number of total observations. We\nfurther propose the pre-training of the latent space embedding with an\nadversarial regularization, and a ranking model for selecting an effective\npre-trained embedding for a given target dataset. Our empirical study\ndemonstrates effectiveness of the proposed method through datasets from OpenML.\n", "date": "2025-02-13", "categories": []}
{"id": "2209.06735", "title": "Falsification of Cyber-Physical Systems using Bayesian Optimization", "abstract": "  Cyber-physical systems (CPSs) are often complex and safety-critical, making\nit both challenging and crucial to ensure that the system's specifications are\nmet. Simulation-based falsification is a practical testing technique for\nincreasing confidence in a CPS's correctness, as it only requires that the\nsystem be simulated. Reducing the number of computationally intensive\nsimulations needed for falsification is a key concern. In this study, we\ninvestigate Bayesian optimization (BO), a sample-efficient approach that learns\na surrogate model to capture the relationship between input signal\nparameterization and specification evaluation. We propose two enhancements to\nthe basic BO for improving falsification: (1) leveraging local surrogate\nmodels, and (2) utilizing the user's prior knowledge. Additionally, we address\nthe formulation of acquisition functions for falsification by proposing and\nevaluating various alternatives. Our benchmark evaluation demonstrates\nsignificant improvements when using local surrogate models in BO for falsifying\nchallenging benchmark examples. Incorporating prior knowledge is found to be\nespecially beneficial when the simulation budget is constrained. For some\nbenchmark problems, the choice of acquisition function noticeably impacts the\nnumber of simulations required for successful falsification.\n", "date": "2022-09-14", "categories": []}
{"id": "2501.09262", "title": "On the convergence rate of noisy Bayesian Optimization with Expected\n  Improvement", "abstract": "  Expected improvement (EI) is one of the most widely used acquisition\nfunctions in Bayesian optimization (BO). Despite its proven success in\napplications for decades, important open questions remain on the theoretical\nconvergence behaviors and rates for EI. In this paper, we contribute to the\nconvergence theory of EI in three novel and critical areas. First, we consider\nobjective functions that fit under the Gaussian process (GP) prior assumption,\nwhereas existing works mostly focus on functions in the reproducing kernel\nHilbert space (RKHS). Second, we establish for the first time the asymptotic\nerror bound and its corresponding rate for GP-EI with noisy observations under\nthe GP prior assumption. Third, by investigating the exploration and\nexploitation properties of the non-convex EI function, we establish improved\nerror bounds of GP-EI for both the noise-free and noisy cases.\n", "date": "2025-01-16", "categories": []}
{"id": "2502.06789", "title": "Information-theoretic Bayesian Optimization: Survey and Tutorial", "abstract": "  Several scenarios require the optimization of non-convex black-box functions,\nthat are noisy expensive to evaluate functions with unknown analytical\nexpression, whose gradients are hence not accessible. For example, the\nhyper-parameter tuning problem of machine learning models. Bayesian\noptimization is a class of methods with state-of-the-art performance delivering\na solution to this problem in real scenarios. It uses an iterative process that\nemploys a probabilistic surrogate model, typically a Gaussian process, of the\nobjective function to be optimized computing a posterior predictive\ndistribution of the black-box function. Based on the information given by this\nposterior predictive distribution, Bayesian optimization includes the\ncomputation of an acquisition function that represents, for every input space\npoint, the utility of evaluating that point in the next iteraiton if the\nobjective of the process is to retrieve a global extremum. This paper is a\nsurvey of the information theoretical acquisition functions, whose performance\ntypically outperforms the rest of acquisition functions. The main concepts of\nthe field of information theory are also described in detail to make the reader\naware of why information theory acquisition functions deliver great results in\nBayesian optimization and how can we approximate them when they are\nintractable. We also cover how information theory acquisition functions can be\nadapted to complex optimization scenarios such as the multi-objective,\nconstrained, non-myopic, multi-fidelity, parallel and asynchronous settings and\nprovide further lines of research.\n", "date": "2025-01-22", "categories": []}
{"id": "2502.00854", "title": "High-Dimensional Bayesian Optimization Using Both Random and Supervised\n  Embeddings", "abstract": "  Bayesian optimization (BO) is one of the most powerful strategies to solve\ncomputationally expensive-to-evaluate blackbox optimization problems. However,\nBO methods are conventionally used for optimization problems of small dimension\nbecause of the curse of dimensionality. In this paper, a high-dimensionnal\noptimization method incorporating linear embedding subspaces of small dimension\nis proposed to efficiently perform the optimization. An adaptive learning\nstrategy for these linear embeddings is carried out in conjunction with the\noptimization. The resulting BO method, named efficient global optimization\ncoupled with random and supervised embedding (EGORSE), combines in an adaptive\nway both random and supervised linear embeddings. EGORSE has been compared to\nstate-of-the-art algorithms and tested on academic examples with a number of\ndesign variables ranging from 10 to 600. The obtained results show the high\npotential of EGORSE to solve high-dimensional blackbox optimization problems,\nin terms of both CPU time and the limited number of calls to the expensive\nblackbox simulation.\n", "date": "2025-02-02", "categories": []}
{"id": "2208.10790", "title": "Event-Triggered Time-Varying Bayesian Optimization", "abstract": "  We consider the problem of sequentially optimizing a time-varying objective\nfunction using time-varying Bayesian optimization (TVBO). Current approaches to\nTVBO require prior knowledge of a constant rate of change to cope with stale\ndata arising from time variations. However, in practice, the rate of change is\nusually unknown. We propose an event-triggered algorithm, ET-GP-UCB, that\ntreats the optimization problem as static until it detects changes in the\nobjective function and then resets the dataset. This allows the algorithm to\nadapt online to realized temporal changes without the need for exact prior\nknowledge. The event trigger is based on probabilistic uniform error bounds\nused in Gaussian process regression. We derive regret bounds for adaptive\nresets without exact prior knowledge of the temporal changes and show in\nnumerical experiments that ET-GP-UCB outperforms competing GP-UCB algorithms on\nboth synthetic and real-world data. The results demonstrate that ET-GP-UCB is\nreadily applicable without extensive hyperparameter tuning.\n", "date": "2022-08-23", "categories": []}
{"id": "2310.09766", "title": "Pseudo-Bayesian Optimization", "abstract": "  Bayesian Optimization is a popular approach for optimizing expensive\nblack-box functions. Its key idea is to use a surrogate model to approximate\nthe objective and, importantly, quantify the associated uncertainty that allows\na sequential search of query points that balance exploitation-exploration.\nGaussian process (GP) has been a primary candidate for the surrogate model,\nthanks to its Bayesian-principled uncertainty quantification power and modeling\nflexibility. However, its challenges have also spurred an array of alternatives\nwhose convergence properties could be more opaque. Motivated by these, we study\nin this paper an axiomatic framework that elicits the minimal requirements to\nguarantee black-box optimization convergence that could apply beyond GP-based\nmethods. Moreover, we leverage the design freedom in our framework, which we\ncall Pseudo-Bayesian Optimization, to construct empirically superior\nalgorithms. In particular, we show how using simple local regression, and a\nsuitable \"randomized prior\" construction to quantify uncertainty, not only\nguarantees convergence but also consistently outperforms state-of-the-art\nbenchmarks in examples ranging from high-dimensional synthetic experiments to\nrealistic hyperparameter tuning and robotic applications.\n", "date": "2023-10-15", "categories": []}
{"id": "2410.01196", "title": "Expected Diverse Utility (EDU): Diverse Bayesian Optimization of\n  Expensive Computer Simulators", "abstract": "  The optimization of expensive black-box simulators arises in a myriad of\nmodern scientific and engineering applications. Bayesian optimization provides\nan appealing solution, by leveraging a fitted surrogate model to guide the\nselection of subsequent simulator evaluations. In practice, however, the\nobjective is often not to obtain a single good solution, but rather a\n``basket'' of good solutions from which users can choose for downstream\ndecision-making. This need arises in our motivating application for real-time\ncontrol of internal combustion engines for flight propulsion, where a diverse\nset of control strategies is essential for stable flight control. There has\nbeen little work on this front for Bayesian optimization. We thus propose a new\nExpected Diverse Utility (EDU) method that searches for diverse\n``$\\epsilon$-optimal'' solutions: locally-optimal solutions within a tolerance\nlevel $\\epsilon > 0$ from a global optimum. We show that EDU yields a\nclosed-form acquisition function under a Gaussian process surrogate model,\nwhich facilitates efficient sequential queries via automatic differentiation.\nThis closed form further reveals a novel exploration-exploitation-diversity\ntrade-off, which incorporates the desired diversity property within the\nwell-known exploration-exploitation trade-off. We demonstrate the improvement\nof EDU over existing methods in a suite of numerical experiments, then explore\nthe EDU in two applications on rover trajectory optimization and engine control\nfor flight propulsion.\n", "date": "2024-10-02", "categories": []}
{"id": "2502.00871", "title": "Modified Adaptive Tree-Structured Parzen Estimator for Hyperparameter\n  Optimization", "abstract": "  In this paper, we review hyperparameter optimization methods for machine\nlearning models, with a particular focus on the Adaptive Tree-Structured Parzen\nEstimator (ATPE) algorithm. We propose several modifications to ATPE and assess\ntheir efficacy on a diverse set of standard benchmark functions. Experimental\nresults demonstrate that the proposed modifications significantly improve the\neffectiveness of ATPE hyperparameter optimization on selected benchmarks, a\nfinding that holds practical relevance for their application in real-world\nmachine learning / optimization tasks.\n", "date": "2025-02-02", "categories": []}
{"id": "2501.04260", "title": "Modeling All Response Surfaces in One for Conditional Search Spaces", "abstract": "  Bayesian Optimization (BO) is a sample-efficient black-box optimizer commonly\nused in search spaces where hyperparameters are independent. However, in many\npractical AutoML scenarios, there will be dependencies among hyperparameters,\nforming a conditional search space, which can be partitioned into structurally\ndistinct subspaces. The structure and dimensionality of hyperparameter\nconfigurations vary across these subspaces, challenging the application of BO.\nSome previous BO works have proposed solutions to develop multiple Gaussian\nProcess models in these subspaces. However, these approaches tend to be\ninefficient as they require a substantial number of observations to guarantee\neach GP's performance and cannot capture relationships between hyperparameters\nacross different subspaces. To address these issues, this paper proposes a\nnovel approach to model the response surfaces of all subspaces in one, which\ncan model the relationships between hyperparameters elegantly via a\nself-attention mechanism. Concretely, we design a structure-aware\nhyperparameter embedding to preserve the structural information. Then, we\nintroduce an attention-based deep feature extractor, capable of projecting\nconfigurations with different structures from various subspaces into a unified\nfeature space, where the response surfaces can be formulated using a single\nstandard Gaussian Process. The empirical results on a simulation function,\nvarious real-world tasks, and HPO-B benchmark demonstrate that our proposed\napproach improves the efficacy and efficiency of BO within conditional search\nspaces.\n", "date": "2025-01-08", "categories": []}
{"id": "2501.15554", "title": "BoTier: Multi-Objective Bayesian Optimization with Tiered Composite\n  Objectives", "abstract": "  Scientific optimization problems are usually concerned with balancing\nmultiple competing objectives, which come as preferences over both the outcomes\nof an experiment (e.g. maximize the reaction yield) and the corresponding input\nparameters (e.g. minimize the use of an expensive reagent). Typically,\npractical and economic considerations define a hierarchy over these objectives,\nwhich must be reflected in algorithms for sample-efficient experiment planning.\nHerein, we introduce BoTier, a composite objective that can flexibly represent\na hierarchy of preferences over both experiment outcomes and input parameters.\nWe provide systematic benchmarks on synthetic and real-life surfaces,\ndemonstrating the robust applicability of BoTier across a number of use cases.\nImportantly, BoTier is implemented in an auto-differentiable fashion, enabling\nseamless integration with the BoTorch library, thereby facilitating adoption by\nthe scientific community.\n", "date": "2025-01-26", "categories": []}
{"id": "2501.13332", "title": "Co-Learning Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is well known to be sample-efficient for solving\nblack-box problems. However, the BO algorithms can sometimes get stuck in\nsuboptimal solutions even with plenty of samples. Intrinsically, such\nsuboptimal problem of BO can attribute to the poor surrogate accuracy of the\ntrained Gaussian process (GP), particularly that in the regions where the\noptimal solutions locate. Hence, we propose to build multiple GP models instead\nof a single GP surrogate to complement each other and thus resolving the\nsuboptimal problem of BO. Nevertheless, according to the bias-variance tradeoff\nequation, the individual prediction errors can increase when increasing the\ndiversity of models, which may lead to even worse overall surrogate accuracy.\nOn the other hand, based on the theory of Rademacher complexity, it has been\nproved that exploiting the agreement of models on unlabeled information can\nhelp to reduce the complexity of the hypothesis space, and therefore achieving\nthe required surrogate accuracy with fewer samples. Such value of model\nagreement has been extensively demonstrated for co-training style algorithms to\nboost model accuracy with a small portion of samples. Inspired by the above, we\npropose a novel BO algorithm labeled as co-learning BO (CLBO), which exploits\nboth model diversity and agreement on unlabeled information to improve the\noverall surrogate accuracy with limited samples, and therefore achieving more\nefficient global optimization. Through tests on five numerical toy problems and\nthree engineering benchmarks, the effectiveness of proposed CLBO has been well\ndemonstrated.\n", "date": "2025-01-23", "categories": []}
{"id": "2405.14440", "title": "Bayesian Adaptive Calibration and Optimal Design", "abstract": "  The process of calibrating computer models of natural phenomena is essential\nfor applications in the physical sciences, where plenty of domain knowledge can\nbe embedded into simulations and then calibrated against real observations.\nCurrent machine learning approaches, however, mostly rely on rerunning\nsimulations over a fixed set of designs available in the observed data,\npotentially neglecting informative correlations across the design space and\nrequiring a large amount of simulations. Instead, we consider the calibration\nprocess from the perspective of Bayesian adaptive experimental design and\npropose a data-efficient algorithm to run maximally informative simulations\nwithin a batch-sequential process. At each round, the algorithm jointly\nestimates the parameters of the posterior distribution and optimal designs by\nmaximising a variational lower bound of the expected information gain. The\nsimulator is modelled as a sample from a Gaussian process, which allows us to\ncorrelate simulations and observed data with the unknown calibration\nparameters. We show the benefits of our method when compared to related\napproaches across synthetic and real-data problems.\n", "date": "2024-05-23", "categories": []}
{"id": "2406.20062", "title": "Cost-aware Bayesian Optimization via the Pandora's Box Gittins Index", "abstract": "  Bayesian optimization is a technique for efficiently optimizing unknown\nfunctions in a black-box manner. To handle practical settings where gathering\ndata requires use of finite resources, it is desirable to explicitly\nincorporate function evaluation costs into Bayesian optimization policies. To\nunderstand how to do so, we develop a previously-unexplored connection between\ncost-aware Bayesian optimization and the Pandora's Box problem, a decision\nproblem from economics. The Pandora's Box problem admits a Bayesian-optimal\nsolution based on an expression called the Gittins index, which can be\nreinterpreted as an acquisition function. We study the use of this acquisition\nfunction for cost-aware Bayesian optimization, and demonstrate empirically that\nit performs well, particularly in medium-high dimensions. We further show that\nthis performance carries over to classical Bayesian optimization without\nexplicit evaluation costs. Our work constitutes a first step towards\nintegrating techniques from Gittins index theory into Bayesian optimization.\n", "date": "2024-06-28", "categories": []}
{"id": "2404.11917", "title": "Expected Coordinate Improvement for High-Dimensional Bayesian\n  Optimization", "abstract": "  Bayesian optimization (BO) algorithm is very popular for solving\nlow-dimensional expensive optimization problems. Extending Bayesian\noptimization to high dimension is a meaningful but challenging task. One of the\nmajor challenges is that it is difficult to find good infill solutions as the\nacquisition functions are also high-dimensional. In this work, we propose the\nexpected coordinate improvement (ECI) criterion for high-dimensional Bayesian\noptimization. The proposed ECI criterion measures the potential improvement we\ncan get by moving the current best solution along one coordinate. The proposed\napproach selects the coordinate with the highest ECI value to refine in each\niteration and covers all the coordinates gradually by iterating over the\ncoordinates. The greatest advantage of the proposed ECI-BO (expected coordinate\nimprovement based Bayesian optimization) algorithm over the standard BO\nalgorithm is that the infill selection problem of the proposed algorithm is\nalways a one-dimensional problem thus can be easily solved. Numerical\nexperiments show that the proposed algorithm can achieve significantly better\nresults than the standard BO algorithm and competitive results when compared\nwith five state-of-the-art high-dimensional BOs. This work provides a simple\nbut efficient approach for high-dimensional Bayesian optimization.\n", "date": "2024-04-18", "categories": []}
{"id": "2403.09570", "title": "Multi-Fidelity Bayesian Optimization With Across-Task Transferable\n  Max-Value Entropy Search", "abstract": "  In many applications, ranging from logistics to engineering, a designer is\nfaced with a sequence of optimization tasks for which the objectives are in the\nform of black-box functions that are costly to evaluate. Furthermore,\nhigher-fidelity evaluations of the optimization objectives often entail a\nlarger cost. Existing multi-fidelity black-box optimization strategies select\ncandidate solutions and fidelity levels with the goal of maximizing the\ninformation about the optimal value or the optimal solution for the current\ntask. Assuming that successive optimization tasks are related, this paper\nintroduces a novel information-theoretic acquisition function that balances the\nneed to acquire information about the current task with the goal of collecting\ninformation transferable to future tasks. The proposed method transfers across\ntasks distributions over parameters of a Gaussian process surrogate model by\nimplementing particle-based variational Bayesian updates. Theoretical insights\nbased on the analysis of the expected regret substantiate the benefits of\nacquiring transferable knowledge across tasks. Furthermore, experimental\nresults across synthetic and real-world examples reveal that the proposed\nacquisition strategy that caters to future tasks can significantly improve the\noptimization efficiency as soon as a sufficient number of tasks is processed.\n", "date": "2024-03-14", "categories": []}
{"id": "2310.20708", "title": "Unexpected Improvements to Expected Improvement for Bayesian\n  Optimization", "abstract": "  Expected Improvement (EI) is arguably the most popular acquisition function\nin Bayesian optimization and has found countless successful applications, but\nits performance is often exceeded by that of more recent methods. Notably, EI\nand its variants, including for the parallel and multi-objective settings, are\nchallenging to optimize because their acquisition values vanish numerically in\nmany regions. This difficulty generally increases as the number of\nobservations, dimensionality of the search space, or the number of constraints\ngrow, resulting in performance that is inconsistent across the literature and\nmost often sub-optimal. Herein, we propose LogEI, a new family of acquisition\nfunctions whose members either have identical or approximately equal optima as\ntheir canonical counterparts, but are substantially easier to optimize\nnumerically. We demonstrate that numerical pathologies manifest themselves in\n\"classic\" analytic EI, Expected Hypervolume Improvement (EHVI), as well as\ntheir constrained, noisy, and parallel variants, and propose corresponding\nreformulations that remedy these pathologies. Our empirical results show that\nmembers of the LogEI family of acquisition functions substantially improve on\nthe optimization performance of their canonical counterparts and surprisingly,\nare on par with or exceed the performance of recent state-of-the-art\nacquisition functions, highlighting the understated role of numerical\noptimization in the literature.\n", "date": "2023-10-31", "categories": []}
{"id": "2405.15119", "title": "Bayesian Optimization of Functions over Node Subsets in Graphs", "abstract": "  We address the problem of optimizing over functions defined on node subsets\nin a graph. The optimization of such functions is often a non-trivial task\ngiven their combinatorial, black-box and expensive-to-evaluate nature. Although\nvarious algorithms have been introduced in the literature, most are either\ntask-specific or computationally inefficient and only utilize information about\nthe graph structure without considering the characteristics of the function. To\naddress these limitations, we utilize Bayesian Optimization (BO), a\nsample-efficient black-box solver, and propose a novel framework for\ncombinatorial optimization on graphs. More specifically, we map each $k$-node\nsubset in the original graph to a node in a new combinatorial graph and adopt a\nlocal modeling approach to efficiently traverse the latter graph by\nprogressively sampling its subgraphs using a recursive algorithm. Extensive\nexperiments under both synthetic and real-world setups demonstrate the\neffectiveness of the proposed BO framework on various types of graphs and\noptimization tasks, where its behavior is analyzed in detail with ablation\nstudies.\n", "date": "2024-05-24", "categories": []}
{"id": "2411.02064", "title": "Amortized Bayesian Experimental Design for Decision-Making", "abstract": "  Many critical decisions, such as personalized medical diagnoses and product\npricing, are made based on insights gained from designing, observing, and\nanalyzing a series of experiments. This highlights the crucial role of\nexperimental design, which goes beyond merely collecting information on system\nparameters as in traditional Bayesian experimental design (BED), but also plays\na key part in facilitating downstream decision-making. Most recent BED methods\nuse an amortized policy network to rapidly design experiments. However, the\ninformation gathered through these methods is suboptimal for down-the-line\ndecision-making, as the experiments are not inherently designed with downstream\nobjectives in mind. In this paper, we present an amortized decision-aware BED\nframework that prioritizes maximizing downstream decision utility. We introduce\na novel architecture, the Transformer Neural Decision Process (TNDP), capable\nof instantly proposing the next experimental design, whilst inferring the\ndownstream decision, thus effectively amortizing both tasks within a unified\nworkflow. We demonstrate the performance of our method across several tasks,\nshowing that it can deliver informative designs and facilitate accurate\ndecision-making.\n", "date": "2024-11-04", "categories": []}
{"id": "2501.00967", "title": "On the Implementation of a Bayesian Optimization Framework for\n  Interconnected Systems", "abstract": "  Bayesian optimization (BO) is an effective paradigm for the optimization of\nexpensive-to-sample systems. Standard BO learns the performance of a system\n$f(x)$ by using a Gaussian Process (GP) model; this treats the system as a\nblack-box and limits its ability to exploit available structural knowledge\n(e.g., physics and sparse interconnections in a complex system). Grey-box\nmodeling, wherein the performance function is treated as a composition of known\nand unknown intermediate functions $f(x, y(x))$ (where $y(x)$ is a GP model)\noffers a solution to this limitation; however, generating an analytical\nprobability density for $f$ from the Gaussian density of $y(x)$ is often an\nintractable problem (e.g., when $f$ is nonlinear). Previous work has handled\nthis issue by using sampling techniques or by solving an auxiliary problem over\nan augmented space where the values of $y(x)$ are constrained by confidence\nintervals derived from the GP models; such solutions are computationally\nintensive. In this work, we provide a detailed implementation of a recently\nproposed grey-box BO paradigm, BOIS, that uses adaptive linearizations of $f$\nto obtain analytical expressions for the statistical moments of the composite\nfunction. We show that the BOIS approach enables the exploitation of structural\nknowledge, such as that arising in interconnected systems as well as systems\nthat embed multiple GP models and combinations of physics and GP models. We\nbenchmark the effectiveness of BOIS against standard BO and existing grey-box\nBO algorithms using a pair of case studies focused on chemical process\noptimization and design. Our results indicate that BOIS performs as well as or\nbetter than existing grey-box methods, while also being less computationally\nintensive.\n", "date": "2025-01-01", "categories": []}
{"id": "2412.20350", "title": "Safe Bayesian Optimization for the Control of High-Dimensional Embodied\n  Systems", "abstract": "  Learning to move is a primary goal for animals and robots, where ensuring\nsafety is often important when optimizing control policies on the embodied\nsystems. For complex tasks such as the control of human or humanoid control,\nthe high-dimensional parameter space adds complexity to the safe optimization\neffort. Current safe exploration algorithms exhibit inefficiency and may even\nbecome infeasible with large high-dimensional input spaces. Furthermore,\nexisting high-dimensional constrained optimization methods neglect safety in\nthe search process. In this paper, we propose High-dimensional Safe Bayesian\nOptimization with local optimistic exploration (HdSafeBO), a novel approach\ndesigned to handle high-dimensional sampling problems under probabilistic\nsafety constraints. We introduce a local optimistic strategy to efficiently and\nsafely optimize the objective function, providing a probabilistic safety\nguarantee and a cumulative safety violation bound. Through the use of isometric\nembedding, HdSafeBO addresses problems ranging from a few hundred to several\nthousand dimensions while maintaining safety guarantees. To our knowledge,\nHdSafeBO is the first algorithm capable of optimizing the control of\nhigh-dimensional musculoskeletal systems with high safety probability. We also\ndemonstrate the real-world applicability of HdSafeBO through its use in the\nsafe online optimization of neural stimulation induced human motion control.\n", "date": "2024-12-29", "categories": []}
{"id": "2411.06710", "title": "Model Fusion through Bayesian Optimization in Language Model Fine-Tuning", "abstract": "  Fine-tuning pre-trained models for downstream tasks is a widely adopted\ntechnique known for its adaptability and reliability across various domains.\nDespite its conceptual simplicity, fine-tuning entails several troublesome\nengineering choices, such as selecting hyperparameters and determining\ncheckpoints from an optimization trajectory. To tackle the difficulty of\nchoosing the best model, one effective solution is model fusion, which combines\nmultiple models in a parameter space. However, we observe a large discrepancy\nbetween loss and metric landscapes during the fine-tuning of pre-trained\nlanguage models. Building on this observation, we introduce a novel model\nfusion technique that optimizes both the desired metric and loss through\nmulti-objective Bayesian optimization. In addition, to effectively select\nhyperparameters, we establish a two-stage procedure by integrating Bayesian\noptimization processes into our framework. Experiments across various\ndownstream tasks show considerable performance improvements using our Bayesian\noptimization-guided method.\n", "date": "2024-11-11", "categories": []}
{"id": "2412.18789", "title": "On Improved Regret Bounds In Bayesian Optimization with Gaussian Noise", "abstract": "  Bayesian optimization (BO) with Gaussian process (GP) surrogate models is a\npowerful black-box optimization method. Acquisition functions are a critical\npart of a BO algorithm as they determine how the new samples are selected. Some\nof the most widely used acquisition functions include upper confidence bound\n(UCB) and Thompson sampling (TS). The convergence analysis of BO algorithms has\nfocused on the cumulative regret under both the Bayesian and frequentist\nsettings for the objective. In this paper, we establish new pointwise bounds on\nthe prediction error of GP under the frequentist setting with Gaussian noise.\nConsequently, we prove improved convergence rates of cumulative regret bound\nfor both GP-UCB and GP-TS. Of note, the new prediction error bound under\nGaussian noise can be applied to general BO algorithms and convergence\nanalysis, e.g., the asymptotic convergence of expected improvement (EI) with\nnoise.\n", "date": "2024-12-25", "categories": []}
{"id": "2412.18518", "title": "Bayesian Optimization of Bilevel Problems", "abstract": "  Bilevel optimization, a hierarchical mathematical framework where one\noptimization problem is nested within another, has emerged as a powerful tool\nfor modeling complex decision-making processes in various fields such as\neconomics, engineering, and machine learning. This paper focuses on bilevel\noptimization where both upper-level and lower-level functions are black boxes\nand expensive to evaluate. We propose a Bayesian Optimization framework that\nmodels the upper and lower-level functions as Gaussian processes over the\ncombined space of upper and lower-level decisions, allowing us to exploit\nknowledge transfer between different sub-problems. Additionally, we propose a\nnovel acquisition function for this model. Our experimental results demonstrate\nthat the proposed algorithm is highly sample-efficient and outperforms existing\nmethods in finding high-quality solutions.\n", "date": "2024-12-24", "categories": []}
{"id": "2412.16554", "title": "High-Dimensional Bayesian Optimization via Random Projection of Manifold\n  Subspaces", "abstract": "  Bayesian Optimization (BO) is a popular approach to optimizing\nexpensive-to-evaluate black-box functions. Despite the success of BO, its\nperformance may decrease exponentially as the dimensionality increases. A\ncommon framework to tackle this problem is to assume that the objective\nfunction depends on a limited set of features that lie on a low-dimensional\nmanifold embedded in the high-dimensional ambient space. The latent space can\nbe linear or more generally nonlinear. To learn feature mapping, existing works\nusually use an encode-decoder framework which is either computationally\nexpensive or susceptible to overfittting when the labeled data is limited. This\npaper proposes a new approach for BO in high dimensions by exploiting a new\nrepresentation of the objective function. Our approach combines a random linear\nprojection to reduce the dimensionality, with a representation learning of the\nnonlinear manifold. When the geometry of the latent manifold is available, a\nsolution to exploit this geometry is proposed for representation learning. In\ncontrast, we use a neural network. To mitigate overfitting by using the neural\nnetwork, we train the feature mapping in a geometry-aware semi-supervised\nmanner. Our approach enables efficient optimizing of BO's acquisition function\nin the low-dimensional space, with the advantage of projecting back to the\noriginal high-dimensional space compared to existing works in the same setting.\nFinally, we show empirically that our algorithm outperforms other\nhigh-dimensional BO baselines in various synthetic functions and real\napplications.\n", "date": "2024-12-21", "categories": []}
{"id": "2412.15863", "title": "Bayesian Optimization for Unknown Cost-Varying Variable Subsets with\n  No-Regret Costs", "abstract": "  Bayesian Optimization (BO) is a widely-used method for optimizing\nexpensive-to-evaluate black-box functions. Traditional BO assumes that the\nlearner has full control over all query variables without additional\nconstraints. However, in many real-world scenarios, controlling certain query\nvariables may incur costs. Therefore, the learner needs to balance the\nselection of informative subsets for targeted learning against leaving some\nvariables to be randomly sampled to minimize costs. This problem is known as\nBayesian Optimization with cost-varying variable subsets (BOCVS). While the\ngoal of BOCVS is to identify the optimal solution with minimal cost, previous\nworks have only guaranteed finding the optimal solution without considering the\ntotal costs incurred. Moreover, these works assume precise knowledge of the\ncost for each subset, which is often unrealistic. In this paper, we propose a\nnovel algorithm for the extension of the BOCVS problem with random and unknown\ncosts that separates the process into exploration and exploitation phases. The\nexploration phase will filter out low-quality variable subsets, while the\nexploitation phase will leverage high-quality ones. Furthermore, we\ntheoretically demonstrate that our algorithm achieves a sub-linear rate in both\nquality regret and cost regret, addressing the objective of the BOCVS problem\nmore effectively than previous analyses. Finally, we show that our proposed\nalgorithm outperforms comparable baselines across a wide range of benchmarks.\n", "date": "2024-12-20", "categories": []}
{"id": "2412.12918", "title": "BOIDS: High-dimensional Bayesian Optimization via Incumbent-guided\n  Direction Lines and Subspace Embeddings", "abstract": "  When it comes to expensive black-box optimization problems, Bayesian\nOptimization (BO) is a well-known and powerful solution. Many real-world\napplications involve a large number of dimensions, hence scaling BO to high\ndimension is of much interest. However, state-of-the-art high-dimensional BO\nmethods still suffer from the curse of dimensionality, highlighting the need\nfor further improvements. In this work, we introduce BOIDS, a novel\nhigh-dimensional BO algorithm that guides optimization by a sequence of\none-dimensional direction lines using a novel tailored line-based optimization\nprocedure. To improve the efficiency, we also propose an adaptive selection\ntechnique to identify most optimal lines for each round of line-based\noptimization. Additionally, we incorporate a subspace embedding technique for\nbetter scaling to high-dimensional spaces. We further provide theoretical\nanalysis of our proposed method to analyze its convergence property. Our\nextensive experimental results show that BOIDS outperforms state-of-the-art\nbaselines on various synthetic and real-world benchmark problems.\n", "date": "2024-12-17", "categories": []}
{"id": "2412.11456", "title": "Regional Expected Improvement for Efficient Trust Region Selection in\n  High-Dimensional Bayesian Optimization", "abstract": "  Real-world optimization problems often involve complex objective functions\nwith costly evaluations. While Bayesian optimization (BO) with Gaussian\nprocesses is effective for these challenges, it suffers in high-dimensional\nspaces due to performance degradation from limited function evaluations. To\novercome this, simplification techniques like dimensionality reduction have\nbeen employed, yet they often rely on assumptions about the problem\ncharacteristics, potentially underperforming when these assumptions do not\nhold. Trust-region-based methods, which avoid such assumptions, focus on local\nsearch but risk stagnation in local optima. In this study, we propose a novel\nacquisition function, regional expected improvement (REI), designed to enhance\ntrust-region-based BO in medium to high-dimensional settings. REI identifies\nregions likely to contain the global optimum, improving performance without\nrelying on specific problem characteristics. We provide a theoretical proof\nthat REI effectively identifies optimal trust regions and empirically\ndemonstrate that incorporating REI into trust-region-based BO outperforms\nconventional BO and other high-dimensional BO methods in medium to\nhigh-dimensional real-world problems.\n", "date": "2024-12-16", "categories": []}
{"id": "2402.02229", "title": "Vanilla Bayesian Optimization Performs Great in High Dimensions", "abstract": "  High-dimensional problems have long been considered the Achilles' heel of\nBayesian optimization algorithms. Spurred by the curse of dimensionality, a\nlarge collection of algorithms aim to make it more performant in this setting,\ncommonly by imposing various simplifying assumptions on the objective. In this\npaper, we identify the degeneracies that make vanilla Bayesian optimization\npoorly suited to high-dimensional tasks, and further show how existing\nalgorithms address these degeneracies through the lens of lowering the model\ncomplexity. Moreover, we propose an enhancement to the prior assumptions that\nare typical to vanilla Bayesian optimization algorithms, which reduces the\ncomplexity to manageable levels without imposing structural restrictions on the\nobjective. Our modification - a simple scaling of the Gaussian process\nlengthscale prior with the dimensionality - reveals that standard Bayesian\noptimization works drastically better than previously thought in high\ndimensions, clearly outperforming existing state-of-the-art algorithms on\nmultiple commonly considered real-world high-dimensional tasks.\n", "date": "2024-02-03", "categories": []}
{"id": "2412.09183", "title": "Dimensionality Reduction Techniques for Global Bayesian Optimisation", "abstract": "  Bayesian Optimisation (BO) is a state-of-the-art global optimisation\ntechnique for black-box problems where derivative information is unavailable,\nand sample efficiency is crucial. However, improving the general scalability of\nBO has proved challenging. Here, we explore Latent Space Bayesian Optimisation\n(LSBO), that applies dimensionality reduction to perform BO in a\nreduced-dimensional subspace. While early LSBO methods used (linear) random\nprojections (Wang et al., 2013), we employ Variational Autoencoders (VAEs) to\nmanage more complex data structures and general DR tasks. Building on Grosnit\net. al. (2021), we analyse the VAE-based LSBO framework, focusing on VAE\nretraining and deep metric loss. We suggest a few key corrections in their\nimplementation, originally designed for tasks such as molecule generation, and\nreformulate the algorithm for broader optimisation purposes. Our numerical\nresults show that structured latent manifolds improve BO performance.\nAdditionally, we examine the use of the Mat\\'{e}rn-$\\frac{5}{2}$ kernel for\nGaussian Processes in this LSBO context. We also integrate Sequential Domain\nReduction (SDR), a standard global optimization efficiency strategy, into BO.\nSDR is included in a GPU-based environment using \\textit{BoTorch}, both in the\noriginal and VAE-generated latent spaces, marking the first application of SDR\nwithin LSBO.\n", "date": "2024-12-12", "categories": []}
{"id": "2412.09477", "title": "Bayesian Optimization via Continual Variational Last Layer Training", "abstract": "  Gaussian Processes (GPs) are widely seen as the state-of-the-art surrogate\nmodels for Bayesian optimization (BO) due to their ability to model uncertainty\nand their performance on tasks where correlations are easily captured (such as\nthose defined by Euclidean metrics) and their ability to be efficiently updated\nonline. However, the performance of GPs depends on the choice of kernel, and\nkernel selection for complex correlation structures is often difficult or must\nbe made bespoke. While Bayesian neural networks (BNNs) are a promising\ndirection for higher capacity surrogate models, they have so far seen limited\nuse due to poor performance on some problem types. In this paper, we propose an\napproach which shows competitive performance on many problem types, including\nsome that BNNs typically struggle with. We build on variational Bayesian last\nlayers (VBLLs), and connect training of these models to exact conditioning in\nGPs. We exploit this connection to develop an efficient online training\nalgorithm that interleaves conditioning and optimization. Our findings suggest\nthat VBLL networks significantly outperform GPs and other BNN architectures on\ntasks with complex input correlations, and match the performance of well-tuned\nGPs on established benchmark tasks.\n", "date": "2024-12-12", "categories": []}
{"id": "2402.16811", "title": "Stopping Bayesian Optimization with Probabilistic Regret Bounds", "abstract": "  Bayesian optimization is a popular framework for efficiently tackling\nblack-box search problems. As a rule, these algorithms operate by iteratively\nchoosing what to evaluate next until some predefined budget has been exhausted.\nWe investigate replacing this de facto stopping rule with criteria based on the\nprobability that a point satisfies a given set of conditions. We focus on the\nprototypical example of an $(\\epsilon, \\delta)$-criterion: stop when a solution\nhas been found whose value is within $\\epsilon > 0$ of the optimum with\nprobability at least $1 - \\delta$ under the model. For Gaussian process priors,\nwe show that Bayesian optimization satisfies this criterion under mild\ntechnical assumptions. Further, we give a practical algorithm for evaluating\nMonte Carlo stopping rules in a manner that is both sample efficient and robust\nto estimation error. These findings are accompanied by empirical results which\ndemonstrate the strengths and weaknesses of the proposed approach.\n", "date": "2024-02-26", "categories": []}
{"id": "2412.07186", "title": "Monte Carlo Tree Search based Space Transfer for Black-box Optimization", "abstract": "  Bayesian optimization (BO) is a popular method for computationally expensive\nblack-box optimization. However, traditional BO methods need to solve new\nproblems from scratch, leading to slow convergence. Recent studies try to\nextend BO to a transfer learning setup to speed up the optimization, where\nsearch space transfer is one of the most promising approaches and has shown\nimpressive performance on many tasks. However, existing search space transfer\nmethods either lack an adaptive mechanism or are not flexible enough, making it\ndifficult to efficiently identify promising search space during the\noptimization process. In this paper, we propose a search space transfer\nlearning method based on Monte Carlo tree search (MCTS), called MCTS-transfer,\nto iteratively divide, select, and optimize in a learned subspace.\nMCTS-transfer can not only provide a well-performing search space for\nwarm-start but also adaptively identify and leverage the information of similar\nsource tasks to reconstruct the search space during the optimization process.\nExperiments on synthetic functions, real-world problems, Design-Bench and\nhyper-parameter optimization show that MCTS-transfer can demonstrate superior\nperformance compared to other search space transfer methods under different\nsettings. Our code is available at\n\\url{https://github.com/lamda-bbo/mcts-transfer}.\n", "date": "2024-12-10", "categories": []}
{"id": "2412.07193", "title": "Epidemiological Model Calibration via Graybox Bayesian Optimization", "abstract": "  In this study, we focus on developing efficient calibration methods via\nBayesian decision-making for the family of compartmental epidemiological\nmodels. The existing calibration methods usually assume that the compartmental\nmodel is cheap in terms of its output and gradient evaluation, which may not\nhold in practice when extending them to more general settings. Therefore, we\nintroduce model calibration methods based on a \"graybox\" Bayesian optimization\n(BO) scheme, more efficient calibration for general epidemiological models.\nThis approach uses Gaussian processes as a surrogate to the expensive model,\nand leverages the functional structure of the compartmental model to enhance\ncalibration performance. Additionally, we develop model calibration methods via\na decoupled decision-making strategy for BO, which further exploits the\ndecomposable nature of the functional structure. The calibration efficiencies\nof the multiple proposed schemes are evaluated based on various data generated\nby a compartmental model mimicking real-world epidemic processes, and\nreal-world COVID-19 datasets. Experimental results demonstrate that our\nproposed graybox variants of BO schemes can efficiently calibrate\ncomputationally expensive models and further improve the calibration\nperformance measured by the logarithm of mean square errors and achieve faster\nperformance convergence in terms of BO iterations. We anticipate that the\nproposed calibration methods can be extended to enable fast calibration of more\ncomplex epidemiological models, such as the agent-based models.\n", "date": "2024-12-10", "categories": []}
{"id": "2412.07763", "title": "Bayesian Optimization of Antibodies Informed by a Generative Model of\n  Evolving Sequences", "abstract": "  To build effective therapeutics, biologists iteratively mutate antibody\nsequences to improve binding and stability. Proposed mutations can be informed\nby previous measurements or by learning from large antibody databases to\npredict only typical antibodies. Unfortunately, the space of typical antibodies\nis enormous to search, and experiments often fail to find suitable antibodies\non a budget. We introduce Clone-informed Bayesian Optimization (CloneBO), a\nBayesian optimization procedure that efficiently optimizes antibodies in the\nlab by teaching a generative model how our immune system optimizes antibodies.\nOur immune system makes antibodies by iteratively evolving specific portions of\ntheir sequences to bind their target strongly and stably, resulting in a set of\nrelated, evolving sequences known as a clonal family. We train a large language\nmodel, CloneLM, on hundreds of thousands of clonal families and use it to\ndesign sequences with mutations that are most likely to optimize an antibody\nwithin the human immune system. We propose to guide our designs to fit previous\nmeasurements with a twisted sequential Monte Carlo procedure. We show that\nCloneBO optimizes antibodies substantially more efficiently than previous\nmethods in realistic in silico experiments and designs stronger and more stable\nbinders in in vitro wet lab experiments.\n", "date": "2024-12-10", "categories": []}
{"id": "2402.04922", "title": "Voronoi Candidates for Bayesian Optimization", "abstract": "  Bayesian optimization (BO) offers an elegant approach for efficiently\noptimizing black-box functions. However, acquisition criteria demand their own\nchallenging inner-optimization, which can induce significant overhead. Many\npractical BO methods, particularly in high dimension, eschew a formal,\ncontinuous optimization of the acquisition function and instead search\ndiscretely over a finite set of space-filling candidates. Here, we propose to\nuse candidates which lie on the boundary of the Voronoi tessellation of the\ncurrent design points, so they are equidistant to two or more of them. We\ndiscuss strategies for efficient implementation by directly sampling the\nVoronoi boundary without explicitly generating the tessellation, thus\naccommodating large designs in high dimension. On a battery of test problems\noptimized via Gaussian processes with expected improvement, our proposed\napproach significantly improves the execution time of a multi-start continuous\nsearch without a loss in accuracy.\n", "date": "2024-02-07", "categories": []}
{"id": "2408.11527", "title": "The Vizier Gaussian Process Bandit Algorithm", "abstract": "  Google Vizier has performed millions of optimizations and accelerated\nnumerous research and production systems at Google, demonstrating the success\nof Bayesian optimization as a large-scale service. Over multiple years, its\nalgorithm has been improved considerably, through the collective experiences of\nnumerous research efforts and user feedback. In this technical report, we\ndiscuss the implementation details and design choices of the current default\nalgorithm provided by Open Source Vizier. Our experiments on standardized\nbenchmarks reveal its robustness and versatility against well-established\nindustry baselines on multiple practical modes.\n", "date": "2024-08-21", "categories": []}
{"id": "2412.04392", "title": "Asynchronous Batch Bayesian Optimization with Pipelining Evaluations for\n  Experimental Resource$\\unicode{x2013}$constrained Conditions", "abstract": "  Bayesian optimization is efficient even with a small amount of data and is\nused in engineering and in science, including biology and chemistry. In\nBayesian optimization, a parameterized model with an uncertainty is fitted to\nexplain the experimental data, and then the model suggests parameters that\nwould most likely improve the results. Batch Bayesian optimization reduces the\nprocessing time of optimization by parallelizing experiments. However, batch\nBayesian optimization cannot be applied if the number of parallelized\nexperiments is limited by the cost or scarcity of equipment; in such cases,\nsequential methods require an unrealistic amount of time. In this study, we\ndeveloped pipelining Bayesian optimization (PipeBO) to reduce the processing\ntime of optimization even with a limited number of parallel experiments. PipeBO\nwas inspired by the pipelining of central processing unit architecture, which\ndivides computational tasks into multiple processes. PipeBO was designed to\nachieve experiment parallelization by overlapping various processes of the\nexperiments. PipeBO uses the results of completed experiments to update the\nparameters of running parallelized experiments. Using the Black-Box\nOptimization Benchmarking, which consists of 24 benchmark functions, we\ncompared PipeBO with the sequential Bayesian optimization methods. PipeBO\nreduced the average processing time of optimization to about 56% for the\nexperiments that consisted of two processes or even less for those with more\nprocesses for 20 out of the 24 functions. Overall, PipeBO parallelizes Bayesian\noptimization in the resource-constrained settings so that efficient\noptimization can be achieved.\n", "date": "2024-12-05", "categories": []}
{"id": "2412.01748", "title": "CBOL-Tuner: Classifier-pruned Bayesian optimization to explore\n  temporally structured latent spaces for particle accelerator tuning", "abstract": "  Complex dynamical systems, such as particle accelerators, often require\ncomplicated and time-consuming tuning procedures for optimal performance. It\nmay also be required that these procedures estimate the optimal system\nparameters, which govern the dynamics of a spatiotemporal beam -- this can be a\nhigh-dimensional optimization problem. To address this, we propose a\nClassifier-pruned Bayesian Optimization-based Latent space Tuner (CBOL-Tuner),\na framework for efficient exploration within a temporally-structured latent\nspace. The CBOL-Tuner integrates a convolutional variational autoencoder (CVAE)\nfor latent space representation, a long short-term memory (LSTM) network for\ntemporal dynamics, a dense neural network (DNN) for parameter estimation, and a\nclassifier-pruned Bayesian optimizer (C-BO) to adaptively search and filter the\nlatent space for optimal solutions. CBOL-Tuner demonstrates superior\nperformance in identifying multiple optimal settings and outperforms\nalternative global optimization methods.\n", "date": "2024-12-02", "categories": []}
{"id": "2409.05354", "title": "Recursive Nested Filtering for Efficient Amortized Bayesian Experimental\n  Design", "abstract": "  This paper introduces the Inside-Out Nested Particle Filter (IO-NPF), a\nnovel, fully recursive, algorithm for amortized sequential Bayesian\nexperimental design in the non-exchangeable setting. We frame policy\noptimization as maximum likelihood estimation in a non-Markovian state-space\nmodel, achieving (at most) $\\mathcal{O}(T^2)$ computational complexity in the\nnumber of experiments. We provide theoretical convergence guarantees and\nintroduce a backward sampling algorithm to reduce trajectory degeneracy. IO-NPF\noffers a practical, extensible, and provably consistent approach to sequential\nBayesian experimental design, demonstrating improved efficiency over existing\nmethods.\n", "date": "2024-09-09", "categories": []}
{"id": "2411.17071", "title": "Fast, Precise Thompson Sampling for Bayesian Optimization", "abstract": "  Thompson sampling (TS) has optimal regret and excellent empirical performance\nin multi-armed bandit problems. Yet, in Bayesian optimization, TS underperforms\npopular acquisition functions (e.g., EI, UCB). TS samples arms according to the\nprobability that they are optimal. A recent algorithm, P-Star Sampler (PSS),\nperforms such a sampling via Hit-and-Run. We present an improved version,\nStagger Thompson Sampler (STS). STS more precisely locates the maximizer than\ndoes TS using less computation time. We demonstrate that STS outperforms TS,\nPSS, and other acquisition methods in numerical experiments of optimizations of\nseveral test functions across a broad range of dimension. Additionally, since\nPSS was originally presented not as a standalone acquisition method but as an\ninput to a batching algorithm called Minimal Terminal Variance (MTV), we also\ndemon-strate that STS matches PSS performance when used as the input to MTV.\n", "date": "2024-11-26", "categories": []}
{"id": "2411.18095", "title": "Derivation of Closed Form of Expected Improvement for Gaussian Process\n  Trained on Log-Transformed Objective", "abstract": "  Expected Improvement (EI) is arguably the most widely used acquisition\nfunction in Bayesian optimization. However, it is often challenging to enhance\nthe performance with EI due to its sensitivity to numerical precision.\nPreviously, Hutter et al. (2009) tackled this problem by using Gaussian process\ntrained on the log-transformed objective function and it was reported that this\ntrick improves the predictive accuracy of GP, leading to substantially better\nperformance. Although Hutter et al. (2009) offered the closed form of their EI,\nits intermediate derivation has not been provided so far. In this paper, we\ngive a friendly derivation of their proposition.\n", "date": "2024-11-27", "categories": []}
{"id": "2410.10384", "title": "Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds\n  Logarithmically Closer to Optimal", "abstract": "  Bayesian Optimization (BO) is widely used for optimising black-box functions\nbut requires us to specify the length scale hyperparameter, which defines the\nsmoothness of the functions the optimizer will consider. Most current BO\nalgorithms choose this hyperparameter by maximizing the marginal likelihood of\nthe observed data, albeit risking misspecification if the objective function is\nless smooth in regions we have not yet explored. The only prior solution\naddressing this problem with theoretical guarantees was A-GP-UCB, proposed by\nBerkenkamp et al. (2019). This algorithm progressively decreases the length\nscale, expanding the class of functions considered by the optimizer. However,\nA-GP-UCB lacks a stopping mechanism, leading to over-exploration and slow\nconvergence. To overcome this, we introduce Length scale Balancing (LB) - a\nnovel approach, aggregating multiple base surrogate models with varying length\nscales. LB intermittently adds smaller length scale candidate values while\nretaining longer scales, balancing exploration and exploitation. We formally\nderive a cumulative regret bound of LB and compare it with the regret of an\noracle BO algorithm using the optimal length scale. Denoting the factor by\nwhich the regret bound of A-GP-UCB was away from oracle as $g(T)$, we show that\nLB is only $\\log g(T)$ away from oracle regret. We also empirically evaluate\nour algorithm on synthetic and real-world benchmarks and show it outperforms\nA-GP-UCB, maximum likelihood estimation and MCMC.\n", "date": "2024-10-14", "categories": []}
{"id": "2411.16267", "title": "Local Bayesian Optimization for Controller Tuning with Crash Constraints", "abstract": "  Controller tuning is crucial for closed-loop performance but often involves\nmanual adjustments. Although Bayesian optimization (BO) has been established as\na data-efficient method for automated tuning, applying it to large and\nhigh-dimensional search spaces remains challenging. We extend a recently\nproposed local variant of BO to include crash constraints, where the controller\ncan only be successfully evaluated in an a-priori unknown feasible region. We\ndemonstrate the efficiency of the proposed method through simulations and\nhardware experiments. Our findings showcase the potential of local BO to\nenhance controller performance and reduce the time and resources necessary for\ntuning.\n", "date": "2024-11-25", "categories": []}
{"id": "2411.16586", "title": "Alpha Entropy Search for New Information-based Bayesian Optimization", "abstract": "  Bayesian optimization (BO) methods based on information theory have obtained\nstate-of-the-art results in several tasks. These techniques heavily rely on the\nKullback-Leibler (KL) divergence to compute the acquisition function. In this\nwork, we introduce a novel information-based class of acquisition functions for\nBO called Alpha Entropy Search (AES). AES is based on the {\\alpha}-divergence,\nthat generalizes the KL divergence. Iteratively, AES selects the next\nevaluation point as the one whose associated target value has the highest level\nof the dependency with respect to the location and associated value of the\nglobal maximum of the optimization problem. Dependency is measured in terms of\nthe {\\alpha}-divergence, as an alternative to the KL divergence. Intuitively,\nthis favors the evaluation of the objective function at the most informative\npoints about the global maximum. The {\\alpha}-divergence has a free parameter\n{\\alpha}, which determines the behavior of the divergence, trading-off\nevaluating differences between distributions at a single mode, and evaluating\ndifferences globally. Therefore, different values of {\\alpha} result in\ndifferent acquisition functions. AES acquisition lacks a closed-form\nexpression. However, we propose an efficient and accurate approximation using a\ntruncated Gaussian distribution. In practice, the value of {\\alpha} can be\nchosen by the practitioner, but here we suggest to use a combination of\nacquisition functions obtained by simultaneously considering a range of values\nof {\\alpha}. We provide an implementation of AES in BOTorch and we evaluate its\nperformance in both synthetic, benchmark and real-world experiments involving\nthe tuning of the hyper-parameters of a deep neural network. These experiments\nshow that the performance of AES is competitive with respect to other\ninformation-based acquisition functions such as JES, MES or PES.\n", "date": "2024-11-25", "categories": []}
{"id": "2408.15590", "title": "Bayesian optimization of atomic structures with prior probabilities from\n  universal interatomic potentials", "abstract": "  The optimization of atomic structures plays a pivotal role in understanding\nand designing materials with desired properties. However, conventional\ncomputational methods often struggle with the formidable task of navigating the\nvast potential energy surface, especially in high-dimensional spaces with\nnumerous local minima. Recent advancements in machine learning-driven surrogate\nmodels offer a promising avenue for alleviating this computational burden. In\nthis study, we propose a novel approach that combines the strengths of\nuniversal machine learning potentials with a Bayesian approach using Gaussian\nprocesses. By using the machine learning potentials as priors for the Gaussian\nprocess, the Gaussian process has to learn only the difference between the\nmachine learning potential and the target energy surface calculated for example\nby density functional theory. This turns out to improve the speed by which the\nglobal optimal structure is identified across diverse systems for a\nwell-behaved machine learning potential. The approach is tested on periodic\nbulk materials, surface structures, and a cluster.\n", "date": "2024-08-28", "categories": []}
{"id": "2401.01981", "title": "Beyond Regrets: Geometric Metrics for Bayesian Optimization", "abstract": "  Bayesian optimization is a principled optimization strategy for a black-box\nobjective function. It shows its effectiveness in a wide variety of real-world\napplications such as scientific discovery and experimental design. In general,\nthe performance of Bayesian optimization is reported through regret-based\nmetrics such as instantaneous, simple, and cumulative regrets. These metrics\nonly rely on function evaluations, so that they do not consider geometric\nrelationships between query points and global solutions, or query points\nthemselves. Notably, they cannot discriminate if multiple global solutions are\nsuccessfully found. Moreover, they do not evaluate Bayesian optimization's\nabilities to exploit and explore a search space given. To tackle these issues,\nwe propose four new geometric metrics, i.e., precision, recall, average degree,\nand average distance. These metrics allow us to compare Bayesian optimization\nalgorithms considering the geometry of both query points and global optima, or\nquery points. However, they are accompanied by an extra parameter, which needs\nto be carefully determined. We therefore devise the parameter-free forms of the\nrespective metrics by integrating out the additional parameter. Finally, we\nvalidate that our proposed metrics can provide more delicate interpretation of\nBayesian optimization, on top of assessment via the conventional metrics.\n", "date": "2024-01-03", "categories": []}
{"id": "2411.05330", "title": "Inversion-based Latent Bayesian Optimization", "abstract": "  Latent Bayesian optimization (LBO) approaches have successfully adopted\nBayesian optimization over a continuous latent space by employing an\nencoder-decoder architecture to address the challenge of optimization in a high\ndimensional or discrete input space. LBO learns a surrogate model to\napproximate the black-box objective function in the latent space. However, we\nobserved that most LBO methods suffer from the `misalignment problem`, which is\ninduced by the reconstruction error of the encoder-decoder architecture. It\nhinders learning an accurate surrogate model and generating high-quality\nsolutions. In addition, several trust region-based LBO methods select the\nanchor, the center of the trust region, based solely on the objective function\nvalue without considering the trust region`s potential to enhance the\noptimization process. To address these issues, we propose Inversion-based\nLatent Bayesian Optimization (InvBO), a plug-and-play module for LBO. InvBO\nconsists of two components: an inversion method and a potential-aware trust\nregion anchor selection. The inversion method searches the latent code that\ncompletely reconstructs the given target data. The potential-aware trust region\nanchor selection considers the potential capability of the trust region for\nbetter local optimization. Experimental results demonstrate the effectiveness\nof InvBO on nine real-world benchmarks, such as molecule design and arithmetic\nexpression fitting tasks. Code is available at https://github.com/mlvlab/InvBO.\n", "date": "2024-11-08", "categories": []}
{"id": "2411.03731", "title": "Reducing Hyperparameter Tuning Costs in ML, Vision and Language Model\n  Training Pipelines via Memoization-Awareness", "abstract": "  The training or fine-tuning of machine learning, vision, and language models\nis often implemented as a pipeline: a sequence of stages encompassing data\npreparation, model training and evaluation. In this paper, we exploit pipeline\nstructures to reduce the cost of hyperparameter tuning for model\ntraining/fine-tuning, which is particularly valuable for language models given\ntheir high costs in GPU-days. We propose a \"memoization-aware\" Bayesian\nOptimization (BO) algorithm, EEIPU, that works in tandem with a pipeline\ncaching system, allowing it to evaluate significantly more hyperparameter\ncandidates per GPU-day than other tuning algorithms. The result is\nbetter-quality hyperparameters in the same amount of search time, or\nequivalently, reduced search time to reach the same hyperparameter quality. In\nour benchmarks on machine learning (model ensembles), vision (convolutional\narchitecture) and language (T5 architecture) pipelines, we compare EEIPU\nagainst recent BO algorithms: EEIPU produces an average of $103\\%$ more\nhyperparameter candidates (within the same budget), and increases the\nvalidation metric by an average of $108\\%$ more than other algorithms (where\nthe increase is measured starting from the end of warm-up iterations).\n", "date": "2024-11-06", "categories": []}
{"id": "2411.03028", "title": "Graph Agnostic Causal Bayesian Optimisation", "abstract": "  We study the problem of globally optimising a target variable of an unknown\ncausal graph on which a sequence of soft or hard interventions can be\nperformed. The problem of optimising the target variable associated with a\ncausal graph is formalised as Causal Bayesian Optimisation (CBO). We study the\nCBO problem under the cumulative regret objective with unknown causal graphs\nfor two settings, namely structural causal models with hard interventions and\nfunction networks with soft interventions. We propose Graph Agnostic Causal\nBayesian Optimisation (GACBO), an algorithm that actively discovers the causal\nstructure that contributes to achieving optimal rewards. GACBO seeks to balance\nexploiting the actions that give the best rewards against exploring the causal\nstructures and functions. To the best of our knowledge, our work is the first\nto study causal Bayesian optimization with cumulative regret objectives in\nscenarios where the graph is unknown or partially known. We show our proposed\nalgorithm outperforms baselines in simulated experiments and real-world\napplications.\n", "date": "2024-11-05", "categories": []}
{"id": "2406.02352", "title": "System-Aware Neural ODE Processes for Few-Shot Bayesian Optimization", "abstract": "  We consider the problem of optimizing initial conditions and termination time\nin dynamical systems governed by unknown ordinary differential equations\n(ODEs), where evaluating different initial conditions is costly and the state's\nvalue can not be measured in real-time but only with a delay while the\nmeasuring device processes the sample. To identify the optimal conditions in\nlimited trials, we introduce a few-shot Bayesian Optimization (BO) framework\nbased on the system's prior information. At the core of our approach is the\nSystem-Aware Neural ODE Processes (SANODEP), an extension of Neural ODE\nProcesses (NODEP) designed to meta-learn ODE systems from multiple trajectories\nusing a novel context embedding block. We further develop a two-stage BO\nframework to effectively incorporate search space constraints, enabling\nefficient optimization of both initial conditions and observation timings. We\nconduct extensive experiments showcasing SANODEP's potential for few-shot BO\nwithin dynamical systems. We also explore SANODEP's adaptability to varying\nlevels of prior information, highlighting the trade-off between prior\nflexibility and model fitting accuracy.\n", "date": "2024-06-04", "categories": []}
{"id": "2406.04739", "title": "A survey and benchmark of high-dimensional Bayesian optimization of\n  discrete sequences", "abstract": "  Optimizing discrete black-box functions is key in several domains, e.g.\nprotein engineering and drug design. Due to the lack of gradient information\nand the need for sample efficiency, Bayesian optimization is an ideal candidate\nfor these tasks. Several methods for high-dimensional continuous and\ncategorical Bayesian optimization have been proposed recently. However, our\nsurvey of the field reveals highly heterogeneous experimental set-ups across\nmethods and technical barriers for the replicability and application of\npublished algorithms to real-world tasks. To address these issues, we develop a\nunified framework to test a vast array of high-dimensional Bayesian\noptimization methods and a collection of standardized black-box functions\nrepresenting real-world application domains in chemistry and biology. These two\ncomponents of the benchmark are each supported by flexible, scalable, and\neasily extendable software libraries (poli and poli-baselines), allowing\npractitioners to readily incorporate new optimization objectives or discrete\noptimizers. Project website:\nhttps://machinelearninglifescience.github.io/hdbo_benchmark\n", "date": "2024-06-07", "categories": []}
{"id": "2407.11917", "title": "Global Optimisation of Black-Box Functions with Generative Models in the\n  Wasserstein Space", "abstract": "  We propose a new uncertainty estimator for gradient-free optimisation of\nblack-box simulators using deep generative surrogate models. Optimisation of\nthese simulators is especially challenging for stochastic simulators and higher\ndimensions. To address these issues, we utilise a deep generative surrogate\napproach to model the black box response for the entire parameter space. We\nthen leverage this knowledge to estimate the proposed uncertainty based on the\nWasserstein distance - the Wasserstein uncertainty. This approach is employed\nin a posterior agnostic gradient-free optimisation algorithm that minimises\nregret over the entire parameter space. A series of tests were conducted to\ndemonstrate that our method is more robust to the shape of both the black box\nfunction and the stochastic response of the black box than state-of-the-art\nmethods, such as efficient global optimisation with a deep Gaussian process\nsurrogate.\n", "date": "2024-07-16", "categories": []}
{"id": "2402.08406", "title": "Transition Constrained Bayesian Optimization via Markov Decision\n  Processes", "abstract": "  Bayesian optimization is a methodology to optimize black-box functions.\nTraditionally, it focuses on the setting where you can arbitrarily query the\nsearch space. However, many real-life problems do not offer this flexibility;\nin particular, the search space of the next query may depend on previous ones.\nExample challenges arise in the physical sciences in the form of local movement\nconstraints, required monotonicity in certain variables, and transitions\ninfluencing the accuracy of measurements. Altogether, such transition\nconstraints necessitate a form of planning. This work extends classical\nBayesian optimization via the framework of Markov Decision Processes. We\niteratively solve a tractable linearization of our utility function using\nreinforcement learning to obtain a policy that plans ahead for the entire\nhorizon. This is a parallel to the optimization of an acquisition function in\npolicy space. The resulting policy is potentially history-dependent and\nnon-Markovian. We showcase applications in chemical reactor optimization,\ninformative path planning, machine calibration, and other synthetic examples.\n", "date": "2024-02-13", "categories": []}
{"id": "2403.00540", "title": "Epsilon-Greedy Thompson Sampling to Bayesian Optimization", "abstract": "  Bayesian optimization (BO) has become a powerful tool for solving\nsimulation-based engineering optimization problems thanks to its ability to\nintegrate physical and mathematical understandings, consider uncertainty, and\naddress the exploitation-exploration dilemma. Thompson sampling (TS) is a\npreferred solution for BO to handle the exploitation-exploration trade-off.\nWhile it prioritizes exploration by generating and minimizing random sample\npaths from probabilistic models -- a fundamental ingredient of BO -- TS weakly\nmanages exploitation by gathering information about the true objective function\nafter it obtains new observations. In this work, we improve the exploitation of\nTS by incorporating the $\\varepsilon$-greedy policy, a well-established\nselection strategy in reinforcement learning. We first delineate two extremes\nof TS, namely the generic TS and the sample-average TS. The former promotes\nexploration, while the latter favors exploitation. We then adopt the\n$\\varepsilon$-greedy policy to randomly switch between these two extremes.\nSmall and large values of $\\varepsilon$ govern exploitation and exploration,\nrespectively. By minimizing two benchmark functions and solving an inverse\nproblem of a steel cantilever beam, we empirically show that\n$\\varepsilon$-greedy TS equipped with an appropriate $\\varepsilon$ is more\nrobust than its two extremes, matching or outperforming the better of the\ngeneric TS and the sample-average TS.\n", "date": "2024-03-01", "categories": []}
{"id": "2410.21886", "title": "Bayesian Optimization for Hyperparameters Tuning in Neural Networks", "abstract": "  This study investigates the application of Bayesian Optimization (BO) for the\nhyperparameter tuning of neural networks, specifically targeting the\nenhancement of Convolutional Neural Networks (CNN) for image classification\ntasks. Bayesian Optimization is a derivative-free global optimization method\nsuitable for expensive black-box functions with continuous inputs and limited\nevaluation budgets. The BO algorithm leverages Gaussian Process regression and\nacquisition functions like Upper Confidence Bound (UCB) and Expected\nImprovement (EI) to identify optimal configurations effectively. Using the Ax\nand BOTorch frameworks, this work demonstrates the efficiency of BO in reducing\nthe number of hyperparameter tuning trials while achieving competitive model\nperformance. Experimental outcomes reveal that BO effectively balances\nexploration and exploitation, converging rapidly towards optimal settings for\nCNN architectures. This approach underlines the potential of BO in automating\nneural network tuning, contributing to improved accuracy and computational\nefficiency in machine learning pipelines.\n", "date": "2024-10-29", "categories": []}
{"id": "2410.20596", "title": "Practical Bayesian Algorithm Execution via Posterior Sampling", "abstract": "  We consider Bayesian algorithm execution (BAX), a framework for efficiently\nselecting evaluation points of an expensive function to infer a property of\ninterest encoded as the output of a base algorithm. Since the base algorithm\ntypically requires more evaluations than are feasible, it cannot be directly\napplied. Instead, BAX methods sequentially select evaluation points using a\nprobabilistic numerical approach. Current BAX methods use expected information\ngain to guide this selection. However, this approach is computationally\nintensive. Observing that, in many tasks, the property of interest corresponds\nto a target set of points defined by the function, we introduce PS-BAX, a\nsimple, effective, and scalable BAX method based on posterior sampling. PS-BAX\nis applicable to a wide range of problems, including many optimization variants\nand level set estimation. Experiments across diverse tasks demonstrate that\nPS-BAX performs competitively with existing baselines while being significantly\nfaster, simpler to implement, and easily parallelizable, setting a strong\nbaseline for future research. Additionally, we establish conditions under which\nPS-BAX is asymptotically convergent, offering new insights into posterior\nsampling as an algorithm design paradigm.\n", "date": "2024-10-27", "categories": []}
{"id": "2305.02614", "title": "High-Dimensional Bayesian Optimization via Semi-Supervised Learning with\n  Optimized Unlabeled Data Sampling", "abstract": "  We introduce a novel semi-supervised learning approach, named Teacher-Student\nBayesian Optimization ($\\texttt{TSBO}$), integrating the teacher-student\nparadigm into BO to minimize expensive labeled data queries for the first time.\n$\\texttt{TSBO}$ incorporates a teacher model, an unlabeled data sampler, and a\nstudent model. The student is trained on unlabeled data locations generated by\nthe sampler, with pseudo labels predicted by the teacher. The interplay between\nthese three components implements a unique selective regularization to the\nteacher in the form of student feedback. This scheme enables the teacher to\npredict high-quality pseudo labels, enhancing the generalization of the GP\nsurrogate model in the search space. To fully exploit $\\texttt{TSBO}$, we\npropose two optimized unlabeled data samplers to construct effective student\nfeedback that well aligns with the objective of Bayesian optimization.\nFurthermore, we quantify and leverage the uncertainty of the teacher-student\nmodel for the provision of reliable feedback to the teacher in the presence of\nrisky pseudo-label predictions. $\\texttt{TSBO}$ demonstrates significantly\nimproved sample-efficiency in several global optimization tasks under tight\nlabeled data budgets.\n", "date": "2023-05-04", "categories": []}
{"id": "2410.18237", "title": "Bayesian optimization for robust robotic grasping using a sensorized\n  compliant hand", "abstract": "  One of the first tasks we learn as children is to grasp objects based on our\ntactile perception. Incorporating such skill in robots will enable multiple\napplications, such as increasing flexibility in industrial processes or\nproviding assistance to people with physical disabilities. However, the\ndifficulty lies in adapting the grasping strategies to a large variety of tasks\nand objects, which can often be unknown. The brute-force solution is to learn\nnew grasps by trial and error, which is inefficient and ineffective. In\ncontrast, Bayesian optimization applies active learning by adding information\nto the approximation of an optimal grasp. This paper proposes the use of\nBayesian optimization techniques to safely perform robotic grasping. We analyze\ndifferent grasp metrics to provide realistic grasp optimization in a real\nsystem including tactile sensors. An experimental evaluation in the robotic\nsystem shows the usefulness of the method for performing unknown object\ngrasping even in the presence of noise and uncertainty inherent to a real-world\nenvironment.\n", "date": "2024-10-23", "categories": []}
{"id": "2402.17704", "title": "Transfer Learning Bayesian Optimization to Design Competitor DNA\n  Molecules for Use in Diagnostic Assays", "abstract": "  With the rise in engineered biomolecular devices, there is an increased need\nfor tailor-made biological sequences. Often, many similar biological sequences\nneed to be made for a specific application meaning numerous, sometimes\nprohibitively expensive, lab experiments are necessary for their optimization.\nThis paper presents a transfer learning design of experiments workflow to make\nthis development feasible. By combining a transfer learning surrogate model\nwith Bayesian optimization, we show how the total number of experiments can be\nreduced by sharing information between optimization tasks. We demonstrate the\nreduction in the number of experiments using data from the development of DNA\ncompetitors for use in an amplification-based diagnostic assay. We use\ncross-validation to compare the predictive accuracy of different transfer\nlearning models, and then compare the performance of the models for both single\nobjective and penalized optimization tasks.\n", "date": "2024-02-27", "categories": []}
{"id": "2406.15291", "title": "Pessimistic asynchronous sampling in high-cost Bayesian optimization", "abstract": "  Asynchronous Bayesian optimization is a recently implemented technique that\nallows for parallel operation of experimental systems and disjointed workflows.\nContrasting with serial Bayesian optimization which individually selects\nexperiments one at a time after conducting a measurement for each experiment,\nasynchronous policies sequentially assign multiple experiments before\nmeasurements can be taken and evaluate new measurements continuously as they\nare made available. This technique allows for faster data generation and\ntherefore faster optimization of an experimental space. This work extends the\ncapabilities of asynchronous optimization methods beyond prior studies by\nevaluating four additional policies that incorporate pessimistic predictions in\nthe training data set. Combined with a conventional policy that uses model\npredictions, the five total policies were evaluated in a simulated environment\nand benchmarked with serial sampling. Under some conditions and parameter space\ndimensionalities, the pessimistic prediction asynchronous policy reached\noptimum experimental conditions in significantly fewer experiments than\nequivalent serial policies and proved to be less susceptible to convergence\nonto local optima at higher dimensions. Without accounting for the faster\nsampling rate, the pessimistic asynchronous algorithm presented in this work\ncould result in more efficient algorithm driven optimization of high-cost\nexperimental spaces. Accounting for sampling rate, the presented asynchronous\nalgorithm could allow for faster optimization in experimental spaces where\nmultiple experiments can be run before results are collected.\n", "date": "2024-06-21", "categories": []}
{"id": "2410.16972", "title": "Sample-efficient Bayesian Optimisation Using Known Invariances", "abstract": "  Bayesian optimisation (BO) is a powerful framework for global optimisation of\ncostly functions, using predictions from Gaussian process models (GPs). In this\nwork, we apply BO to functions that exhibit invariance to a known group of\ntransformations. We show that vanilla and constrained BO algorithms are\ninefficient when optimising such invariant objectives, and provide a method for\nincorporating group invariances into the kernel of the GP to produce\ninvariance-aware algorithms that achieve significant improvements in sample\nefficiency. We derive a bound on the maximum information gain of these\ninvariant kernels, and provide novel upper and lower bounds on the number of\nobservations required for invariance-aware BO algorithms to achieve\n$\\epsilon$-optimality. We demonstrate our method's improved performance on a\nrange of synthetic invariant and quasi-invariant functions. We also apply our\nmethod in the case where only some of the invariance is incorporated into the\nkernel, and find that these kernels achieve similar gains in sample efficiency\nat significantly reduced computational cost. Finally, we use invariant BO to\ndesign a current drive system for a nuclear fusion reactor, finding a\nhigh-performance solution where non-invariant methods failed.\n", "date": "2024-10-22", "categories": []}
{"id": "2405.14540", "title": "This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian\n  Optimization", "abstract": "  Bayesian Optimization (BO) has proven to be very successful at optimizing a\nstatic, noisy, costly-to-evaluate black-box function $f : \\mathcal{S} \\to\n\\mathbb{R}$. However, optimizing a black-box which is also a function of time\n(i.e., a dynamic function) $f : \\mathcal{S} \\times \\mathcal{T} \\to \\mathbb{R}$\nremains a challenge, since a dynamic Bayesian Optimization (DBO) algorithm has\nto keep track of the optimum over time. This changes the nature of the\noptimization problem in at least three aspects: (i) querying an arbitrary point\nin $\\mathcal{S} \\times \\mathcal{T}$ is impossible, (ii) past observations\nbecome less and less relevant for keeping track of the optimum as time goes by\nand (iii) the DBO algorithm must have a high sampling frequency so it can\ncollect enough relevant observations to keep track of the optimum through time.\nIn this paper, we design a Wasserstein distance-based criterion able to\nquantify the relevancy of an observation with respect to future predictions.\nThen, we leverage this criterion to build W-DBO, a DBO algorithm able to remove\nirrelevant observations from its dataset on the fly, thus maintaining\nsimultaneously a good predictive performance and a high sampling frequency,\neven in continuous-time optimization tasks with unknown horizon. Numerical\nexperiments establish the superiority of W-DBO, which outperforms\nstate-of-the-art methods by a comfortable margin.\n", "date": "2024-05-23", "categories": []}
{"id": "2410.16052", "title": "Near-Optimal Algorithm for Non-Stationary Kernelized Bandits", "abstract": "  This paper studies a non-stationary kernelized bandit (KB) problem, also\ncalled time-varying Bayesian optimization, where one seeks to minimize the\nregret under an unknown reward function that varies over time. In particular,\nwe focus on a near-optimal algorithm whose regret upper bound matches the\nregret lower bound. For this goal, we show the first algorithm-independent\nregret lower bound for non-stationary KB with squared exponential and Mat\\'ern\nkernels, which reveals that an existing optimization-based KB algorithm with\nslight modification is near-optimal. However, this existing algorithm suffers\nfrom feasibility issues due to its huge computational cost. Therefore, we\npropose a novel near-optimal algorithm called restarting phased elimination\nwith random permutation (R-PERP), which bypasses the huge computational cost. A\ntechnical key point is the simple permutation procedures of query candidates,\nwhich enable us to derive a novel tighter confidence bound tailored to the\nnon-stationary problems.\n", "date": "2024-10-21", "categories": []}
{"id": "2410.12984", "title": "Double-Bayesian Learning", "abstract": "  Contemporary machine learning methods will try to approach the Bayes error,\nas it is the lowest possible error any model can achieve. This paper postulates\nthat any decision is composed of not one but two Bayesian decisions and that\ndecision-making is, therefore, a double-Bayesian process. The paper shows how\nthis duality implies intrinsic uncertainty in decisions and how it incorporates\nexplainability. The proposed approach understands that Bayesian learning is\ntantamount to finding a base for a logarithmic function measuring uncertainty,\nwith solutions being fixed points. Furthermore, following this approach, the\ngolden ratio describes possible solutions satisfying Bayes' theorem. The\ndouble-Bayesian framework suggests using a learning rate and momentum weight\nwith values similar to those used in the literature to train neural networks\nwith stochastic gradient descent.\n", "date": "2024-10-16", "categories": []}
{"id": "2402.07160", "title": "PASOA- PArticle baSed Bayesian Optimal Adaptive design", "abstract": "  We propose a new procedure named PASOA, for Bayesian experimental design,\nthat performs sequential design optimization by simultaneously providing\naccurate estimates of successive posterior distributions for parameter\ninference. The sequential design process is carried out via a contrastive\nestimation principle, using stochastic optimization and Sequential Monte Carlo\n(SMC) samplers to maximise the Expected Information Gain (EIG). As larger\ninformation gains are obtained for larger distances between successive\nposterior distributions, this EIG objective may worsen classical SMC\nperformance. To handle this issue, tempering is proposed to have both a large\ninformation gain and an accurate SMC sampling, that we show is crucial for\nperformance. This novel combination of stochastic optimization and tempered SMC\nallows to jointly handle design optimization and parameter inference. We\nprovide a proof that the obtained optimal design estimators benefit from some\nconsistency property. Numerical experiments confirm the potential of the\napproach, which outperforms other recent existing procedures.\n", "date": "2024-02-11", "categories": []}
{"id": "2410.10452", "title": "Principled Bayesian Optimisation in Collaboration with Human Experts", "abstract": "  Bayesian optimisation for real-world problems is often performed\ninteractively with human experts, and integrating their domain knowledge is key\nto accelerate the optimisation process. We consider a setup where experts\nprovide advice on the next query point through binary accept/reject\nrecommendations (labels). Experts' labels are often costly, requiring efficient\nuse of their efforts, and can at the same time be unreliable, requiring careful\nadjustment of the degree to which any expert is trusted. We introduce the first\nprincipled approach that provides two key guarantees. (1) Handover guarantee:\nsimilar to a no-regret property, we establish a sublinear bound on the\ncumulative number of experts' binary labels. Initially, multiple labels per\nquery are needed, but the number of expert labels required asymptotically\nconverges to zero, saving both expert effort and computation time. (2) No-harm\nguarantee with data-driven trust level adjustment: our adaptive trust level\nensures that the convergence rate will not be worse than the one without using\nadvice, even if the advice from experts is adversarial. Unlike existing methods\nthat employ a user-defined function that hand-tunes the trust level adjustment,\nour approach enables data-driven adjustments. Real-world applications\nempirically demonstrate that our method not only outperforms existing\nbaselines, but also maintains robustness despite varying labelling accuracy, in\ntasks of battery design with human experts.\n", "date": "2024-10-14", "categories": []}
{"id": "2410.08804", "title": "Batched Energy-Entropy acquisition for Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is an attractive machine learning framework for\nperforming sample-efficient global optimization of black-box functions. The\noptimization process is guided by an acquisition function that selects points\nto acquire in each round of BO. In batched BO, when multiple points are\nacquired in parallel, commonly used acquisition functions are often\nhigh-dimensional and intractable, leading to the use of sampling-based\nalternatives. We propose a statistical physics inspired acquisition function\nfor BO with Gaussian processes that can natively handle batches. Batched\nEnergy-Entropy acquisition for BO (BEEBO) enables tight control of the\nexplore-exploit trade-off of the optimization process and generalizes to\nheteroskedastic black-box problems. We demonstrate the applicability of BEEBO\non a range of problems, showing competitive performance to existing methods.\n", "date": "2024-10-11", "categories": []}
{"id": "2410.08071", "title": "Gaussian Process Thompson Sampling via Rootfinding", "abstract": "  Thompson sampling (TS) is a simple, effective stochastic policy in Bayesian\ndecision making. It samples the posterior belief about the reward profile and\noptimizes the sample to obtain a candidate decision. In continuous\noptimization, the posterior of the objective function is often a Gaussian\nprocess (GP), whose sample paths have numerous local optima, making their\nglobal optimization challenging. In this work, we introduce an efficient global\noptimization strategy for GP-TS that carefully selects starting points for\ngradient-based multi-start optimizers. It identifies all local optima of the\nprior sample via univariate global rootfinding, and optimizes the posterior\nsample using a differentiable, decoupled representation. We demonstrate\nremarkable improvement in the global optimization of GP posterior samples,\nespecially in high dimensions. This leads to dramatic improvements in the\noverall performance of Bayesian optimization using GP-TS acquisition functions,\nsurprisingly outperforming alternatives like GP-UCB and EI.\n", "date": "2024-10-10", "categories": []}
{"id": "2410.02717", "title": "Measurements with Noise: Bayesian Optimization for Co-optimizing Noise\n  and Property Discovery in Automated Experiments", "abstract": "  We have developed a Bayesian optimization (BO) workflow that integrates\nintra-step noise optimization into automated experimental cycles. Traditional\nBO approaches in automated experiments focus on optimizing experimental\ntrajectories but often overlook the impact of measurement noise on data quality\nand cost. Our proposed framework simultaneously optimizes both the target\nproperty and the associated measurement noise by introducing time as an\nadditional input parameter, thereby balancing the signal-to-noise ratio and\nexperimental duration. Two approaches are explored: a reward-driven noise\noptimization and a double-optimization acquisition function, both enhancing the\nefficiency of automated workflows by considering noise and cost within the\noptimization process. We validate our method through simulations and real-world\nexperiments using Piezoresponse Force Microscopy (PFM), demonstrating the\nsuccessful optimization of measurement duration and property exploration. Our\napproach offers a scalable solution for optimizing multiple variables in\nautomated experimental workflows, improving data quality, and reducing resource\nexpenditure in materials science and beyond.\n", "date": "2024-10-03", "categories": []}
{"id": "2405.17881", "title": "Crystal-LSBO: Automated Design of De Novo Crystals with Latent Space\n  Bayesian Optimization", "abstract": "  Generative modeling of crystal structures is significantly challenged by the\ncomplexity of input data, which constrains the ability of these models to\nexplore and discover novel crystals. This complexity often confines de novo\ndesign methodologies to merely small perturbations of known crystals and\nhampers the effective application of advanced optimization techniques. One such\noptimization technique, Latent Space Bayesian Optimization (LSBO) has\ndemonstrated promising results in uncovering novel objects across various\ndomains, especially when combined with Variational Autoencoders (VAEs).\nRecognizing LSBO's potential and the critical need for innovative crystal\ndiscovery, we introduce Crystal-LSBO, a de novo design framework for crystals\nspecifically tailored to enhance explorability within LSBO frameworks.\nCrystal-LSBO employs multiple VAEs, each dedicated to a distinct aspect of\ncrystal structure: lattice, coordinates, and chemical elements, orchestrated by\nan integrative model that synthesizes these components into a cohesive output.\nThis setup not only streamlines the learning process but also produces\nexplorable latent spaces thanks to the decreased complexity of the learning\ntask for each model, enabling LSBO approaches to operate. Our study pioneers\nthe use of LSBO for de novo crystal design, demonstrating its efficacy through\noptimization tasks focused mainly on formation energy values. Our results\nhighlight the effectiveness of our methodology, offering a new perspective for\nde novo crystal discovery.\n", "date": "2024-05-28", "categories": []}
{"id": "2409.12295", "title": "SANE: Strategic Autonomous Non-Smooth Exploration for Multiple Optima\n  Discovery in Multi-modal and Non-differentiable Black-box Functions", "abstract": "  Both computational and experimental material discovery bring forth the\nchallenge of exploring multidimensional and multimodal parameter spaces, such\nas phase diagrams of Hamiltonians with multiple interactions, composition\nspaces of combinatorial libraries, material structure image spaces, and\nmolecular embedding spaces. Often these systems are black-box and\ntime-consuming to evaluate, which resulted in strong interest towards active\nlearning methods such as Bayesian optimization (BO). However, these systems are\noften noisy which make the black box function severely multi-modal and\nnon-differentiable, where a vanilla BO can get overly focused near a single or\nfaux optimum, deviating from the broader goal of scientific discovery. To\naddress these limitations, here we developed Strategic Autonomous Non-Smooth\nExploration (SANE) to facilitate an intelligent Bayesian optimized navigation\nwith a proposed cost-driven probabilistic acquisition function to find multiple\nglobal and local optimal regions, avoiding the tendency to becoming trapped in\na single optimum. To distinguish between a true and false optimal region due to\nnoisy experimental measurements, a human (domain) knowledge driven dynamic\nsurrogate gate is integrated with SANE. We implemented the gate-SANE into a\npre-acquired Piezoresponse spectroscopy data of a ferroelectric combinatorial\nlibrary with high noise levels in specific regions, and a piezoresponse force\nmicroscopy (PFM) hyperspectral data. SANE demonstrated better performance than\nclassical BO to facilitate the exploration of multiple optimal regions and\nthereby prioritized learning with higher coverage of scientific values in\nautonomous experiments. Our work showcases the potential application of this\nmethod to real-world experiment, where such combined strategic and human\nintervening approaches can be critical to unlocking new discoveries in\nautonomous research.\n", "date": "2024-09-18", "categories": []}
{"id": "2409.09192", "title": "Automated design of nonreciprocal thermal emitters via Bayesian\n  optimization", "abstract": "  Nonreciprocal thermal emitters that break Kirchhoff's law of thermal\nradiation promise exciting applications for thermal and energy applications.\nThe design of the bandwidth and angular range of the nonreciprocal effect,\nwhich directly affects the performance of nonreciprocal emitters, typically\nrelies on physical intuition. In this study, we present a general numerical\napproach to maximize the nonreciprocal effect. We choose doped magneto-optic\nmaterials and magnetic Weyl semimetal materials as model materials and focus on\npattern-free multilayer structures. The optimization randomly starts from a\nless effective structure and incrementally improves the broadband\nnonreciprocity through the combination of Bayesian optimization and\nreparameterization. Optimization results show that the proposed approach can\ndiscover structures that can achieve broadband nonreciprocal emission at\nwavelengths from 5 to 40 micrometers using only a fewer layers, significantly\noutperforming current state-of-the-art designs based on intuition in terms of\nboth performance and simplicity.\n", "date": "2024-09-13", "categories": []}
{"id": "2409.07190", "title": "Applying Multi-Fidelity Bayesian Optimization in Chemistry: Open\n  Challenges and Major Considerations", "abstract": "  Multi fidelity Bayesian optimization (MFBO) leverages experimental and or\ncomputational data of varying quality and resource cost to optimize towards\ndesired maxima cost effectively. This approach is particularly attractive for\nchemical discovery due to MFBO's ability to integrate diverse data sources.\nHere, we investigate the application of MFBO to accelerate the identification\nof promising molecules or materials. We specifically analyze the conditions\nunder which lower fidelity data can enhance performance compared to\nsingle-fidelity problem formulations. We address two key challenges, selecting\nthe optimal acquisition function, understanding the impact of cost, and data\nfidelity correlation. We then discuss how to assess the effectiveness of MFBO\nfor chemical discovery.\n", "date": "2024-09-11", "categories": []}
{"id": "2409.05325", "title": "Sample-Efficient Bayesian Optimization with Transfer Learning for\n  Heterogeneous Search Spaces", "abstract": "  Bayesian optimization (BO) is a powerful approach to sample-efficient\noptimization of black-box functions. However, in settings with very few\nfunction evaluations, a successful application of BO may require transferring\ninformation from historical experiments. These related experiments may not have\nexactly the same tunable parameters (search spaces), motivating the need for BO\nwith transfer learning for heterogeneous search spaces. In this paper, we\npropose two methods for this setting. The first approach leverages a Gaussian\nprocess (GP) model with a conditional kernel to transfer information between\ndifferent search spaces. Our second approach treats the missing parameters as\nhyperparameters of the GP model that can be inferred jointly with the other GP\nhyperparameters or set to fixed values. We show that these two methods perform\nwell on several benchmark problems.\n", "date": "2024-09-09", "categories": []}
{"id": "2306.01095", "title": "Large-Batch, Iteration-Efficient Neural Bayesian Design Optimization", "abstract": "  Bayesian optimization (BO) provides a powerful framework for optimizing\nblack-box, expensive-to-evaluate functions. It is therefore an attractive tool\nfor engineering design problems, typically involving multiple objectives.\nThanks to the rapid advances in fabrication and measurement methods as well as\nparallel computing infrastructure, querying many design problems can be heavily\nparallelized. This class of problems challenges BO with an unprecedented setup\nwhere it has to deal with very large batches, shifting its focus from sample\nefficiency to iteration efficiency. We present a novel Bayesian optimization\nframework specifically tailored to address these limitations. Our key\ncontribution is a highly scalable, sample-based acquisition function that\nperforms a non-dominated sorting of not only the objectives but also their\nassociated uncertainty. We show that our acquisition function in combination\nwith different Bayesian neural network surrogates is effective in\ndata-intensive environments with a minimal number of iterations. We demonstrate\nthe superiority of our method by comparing it with state-of-the-art\nmulti-objective optimizations. We perform our evaluation on two real-world\nproblems -- airfoil design and 3D printing -- showcasing the applicability and\nefficiency of our approach. Our code is available at:\nhttps://github.com/an-on-ym-ous/lbn_mobo\n", "date": "2023-06-01", "categories": []}
{"id": "2408.07812", "title": "Differentiating Policies for Non-Myopic Bayesian Optimization", "abstract": "  Bayesian optimization (BO) methods choose sample points by optimizing an\nacquisition function derived from a statistical model of the objective. These\nacquisition functions are chosen to balance sampling regions with predicted\ngood objective values against exploring regions where the objective is\nuncertain. Standard acquisition functions are myopic, considering only the\nimpact of the next sample, but non-myopic acquisition functions may be more\neffective. In principle, one could model the sampling by a Markov decision\nprocess, and optimally choose the next sample by maximizing an expected reward\ncomputed by dynamic programming; however, this is infeasibly expensive. More\npractical approaches, such as rollout, consider a parametric family of sampling\npolicies. In this paper, we show how to efficiently estimate rollout\nacquisition functions and their gradients, enabling stochastic gradient-based\noptimization of sampling policies.\n", "date": "2024-08-14", "categories": []}
{"id": "2408.06540", "title": "Dynamic Exclusion of Low-Fidelity Data in Bayesian Optimization for\n  Autonomous Beamline Alignment", "abstract": "  Aligning beamlines at synchrotron light sources is a high-dimensional,\nexpensive-to-sample optimization problem, as beams are focused using a series\nof dynamic optical components. Bayesian Optimization is an efficient machine\nlearning approach to finding global optima of beam quality, but the model can\neasily be impaired by faulty data points caused by the beam going off the edge\nof the sensor or by background noise. This study, conducted at the National\nSynchrotron Light Source II (NSLS-II) facility at Brookhaven National\nLaboratory (BNL), is an investigation of methods to identify untrustworthy\nreadings of beam quality and discourage the optimization model from seeking out\npoints likely to yield low-fidelity beams. The approaches explored include\ndynamic pruning using loss analysis of size and position models and a\nlengthscale-based genetic algorithm to determine which points to include in the\nmodel for optimal fit. Each method successfully classified high and low\nfidelity points. This research advances BNL's mission to tackle our nation's\nenergy challenges by providing scientists at all beamlines with access to\nhigher quality beams, and faster convergence to these optima for their\nexperiments.\n", "date": "2024-08-13", "categories": []}
{"id": "2408.04860", "title": "High dimensional Bayesian Optimization via Condensing-Expansion\n  Projection", "abstract": "  In high-dimensional settings, Bayesian optimization (BO) can be expensive and\ninfeasible. The random embedding Bayesian optimization algorithm is commonly\nused to address high-dimensional BO challenges. However, this method relies on\nthe effective subspace assumption on the optimization problem's objective\nfunction, which limits its applicability. In this paper, we introduce\nCondensing-Expansion Projection Bayesian optimization (CEPBO), a novel random\nprojection-based approach for high-dimensional BO that does not reply on the\neffective subspace assumption. The approach is both simple to implement and\nhighly practical. We present two algorithms based on different random\nprojection matrices: the Gaussian projection matrix and the hashing projection\nmatrix. Experimental results demonstrate that both algorithms outperform\nexisting random embedding-based algorithms in most cases, achieving superior\nperformance on high-dimensional BO problems. The code is available in\n\\url{https://anonymous.4open.science/r/CEPBO-14429}.\n", "date": "2024-08-09", "categories": []}
{"id": "2408.05040", "title": "BoFire: Bayesian Optimization Framework Intended for Real Experiments", "abstract": "  Our open-source Python package BoFire combines Bayesian Optimization (BO)\nwith other design of experiments (DoE) strategies focusing on developing and\noptimizing new chemistry. Previous BO implementations, for example as they\nexist in the literature or software, require substantial adaptation for\neffective real-world deployment in chemical industry. BoFire provides a rich\nfeature-set with extensive configurability and realizes our vision of\nfast-tracking research contributions into industrial use via maintainable\nopen-source software. Owing to quality-of-life features like\nJSON-serializability of problem formulations, BoFire enables seamless\nintegration of BO into RESTful APIs, a common architecture component for both\nself-driving laboratories and human-in-the-loop setups. This paper discusses\nthe differences between BoFire and other BO implementations and outlines ways\nthat BO research needs to be adapted for real-world use in a chemistry setting.\n", "date": "2024-08-09", "categories": []}
{"id": "2408.02551", "title": "Process-constrained batch Bayesian approaches for yield optimization in\n  multi-reactor systems", "abstract": "  The optimization of yields in multi-reactor systems, which are advanced tools\nin heterogeneous catalysis research, presents a significant challenge due to\nhierarchical technical constraints. To this respect, this work introduces a\nnovel approach called process-constrained batch Bayesian optimization via\nThompson sampling (pc-BO-TS) and its generalized hierarchical extension\n(hpc-BO-TS). This method, tailored for the efficiency demands in multi-reactor\nsystems, integrates experimental constraints and balances between exploration\nand exploitation in a sequential batch optimization strategy. It offers an\nimprovement over other Bayesian optimization methods. The performance of\npc-BO-TS and hpc-BO-TS is validated in synthetic cases as well as in a\nrealistic scenario based on data obtained from high-throughput experiments done\non a multi-reactor system available in the REALCAT platform. The proposed\nmethods often outperform other sequential Bayesian optimizations and existing\nprocess-constrained batch Bayesian optimization methods. This work proposes a\nnovel approach to optimize the yield of a reaction in a multi-reactor system,\nmarking a significant step forward in digital catalysis and generally in\noptimization methods for chemical engineering.\n", "date": "2024-08-05", "categories": []}
{"id": "2402.02111", "title": "Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo\n  is All you Need", "abstract": "  We leverage multilevel Monte Carlo (MLMC) to improve the performance of\nmulti-step look-ahead Bayesian optimization (BO) methods that involve nested\nexpectations and maximizations. Often these expectations must be computed by\nMonte Carlo (MC). The complexity rate of naive MC degrades for nested\noperations, whereas MLMC is capable of achieving the canonical MC convergence\nrate for this type of problem, independently of dimension and without any\nsmoothness assumptions. Our theoretical study focuses on the approximation\nimprovements for twoand three-step look-ahead acquisition functions, but, as we\ndiscuss, the approach is generalizable in various ways, including beyond the\ncontext of BO. Our findings are verified numerically and the benefits of MLMC\nfor BO are illustrated on several benchmark examples. Code is available at\nhttps://github.com/Shangda-Yang/MLMCBO .\n", "date": "2024-02-03", "categories": []}
{"id": "2406.07709", "title": "Diagnosing and fixing common problems in Bayesian optimization for\n  molecule design", "abstract": "  Bayesian optimization (BO) is a principled approach to molecular design\ntasks. In this paper we explain three pitfalls of BO which can cause poor\nempirical performance: an incorrect prior width, over-smoothing, and inadequate\nacquisition function maximization. We show that with these issues addressed,\neven a basic BO setup is able to achieve the highest overall performance on the\nPMO benchmark for molecule design (Gao et al 2022). These results suggest that\nBO may benefit from more attention in the machine learning for molecules\ncommunity.\n", "date": "2024-06-11", "categories": []}
{"id": "2401.17037", "title": "Enhancing Gaussian Process Surrogates for Optimization and Posterior\n  Approximation via Random Exploration", "abstract": "  This paper proposes novel noise-free Bayesian optimization strategies that\nrely on a random exploration step to enhance the accuracy of Gaussian process\nsurrogate models. The new algorithms retain the ease of implementation of the\nclassical GP-UCB algorithm, but the additional random exploration step\naccelerates their convergence, nearly achieving the optimal convergence rate.\nFurthermore, to facilitate Bayesian inference with an intractable likelihood,\nwe propose to utilize optimization iterates for maximum a posteriori estimation\nto build a Gaussian process surrogate model for the unnormalized log-posterior\ndensity. We provide bounds for the Hellinger distance between the true and the\napproximate posterior distributions in terms of the number of design points. We\ndemonstrate the effectiveness of our Bayesian optimization algorithms in\nnon-convex benchmark objective functions, in a machine learning hyperparameter\ntuning problem, and in a black-box engineering design problem. The\neffectiveness of our posterior approximation approach is demonstrated in two\nBayesian inference problems for parameters of dynamical systems.\n", "date": "2024-01-30", "categories": []}
{"id": "2311.02213", "title": "Joint Composite Latent Space Bayesian Optimization", "abstract": "  Bayesian Optimization (BO) is a technique for sample-efficient black-box\noptimization that employs probabilistic models to identify promising input\nlocations for evaluation. When dealing with composite-structured functions,\nsuch as f=g o h, evaluating a specific location x yields observations of both\nthe final outcome f(x) = g(h(x)) as well as the intermediate output(s) h(x).\nPrevious research has shown that integrating information from these\nintermediate outputs can enhance BO performance substantially. However,\nexisting methods struggle if the outputs h(x) are high-dimensional. Many\nrelevant problems fall into this setting, including in the context of\ngenerative AI, molecular design, or robotics. To effectively tackle these\nchallenges, we introduce Joint Composite Latent Space Bayesian Optimization\n(JoCo), a novel framework that jointly trains neural network encoders and\nprobabilistic models to adaptively compress high-dimensional input and output\nspaces into manageable latent representations. This enables viable BO on these\ncompressed representations, allowing JoCo to outperform other state-of-the-art\nmethods in high-dimensional BO on a wide variety of simulated and real-world\nproblems.\n", "date": "2023-11-03", "categories": []}
{"id": "2303.01560", "title": "Active Learning and Bayesian Optimization: a Unified Perspective to\n  Learn with a Goal", "abstract": "  Science and Engineering applications are typically associated with expensive\noptimization problems to identify optimal design solutions and states of the\nsystem of interest. Bayesian optimization and active learning compute surrogate\nmodels through efficient adaptive sampling schemes to assist and accelerate\nthis search task toward a given optimization goal. Both those methodologies are\ndriven by specific infill/learning criteria which quantify the utility with\nrespect to the set goal of evaluating the objective function for unknown\ncombinations of optimization variables. While the two fields have seen an\nexponential growth in popularity in the past decades, their dualism and synergy\nhave received relatively little attention to date. This paper discusses and\nformalizes the synergy between Bayesian optimization and active learning as\nsymbiotic adaptive sampling methodologies driven by common principles. In\nparticular, we demonstrate this unified perspective through the formalization\nof the analogy between the Bayesian infill criteria and active learning\ncriteria as driving principles of both the goal-driven procedures. To support\nour original perspective, we propose a general classification of adaptive\nsampling techniques to highlight similarities and differences between the vast\nfamilies of adaptive sampling, active learning, and Bayesian optimization.\nAccordingly, the synergy is demonstrated mapping the Bayesian infill criteria\nwith the active learning criteria, and is formalized for searches informed by\nboth a single information source and multiple levels of fidelity. In addition,\nwe provide guidelines to apply those learning criteria investigating the\nperformance of different Bayesian schemes for a variety of benchmark problems\nto highlight benefits and limitations over mathematical properties that\ncharacterize real-world applications.\n", "date": "2023-03-02", "categories": []}
{"id": "2407.04864", "title": "Augmented Bayesian Policy Search", "abstract": "  Deterministic policies are often preferred over stochastic ones when\nimplemented on physical systems. They can prevent erratic and harmful behaviors\nwhile being easier to implement and interpret. However, in practice,\nexploration is largely performed by stochastic policies. First-order Bayesian\nOptimization (BO) methods offer a principled way of performing exploration\nusing deterministic policies. This is done through a learned probabilistic\nmodel of the objective function and its gradient. Nonetheless, such approaches\ntreat policy search as a black-box problem, and thus, neglect the reinforcement\nlearning nature of the problem. In this work, we leverage the performance\ndifference lemma to introduce a novel mean function for the probabilistic\nmodel. This results in augmenting BO methods with the action-value function.\nHence, we call our method Augmented Bayesian Search~(ABS). Interestingly, this\nnew mean function enhances the posterior gradient with the deterministic policy\ngradient, effectively bridging the gap between BO and policy gradient methods.\nThe resulting algorithm combines the convenience of the direct policy search\nwith the scalability of reinforcement learning. We validate ABS on\nhigh-dimensional locomotion problems and demonstrate competitive performance\ncompared to existing direct policy search schemes.\n", "date": "2024-07-05", "categories": []}
{"id": "2407.05788", "title": "Automated Computational Energy Minimization of ML Algorithms using\n  Constrained Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is an efficient framework for optimization of\nblack-box objectives when function evaluations are costly and gradient\ninformation is not easily accessible. BO has been successfully applied to\nautomate the task of hyperparameter optimization (HPO) in machine learning (ML)\nmodels with the primary objective of optimizing predictive performance on\nheld-out data. In recent years, however, with ever-growing model sizes, the\nenergy cost associated with model training has become an important factor for\nML applications. Here we evaluate Constrained Bayesian Optimization (CBO) with\nthe primary objective of minimizing energy consumption and subject to the\nconstraint that the generalization performance is above some threshold. We\nevaluate our approach on regression and classification tasks and demonstrate\nthat CBO achieves lower energy consumption without compromising the predictive\nperformance of ML models.\n", "date": "2024-07-08", "categories": []}
{"id": "2207.06325", "title": "Non-Myopic Multifidelity Bayesian Optimization", "abstract": "  Bayesian optimization is a popular framework for the optimization of black\nbox functions. Multifidelity methods allows to accelerate Bayesian optimization\nby exploiting low-fidelity representations of expensive objective functions.\nPopular multifidelity Bayesian strategies rely on sampling policies that\naccount for the immediate reward obtained evaluating the objective function at\na specific input, precluding greater informative gains that might be obtained\nlooking ahead more steps. This paper proposes a non-myopic multifidelity\nBayesian framework to grasp the long-term reward from future steps of the\noptimization. Our computational strategy comes with a two-step lookahead\nmultifidelity acquisition function that maximizes the cumulative reward\nobtained measuring the improvement in the solution over two steps ahead. We\ndemonstrate that the proposed algorithm outperforms a standard multifidelity\nBayesian framework on popular benchmark optimization problems.\n", "date": "2022-07-13", "categories": []}
{"id": "2306.17815", "title": "Bayesian Optimization with Formal Safety Guarantees via Online Conformal\n  Prediction", "abstract": "  Black-box zero-th order optimization is a central primitive for applications\nin fields as diverse as finance, physics, and engineering. In a common\nformulation of this problem, a designer sequentially attempts candidate\nsolutions, receiving noisy feedback on the value of each attempt from the\nsystem. In this paper, we study scenarios in which feedback is also provided on\nthe safety of the attempted solution, and the optimizer is constrained to limit\nthe number of unsafe solutions that are tried throughout the optimization\nprocess. Focusing on methods based on Bayesian optimization (BO), prior art has\nintroduced an optimization scheme -- referred to as SAFEOPT -- that is\nguaranteed not to select any unsafe solution with a controllable probability\nover feedback noise as long as strict assumptions on the safety constraint\nfunction are met. In this paper, a novel BO-based approach is introduced that\nsatisfies safety requirements irrespective of properties of the constraint\nfunction. This strong theoretical guarantee is obtained at the cost of allowing\nfor an arbitrary, controllable but non-zero, rate of violation of the safety\nconstraint. The proposed method, referred to as SAFE-BOCP, builds on online\nconformal prediction (CP) and is specialized to the cases in which feedback on\nthe safety constraint is either noiseless or noisy. Experimental results on\nsynthetic and real-world data validate the advantages and flexibility of the\nproposed SAFE-BOCP.\n", "date": "2023-06-30", "categories": []}
{"id": "2312.05831", "title": "Physics-Aware Multifidelity Bayesian Optimization: a Generalized\n  Formulation", "abstract": "  The adoption of high-fidelity models for many-query optimization problems is\nmajorly limited by the significant computational cost required for their\nevaluation at every query. Multifidelity Bayesian methods (MFBO) allow to\ninclude costly high-fidelity responses for a sub-selection of queries only, and\nuse fast lower-fidelity models to accelerate the optimization process.\nState-of-the-art methods rely on a purely data-driven search and do not include\nexplicit information about the physical context. This paper acknowledges that\nprior knowledge about the physical domains of engineering problems can be\nleveraged to accelerate these data-driven searches, and proposes a generalized\nformulation for MFBO to embed a form of domain awareness during the\noptimization procedure. In particular, we formalize a bias as a multifidelity\nacquisition function that captures the physical structure of the domain. This\npermits to partially alleviate the data-driven search from learning the domain\nproperties on-the-fly, and sensitively enhances the management of multiple\nsources of information. The method allows to efficiently include high-fidelity\nsimulations to guide the optimization search while containing the overall\ncomputational expense. Our physics-aware multifidelity Bayesian optimization is\npresented and illustrated for two classes of optimization problems frequently\nmet in science and engineering, namely design optimization and health\nmonitoring problems.\n", "date": "2023-12-10", "categories": []}
{"id": "2302.11533", "title": "MONGOOSE: Path-wise Smooth Bayesian Optimisation via Meta-learning", "abstract": "  In Bayesian optimisation, we often seek to minimise the black-box objective\nfunctions that arise in real-world physical systems. A primary contributor to\nthe cost of evaluating such black-box objective functions is often the effort\nrequired to prepare the system for measurement. We consider a common scenario\nwhere preparation costs grow as the distance between successive evaluations\nincreases. In this setting, smooth optimisation trajectories are preferred and\nthe jumpy paths produced by the standard myopic (i.e.\\ one-step-optimal)\nBayesian optimisation methods are sub-optimal. Our algorithm, MONGOOSE, uses a\nmeta-learnt parametric policy to generate smooth optimisation trajectories,\nachieving performance gains over existing methods when optimising functions\nwith large movement costs.\n", "date": "2023-02-22", "categories": []}
{"id": "2305.02449", "title": "Bayesian Safety Validation for Failure Probability Estimation of\n  Black-Box Systems", "abstract": "  Estimating the probability of failure is an important step in the\ncertification of safety-critical systems. Efficient estimation methods are\noften needed due to the challenges posed by high-dimensional input spaces,\nrisky test scenarios, and computationally expensive simulators. This work\nframes the problem of black-box safety validation as a Bayesian optimization\nproblem and introduces a method that iteratively fits a probabilistic surrogate\nmodel to efficiently predict failures. The algorithm is designed to search for\nfailures, compute the most-likely failure, and estimate the failure probability\nover an operating domain using importance sampling. We introduce three\nacquisition functions that aim to reduce uncertainty by covering the design\nspace, optimize the analytically derived failure boundaries, and sample the\npredicted failure regions. Results show this Bayesian safety validation\napproach provides a more accurate estimate of failure probability with orders\nof magnitude fewer samples and performs well across various safety validation\nmetrics. We demonstrate this approach on three test problems, a stochastic\ndecision making system, and a neural network-based runway detection system.\nThis work is open sourced (https://github.com/sisl/BayesianSafetyValidation.jl)\nand currently being used to supplement the FAA certification process of the\nmachine learning components for an autonomous cargo aircraft.\n", "date": "2023-05-03", "categories": []}
{"id": "2406.04824", "title": "FunBO: Discovering Acquisition Functions for Bayesian Optimization with\n  FunSearch", "abstract": "  The sample efficiency of Bayesian optimization algorithms depends on\ncarefully crafted acquisition functions (AFs) guiding the sequential collection\nof function evaluations. The best-performing AF can vary significantly across\noptimization problems, often requiring ad-hoc and problem-specific choices.\nThis work tackles the challenge of designing novel AFs that perform well across\na variety of experimental settings. Based on FunSearch, a recent work using\nLarge Language Models (LLMs) for discovery in mathematical sciences, we propose\nFunBO, an LLM-based method that can be used to learn new AFs written in\ncomputer code by leveraging access to a limited number of evaluations for a set\nof objective functions. We provide the analytic expression of all discovered\nAFs and evaluate them on various global optimization benchmarks and\nhyperparameter optimization tasks. We show how FunBO identifies AFs that\ngeneralize well in and out of the training distribution of functions, thus\noutperforming established general-purpose AFs and achieving competitive\nperformance against AFs that are customized to specific function types and are\nlearned via transfer-learning algorithms.\n", "date": "2024-06-07", "categories": []}
{"id": "2307.03565", "title": "MALIBO: Meta-learning for Likelihood-free Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is a popular method to optimize costly black-box\nfunctions. While traditional BO optimizes each new target task from scratch,\nmeta-learning has emerged as a way to leverage knowledge from related tasks to\noptimize new tasks faster. However, existing meta-learning BO methods rely on\nsurrogate models that suffer from scalability issues and are sensitive to\nobservations with different scales and noise types across tasks. Moreover, they\noften overlook the uncertainty associated with task similarity. This leads to\nunreliable task adaptation when only limited observations are obtained or when\nthe new tasks differ significantly from the related tasks. To address these\nlimitations, we propose a novel meta-learning BO approach that bypasses the\nsurrogate model and directly learns the utility of queries across tasks. Our\nmethod explicitly models task uncertainty and includes an auxiliary model to\nenable robust adaptation to new tasks. Extensive experiments show that our\nmethod demonstrates strong anytime performance and outperforms state-of-the-art\nmeta-learning BO methods in various benchmarks.\n", "date": "2023-07-07", "categories": []}
{"id": "2303.00890", "title": "Comparison of High-Dimensional Bayesian Optimization Algorithms on BBOB", "abstract": "  Bayesian Optimization (BO) is a class of black-box, surrogate-based\nheuristics that can efficiently optimize problems that are expensive to\nevaluate, and hence admit only small evaluation budgets. BO is particularly\npopular for solving numerical optimization problems in industry, where the\nevaluation of objective functions often relies on time-consuming simulations or\nphysical experiments. However, many industrial problems depend on a large\nnumber of parameters. This poses a challenge for BO algorithms, whose\nperformance is often reported to suffer when the dimension grows beyond 15\nvariables. Although many new algorithms have been proposed to address this\nproblem, it is not well understood which one is the best for which optimization\nscenario.\n  In this work, we compare five state-of-the-art high-dimensional BO\nalgorithms, with vanilla BO and CMA-ES on the 24 BBOB functions of the COCO\nenvironment at increasing dimensionality, ranging from 10 to 60 variables. Our\nresults confirm the superiority of BO over CMA-ES for limited evaluation\nbudgets and suggest that the most promising approach to improve BO is the use\nof trust regions. However, we also observe significant performance differences\nfor different function landscapes and budget exploitation phases, indicating\nimprovement potential, e.g., through hybridization of algorithmic components.\n", "date": "2023-03-02", "categories": []}
{"id": "2310.02905", "title": "Use Your INSTINCT: INSTruction optimization for LLMs usIng Neural\n  bandits Coupled with Transformers", "abstract": "  Large language models (LLMs) have shown remarkable instruction-following\ncapabilities and achieved impressive performances in various applications.\nHowever, the performances of LLMs depend heavily on the instructions given to\nthem, which are typically manually tuned with substantial human efforts. Recent\nwork has used the query-efficient Bayesian optimization (BO) algorithm to\nautomatically optimize the instructions given to black-box LLMs. However, BO\nusually falls short when optimizing highly sophisticated (e.g.,\nhigh-dimensional) objective functions, such as the functions mapping an\ninstruction to the performance of an LLM. This is mainly due to the limited\nexpressive power of the Gaussian process (GP) which is used by BO as a\nsurrogate to model the objective function. Meanwhile, it has been repeatedly\nshown that neural networks (NNs), especially pre-trained transformers, possess\nstrong expressive power and can model highly complex functions. So, we adopt a\nneural bandit algorithm which replaces the GP in BO by an NN surrogate to\noptimize instructions for black-box LLMs. More importantly, the neural bandit\nalgorithm allows us to naturally couple the NN surrogate with the hidden\nrepresentation learned by a pre-trained transformer (i.e., an open-source LLM),\nwhich significantly boosts its performance. These motivate us to propose our\nINSTruction optimization usIng Neural bandits Coupled with Transformers\n(INSTINCT) algorithm. We perform instruction optimization for ChatGPT and use\nextensive experiments to show that INSTINCT consistently outperforms baselines\nin different tasks, e.g., various instruction induction tasks and the task of\nimproving zero-shot chain-of-thought instructions. Our code is available at\nhttps://github.com/xqlin98/INSTINCT.\n", "date": "2023-10-02", "categories": []}
{"id": "2401.11665", "title": "Accelerating Approximate Thompson Sampling with Underdamped Langevin\n  Monte Carlo", "abstract": "  Approximate Thompson sampling with Langevin Monte Carlo broadens its reach\nfrom Gaussian posterior sampling to encompass more general smooth posteriors.\nHowever, it still encounters scalability issues in high-dimensional problems\nwhen demanding high accuracy. To address this, we propose an approximate\nThompson sampling strategy, utilizing underdamped Langevin Monte Carlo, where\nthe latter is the go-to workhorse for simulations of high-dimensional\nposteriors. Based on the standard smoothness and log-concavity conditions, we\nstudy the accelerated posterior concentration and sampling using a specific\npotential function. This design improves the sample complexity for realizing\nlogarithmic regrets from $\\mathcal{\\tilde O}(d)$ to $\\mathcal{\\tilde\nO}(\\sqrt{d})$. The scalability and robustness of our algorithm are also\nempirically validated through synthetic experiments in high-dimensional bandit\nproblems.\n", "date": "2024-01-22", "categories": []}
{"id": "2406.14699", "title": "Preferential Multi-Objective Bayesian Optimization", "abstract": "  Preferential Bayesian optimization (PBO) is a framework for optimizing a\ndecision-maker's latent preferences over available design choices. While\npreferences often involve multiple conflicting objectives, existing work in PBO\nassumes that preferences can be encoded by a single objective function. For\nexample, in robotic assistive devices, technicians often attempt to maximize\nuser comfort while simultaneously minimizing mechanical energy consumption for\nlonger battery life. Similarly, in autonomous driving policy design,\ndecision-makers wish to understand the trade-offs between multiple safety and\nperformance attributes before committing to a policy. To address this gap, we\npropose the first framework for PBO with multiple objectives. Within this\nframework, we present dueling scalarized Thompson sampling (DSTS), a\nmulti-objective generalization of the popular dueling Thompson algorithm, which\nmay be of interest beyond the PBO setting. We evaluate DSTS across four\nsynthetic test functions and two simulated exoskeleton personalization and\ndriving policy design tasks, showing that it outperforms several benchmarks.\nFinally, we prove that DSTS is asymptotically consistent. As a direct\nconsequence, this result provides, to our knowledge, the first convergence\nguarantee for dueling Thompson sampling in the PBO setting.\n", "date": "2024-06-20", "categories": []}
{"id": "2406.12661", "title": "SCORE: A 1D Reparameterization Technique to Break Bayesian\n  Optimization's Curse of Dimensionality", "abstract": "  Bayesian optimization (BO) has emerged as a powerful tool for navigating\ncomplex search spaces, showcasing practical applications in the fields of\nscience and engineering.However, since it typically relies on a surrogate model\nto approximate the objective function, BO grapples with heightened\ncomputational costs that tend to escalate as the number of parameters and\nexperiments grows. Several methods such as parallelization, surrogate model\napproximations, and memory pruning have been proposed to cut down computing\ntime, but they all fall short of resolving the core issue behind BO's curse of\ndimensionality. In this paper, a 1D reparametrization trick is proposed to\nbreak this curse and sustain linear time complexity for BO in high-dimensional\nlandscapes. This fast and scalable approach named SCORE can successfully find\nthe global minimum of needle-in-a-haystack optimization functions and fit\nreal-world data without the high-performance computing resources typically\nrequired by state-of-the-art techniques.\n", "date": "2024-06-18", "categories": []}
{"id": "2311.11328", "title": "LABCAT: Locally adaptive Bayesian optimization using\n  principal-component-aligned trust regions", "abstract": "  Bayesian optimization (BO) is a popular method for optimizing expensive\nblack-box functions. BO has several well-documented shortcomings, including\ncomputational slowdown with longer optimization runs, poor suitability for\nnon-stationary or ill-conditioned objective functions, and poor convergence\ncharacteristics. Several algorithms have been proposed that incorporate local\nstrategies, such as trust regions, into BO to mitigate these limitations;\nhowever, none address all of them satisfactorily. To address these\nshortcomings, we propose the LABCAT algorithm, which extends trust-region-based\nBO by adding a rotation aligning the trust region with the weighted principal\ncomponents and an adaptive rescaling strategy based on the length-scales of a\nlocal Gaussian process surrogate model with automatic relevance determination.\nThrough extensive numerical experiments using a set of synthetic test functions\nand the well-known COCO benchmarking software, we show that the LABCAT\nalgorithm outperforms several state-of-the-art BO and other black-box\noptimization algorithms.\n", "date": "2023-11-19", "categories": []}
{"id": "2312.07281", "title": "Towards Safe Multi-Task Bayesian Optimization", "abstract": "  Bayesian optimization has emerged as a highly effective tool for the safe\nonline optimization of systems, due to its high sample efficiency and noise\nrobustness. To further enhance its efficiency, reduced physical models of the\nsystem can be incorporated into the optimization process, accelerating it.\nThese models are able to offer an approximation of the actual system, and\nevaluating them is significantly cheaper. The similarity between the model and\nreality is represented by additional hyperparameters, which are learned within\nthe optimization process. Safety is a crucial criterion for online optimization\nmethods such as Bayesian optimization, which has been addressed by recent works\nthat provide safety guarantees under the assumption of known hyperparameters.\nIn practice, however, this does not apply. Therefore, we extend the robust\nGaussian process uniform error bounds to meet the multi-task setting, which\ninvolves the calculation of a confidence region from the hyperparameter\nposterior distribution utilizing Markov chain Monte Carlo methods.\nSubsequently, the robust safety bounds are employed to facilitate the safe\noptimization of the system, while incorporating measurements of the models.\nSimulation results indicate that the optimization can be significantly\naccelerated for expensive to evaluate functions in comparison to other\nstate-of-the-art safe Bayesian optimization methods, contingent on the fidelity\nof the models.\n", "date": "2023-12-12", "categories": []}
{"id": "2406.10917", "title": "Bayesian Intervention Optimization for Causal Discovery", "abstract": "  Causal discovery is crucial for understanding complex systems and informing\ndecisions. While observational data can uncover causal relationships under\ncertain assumptions, it often falls short, making active interventions\nnecessary. Current methods, such as Bayesian and graph-theoretical approaches,\ndo not prioritize decision-making and often rely on ideal conditions or\ninformation gain, which is not directly related to hypothesis testing. We\npropose a novel Bayesian optimization-based method inspired by Bayes factors\nthat aims to maximize the probability of obtaining decisive and correct\nevidence. Our approach uses observational data to estimate causal models under\ndifferent hypotheses, evaluates potential interventions pre-experimentally, and\niteratively updates priors to refine interventions. We demonstrate the\neffectiveness of our method through various experiments. Our contributions\nprovide a robust framework for efficient causal discovery through active\ninterventions, enhancing the practical application of theoretical advancements.\n", "date": "2024-06-16", "categories": []}
{"id": "2311.02146", "title": "Bayesian Optimization of Function Networks with Partial Evaluations", "abstract": "  Bayesian optimization is a powerful framework for optimizing functions that\nare expensive or time-consuming to evaluate. Recent work has considered\nBayesian optimization of function networks (BOFN), where the objective function\nis given by a network of functions, each taking as input the output of previous\nnodes in the network as well as additional parameters. Leveraging this network\nstructure has been shown to yield significant performance improvements.\nExisting BOFN algorithms for general-purpose networks evaluate the full network\nat each iteration. However, many real-world applications allow for evaluating\nnodes individually. To exploit this, we propose a novel knowledge gradient\nacquisition function that chooses which node and corresponding inputs to\nevaluate in a cost-aware manner, thereby reducing query costs by evaluating\nonly on a part of the network at each step. We provide an efficient approach to\noptimizing our acquisition function and show that it outperforms existing BOFN\nmethods and other benchmarks across several synthetic and real-world problems.\nOur acquisition function is the first to enable cost-aware optimization of a\nbroad class of function networks.\n", "date": "2023-11-03", "categories": []}
{"id": "2404.16906", "title": "Evolve Cost-aware Acquisition Functions Using Large Language Models", "abstract": "  Many real-world optimization scenarios involve expensive evaluation with\nunknown and heterogeneous costs. Cost-aware Bayesian optimization stands out as\na prominent solution in addressing these challenges. To approach the global\noptimum within a limited budget in a cost-efficient manner, the design of\ncost-aware acquisition functions (AFs) becomes a crucial step. However,\ntraditional manual design paradigm typically requires extensive domain\nknowledge and involves a labor-intensive trial-and-error process. This paper\nintroduces EvolCAF, a novel framework that integrates large language models\n(LLMs) with evolutionary computation (EC) to automatically design cost-aware\nAFs. Leveraging the crossover and mutation in the algorithmic space, EvolCAF\noffers a novel design paradigm, significantly reduces the reliance on domain\nexpertise and model training. The designed cost-aware AF maximizes the\nutilization of available information from historical data, surrogate models and\nbudget details. It introduces novel ideas not previously explored in the\nexisting literature on acquisition function design, allowing for clear\ninterpretations to provide insights into its behavior and decision-making\nprocess. In comparison to the well-known EIpu and EI-cool methods designed by\nhuman experts, our approach showcases remarkable efficiency and generalization\nacross various tasks, including 12 synthetic problems and 3 real-world\nhyperparameter tuning test sets.\n", "date": "2024-04-25", "categories": []}
{"id": "2406.06150", "title": "Physics-Informed Bayesian Optimization of Variational Quantum Circuits", "abstract": "  In this paper, we propose a novel and powerful method to harness Bayesian\noptimization for Variational Quantum Eigensolvers (VQEs) -- a hybrid\nquantum-classical protocol used to approximate the ground state of a quantum\nHamiltonian. Specifically, we derive a VQE-kernel which incorporates important\nprior information about quantum circuits: the kernel feature map of the\nVQE-kernel exactly matches the known functional form of the VQE's objective\nfunction and thereby significantly reduces the posterior uncertainty. Moreover,\nwe propose a novel acquisition function for Bayesian optimization called\nExpected Maximum Improvement over Confident Regions (EMICoRe) which can\nactively exploit the inductive bias of the VQE-kernel by treating regions with\nlow predictive uncertainty as indirectly ``observed''. As a result,\nobservations at as few as three points in the search domain are sufficient to\ndetermine the complete objective function along an entire one-dimensional\nsubspace of the optimization landscape. Our numerical experiments demonstrate\nthat our approach improves over state-of-the-art baselines.\n", "date": "2024-06-10", "categories": []}
{"id": "2406.06459", "title": "How Useful is Intermittent, Asynchronous Expert Feedback for Bayesian\n  Optimization?", "abstract": "  Bayesian optimization (BO) is an integral part of automated scientific\ndiscovery -- the so-called self-driving lab -- where human inputs are ideally\nminimal or at least non-blocking. However, scientists often have strong\nintuition, and thus human feedback is still useful. Nevertheless, prior works\nin enhancing BO with expert feedback, such as by incorporating it in an offline\nor online but blocking (arrives at each BO iteration) manner, are incompatible\nwith the spirit of self-driving labs. In this work, we study whether a small\namount of randomly arriving expert feedback that is being incorporated in a\nnon-blocking manner can improve a BO campaign. To this end, we run an\nadditional, independent computing thread on top of the BO loop to handle the\nfeedback-gathering process. The gathered feedback is used to learn a Bayesian\npreference model that can readily be incorporated into the BO thread, to steer\nits exploration-exploitation process. Experiments on toy and chemistry datasets\nsuggest that even just a few intermittent, asynchronous expert feedback can be\nuseful for improving or constraining BO. This can especially be useful for its\nimplication in improving self-driving labs, e.g. making them more\ndata-efficient and less costly.\n", "date": "2024-06-10", "categories": []}
{"id": "2306.06844", "title": "Provably Efficient Bayesian Optimization with Unknown Gaussian Process\n  Hyperparameter Estimation", "abstract": "  Gaussian process (GP) based Bayesian optimization (BO) is a powerful method\nfor optimizing black-box functions efficiently. The practical performance and\ntheoretical guarantees of this approach depend on having the correct GP\nhyperparameter values, which are usually unknown in advance and need to be\nestimated from the observed data. However, in practice, these estimations could\nbe incorrect due to biased data sampling strategies used in BO. This can lead\nto degraded performance and break the sub-linear global convergence guarantee\nof BO. To address this issue, we propose a new BO method that can sub-linearly\nconverge to the objective function's global optimum even when the true GP\nhyperparameters are unknown in advance and need to be estimated from the\nobserved data. Our method uses a multi-armed bandit technique (EXP3) to add\nrandom data points to the BO process, and employs a novel training loss\nfunction for the GP hyperparameter estimation process that ensures consistent\nestimation. We further provide theoretical analysis of our proposed method.\nFinally, we demonstrate empirically that our method outperforms existing\napproaches on various synthetic and real-world problems.\n", "date": "2023-06-12", "categories": []}
{"id": "2311.03760", "title": "Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian\n  Regret Bounds", "abstract": "  Among various acquisition functions (AFs) in Bayesian optimization (BO),\nGaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are\nwell-known options with established theoretical properties regarding Bayesian\ncumulative regret (BCR). Recently, it has been shown that a randomized variant\nof GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the\ntighter BCR bound for brevity. Inspired by this study, this paper first shows\nthat TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often\npractically suffer from manual hyperparameter tuning and over-exploration\nissues, respectively. Therefore, we analyze yet another AF called a probability\nof improvement from the maximum of a sample path (PIMS). We show that PIMS\nachieves the tighter BCR bound and avoids the hyperparameter tuning, unlike\nGP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on\nthe effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.\n", "date": "2023-11-07", "categories": []}
{"id": "2405.19059", "title": "Robust Entropy Search for Safe Efficient Bayesian Optimization", "abstract": "  The practical use of Bayesian Optimization (BO) in engineering applications\nimposes special requirements: high sampling efficiency on the one hand and\nfinding a robust solution on the other hand. We address the case of adversarial\nrobustness, where all parameters are controllable during the optimization\nprocess, but a subset of them is uncontrollable or even adversely perturbed at\nthe time of application. To this end, we develop an efficient information-based\nacquisition function that we call Robust Entropy Search (RES). We empirically\ndemonstrate its benefits in experiments on synthetic and real-life data. The\nresults showthat RES reliably finds robust optima, outperforming\nstate-of-the-art algorithms.\n", "date": "2024-05-29", "categories": []}
{"id": "2402.05015", "title": "A Sober Look at LLMs for Material Discovery: Are They Actually Good for\n  Bayesian Optimization Over Molecules?", "abstract": "  Automation is one of the cornerstones of contemporary material discovery.\nBayesian optimization (BO) is an essential part of such workflows, enabling\nscientists to leverage prior domain knowledge into efficient exploration of a\nlarge molecular space. While such prior knowledge can take many forms, there\nhas been significant fanfare around the ancillary scientific knowledge\nencapsulated in large language models (LLMs). However, existing work thus far\nhas only explored LLMs for heuristic materials searches. Indeed, recent work\nobtains the uncertainty estimate -- an integral part of BO -- from\npoint-estimated, non-Bayesian LLMs. In this work, we study the question of\nwhether LLMs are actually useful to accelerate principled Bayesian optimization\nin the molecular space. We take a sober, dispassionate stance in answering this\nquestion. This is done by carefully (i) viewing LLMs as fixed feature\nextractors for standard but principled BO surrogate models and by (ii)\nleveraging parameter-efficient finetuning methods and Bayesian neural networks\nto obtain the posterior of the LLM surrogate. Our extensive experiments with\nreal-world chemistry problems show that LLMs can be useful for BO over\nmolecules, but only if they have been pretrained or finetuned with\ndomain-specific data.\n", "date": "2024-02-07", "categories": []}
{"id": "2402.05367", "title": "Principled Preferential Bayesian Optimization", "abstract": "  We study the problem of preferential Bayesian optimization (BO), where we aim\nto optimize a black-box function with only preference feedback over a pair of\ncandidate solutions. Inspired by the likelihood ratio idea, we construct a\nconfidence set of the black-box function using only the preference feedback. An\noptimistic algorithm with an efficient computational method is then developed\nto solve the problem, which enjoys an information-theoretic bound on the total\ncumulative regret, a first-of-its-kind for preferential BO. This bound further\nallows us to design a scheme to report an estimated best solution, with a\nguaranteed convergence rate. Experimental results on sampled instances from\nGaussian processes, standard test functions, and a thermal comfort optimization\nproblem all show that our method stably achieves better or competitive\nperformance as compared to the existing state-of-the-art heuristics, which,\nhowever, do not have theoretical guarantees on regret bounds or convergence.\n", "date": "2024-02-08", "categories": []}
{"id": "2402.07868", "title": "Nesting Particle Filters for Experimental Design in Dynamical Systems", "abstract": "  In this paper, we propose a novel approach to Bayesian experimental design\nfor non-exchangeable data that formulates it as risk-sensitive policy\noptimization. We develop the Inside-Out SMC$^2$ algorithm, a nested sequential\nMonte Carlo technique to infer optimal designs, and embed it into a particle\nMarkov chain Monte Carlo framework to perform gradient-based policy\namortization. Our approach is distinct from other amortized experimental design\ntechniques, as it does not rely on contrastive estimators. Numerical validation\non a set of dynamical systems showcases the efficacy of our method in\ncomparison to other state-of-the-art strategies.\n", "date": "2024-02-12", "categories": []}
{"id": "2402.11101", "title": "Physics-based material parameters extraction from perovskite experiments\n  via Bayesian optimization", "abstract": "  The ability to extract material parameters of perovskite from quantitative\nexperimental analysis is essential for rational design of photovoltaic and\noptoelectronic applications. However, the difficulty of this analysis increases\nsignificantly with the complexity of the theoretical model and the number of\nmaterial parameters for perovskite. Here we use Bayesian optimization to\ndevelop an analysis platform that can extract up to 8 fundamental material\nparameters of an organometallic perovskite semiconductor from a transient\nphotoluminescence experiment, based on a complex full physics model that\nincludes drift-diffusion of carriers and dynamic defect occupation. An example\nstudy of thermal degradation reveals that the carrier mobility and\ntrap-assisted recombination coefficient are reduced noticeably, while the\ndefect energy level remains nearly unchanged. The reduced carrier mobility can\ndominate the overall effect on thermal degradation of perovskite solar cells by\nreducing the fill factor, despite the opposite effect of the reduced\ntrap-assisted recombination coefficient on increasing the fill factor. In\nfuture, this platform can be conveniently applied to other experiments or to\ncombinations of experiments, accelerating materials discovery and optimization\nof semiconductor materials for photovoltaics and other applications.\n", "date": "2024-02-16", "categories": []}
{"id": "2405.19098", "title": "Efficient Black-box Adversarial Attacks via Bayesian Optimization Guided\n  by a Function Prior", "abstract": "  This paper studies the challenging black-box adversarial attack that aims to\ngenerate adversarial examples against a black-box model by only using output\nfeedback of the model to input queries. Some previous methods improve the query\nefficiency by incorporating the gradient of a surrogate white-box model into\nquery-based attacks due to the adversarial transferability. However, the\nlocalized gradient is not informative enough, making these methods still\nquery-intensive. In this paper, we propose a Prior-guided Bayesian Optimization\n(P-BO) algorithm that leverages the surrogate model as a global function prior\nin black-box adversarial attacks. As the surrogate model contains rich prior\ninformation of the black-box one, P-BO models the attack objective with a\nGaussian process whose mean function is initialized as the surrogate model's\nloss. Our theoretical analysis on the regret bound indicates that the\nperformance of P-BO may be affected by a bad prior. Therefore, we further\npropose an adaptive integration strategy to automatically adjust a coefficient\non the function prior by minimizing the regret bound. Extensive experiments on\nimage classifiers and large vision-language models demonstrate the superiority\nof the proposed algorithm in reducing queries and improving attack success\nrates compared with the state-of-the-art black-box attacks. Code is available\nat https://github.com/yibo-miao/PBO-Attack.\n", "date": "2024-05-29", "categories": []}
{"id": "2405.17875", "title": "BO4IO: A Bayesian optimization approach to inverse optimization with\n  uncertainty quantification", "abstract": "  This work addresses data-driven inverse optimization (IO), where the goal is\nto estimate unknown parameters in an optimization model from observed decisions\nthat can be assumed to be optimal or near-optimal solutions to the optimization\nproblem. The IO problem is commonly formulated as a large-scale bilevel program\nthat is notoriously difficult to solve. Deviating from traditional exact\nsolution methods, we propose a derivative-free optimization approach based on\nBayesian optimization, which we call BO4IO, to solve general IO problems. We\ntreat the IO loss function as a black box and approximate it with a Gaussian\nprocess model. Using the predicted posterior function, an acquisition function\nis minimized at each iteration to query new candidate solutions and\nsequentially converge to the optimal parameter estimates. The main advantages\nof using Bayesian optimization for IO are two-fold: (i) it circumvents the need\nof complex reformulations of the bilevel program or specialized algorithms and\ncan hence enable computational tractability even when the underlying\noptimization problem is nonconvex or involves discrete variables, and (ii) it\nallows approximations of the profile likelihood, which provide uncertainty\nquantification on the IO parameter estimates. We apply the proposed method to\nthree computational case studies, covering different classes of forward\noptimization problems ranging from convex nonlinear to nonconvex mixed-integer\nnonlinear programs. Our extensive computational results demonstrate the\nefficacy and robustness of BO4IO to accurately estimate unknown model\nparameters from small and noisy datasets. In addition, the proposed profile\nlikelihood analysis has proven to be effective in providing good approximations\nof the confidence intervals on the parameter estimates and assessing the\nidentifiability of the unknown parameters.\n", "date": "2024-05-28", "categories": []}
{"id": "2405.17918", "title": "Cost-Sensitive Multi-Fidelity Bayesian Optimization with Transfer of\n  Learning Curve Extrapolation", "abstract": "  In this paper, we address the problem of cost-sensitive multi-fidelity\nBayesian Optimization (BO) for efficient hyperparameter optimization (HPO).\nSpecifically, we assume a scenario where users want to early-stop the BO when\nthe performance improvement is not satisfactory with respect to the required\ncomputational cost. Motivated by this scenario, we introduce utility, which is\na function predefined by each user and describes the trade-off between cost and\nperformance of BO. This utility function, combined with our novel acquisition\nfunction and stopping criterion, allows us to dynamically choose for each BO\nstep the best configuration that we expect to maximally improve the utility in\nfuture, and also automatically stop the BO around the maximum utility. Further,\nwe improve the sample efficiency of existing learning curve (LC) extrapolation\nmethods with transfer learning, while successfully capturing the correlations\nbetween different configurations to develop a sensible surrogate function for\nmulti-fidelity BO. We validate our algorithm on various LC datasets and found\nit outperform all the previous multi-fidelity BO and transfer-BO baselines we\nconsider, achieving significantly better trade-off between cost and performance\nof BO.\n", "date": "2024-05-28", "categories": []}
{"id": "2305.14120", "title": "Learning Relevant Contextual Variables Within Bayesian Optimization", "abstract": "  Contextual Bayesian Optimization (CBO) efficiently optimizes black-box\nfunctions with respect to design variables, while simultaneously integrating\ncontextual information regarding the environment, such as experimental\nconditions. However, the relevance of contextual variables is not necessarily\nknown beforehand. Moreover, contextual variables can sometimes be optimized\nthemselves at an additional cost, a setting overlooked by current CBO\nalgorithms. Cost-sensitive CBO would simply include optimizable contextual\nvariables as part of the design variables based on their cost. Instead, we\nadaptively select a subset of contextual variables to include in the\noptimization, based on the trade-off between their relevance and the additional\ncost incurred by optimizing them compared to leaving them to be determined by\nthe environment. We learn the relevance of contextual variables by sensitivity\nanalysis of the posterior surrogate model while minimizing the cost of\noptimization by leveraging recent developments on early stopping for BO. We\nempirically evaluate our proposed Sensitivity-Analysis-Driven Contextual BO\n(SADCBO) method against alternatives on both synthetic and real-world\nexperiments, together with extensive ablation studies, and demonstrate a\nconsistent improvement across examples.\n", "date": "2023-05-23", "categories": []}
{"id": "2405.15285", "title": "Minimizing UCB: a Better Local Search Strategy in Local Bayesian\n  Optimization", "abstract": "  Local Bayesian optimization is a promising practical approach to solve the\nhigh dimensional black-box function optimization problem. Among them is the\napproximated gradient class of methods, which implements a strategy similar to\ngradient descent. These methods have achieved good experimental results and\ntheoretical guarantees. However, given the distributional properties of the\nGaussian processes applied on these methods, there may be potential to further\nexploit the information of the Gaussian processes to facilitate the BO search.\nIn this work, we develop the relationship between the steps of the gradient\ndescent method and one that minimizes the Upper Confidence Bound (UCB), and\nshow that the latter can be a better strategy than direct gradient descent when\na Gaussian process is applied as a surrogate. Through this insight, we propose\na new local Bayesian optimization algorithm, MinUCB, which replaces the\ngradient descent step with minimizing UCB in GIBO. We further show that MinUCB\nmaintains a similar convergence rate with GIBO. We then improve the acquisition\nfunction of MinUCB further through a look ahead strategy, and obtain a more\nefficient algorithm LA-MinUCB. We apply our algorithms on different synthetic\nand real-world functions, and the results show the effectiveness of our method.\nOur algorithms also illustrate improvements on local search strategies from an\nupper bound perspective in Bayesian optimization, and provides a new direction\nfor future algorithm design.\n", "date": "2024-05-24", "categories": []}
{"id": "2402.07692", "title": "Boundary Exploration for Bayesian Optimization With Unknown Physical\n  Constraints", "abstract": "  Bayesian optimization has been successfully applied to optimize black-box\nfunctions where the number of evaluations is severely limited. However, in many\nreal-world applications, it is hard or impossible to know in advance which\ndesigns are feasible due to some physical or system limitations. These issues\nlead to an even more challenging problem of optimizing an unknown function with\nunknown constraints. In this paper, we observe that in such scenarios optimal\nsolution typically lies on the boundary between feasible and infeasible regions\nof the design space, making it considerably more difficult than that with\ninterior optima. Inspired by this observation, we propose BE-CBO, a new\nBayesian optimization method that efficiently explores the boundary between\nfeasible and infeasible designs. To identify the boundary, we learn the\nconstraints with an ensemble of neural networks that outperform the standard\nGaussian Processes for capturing complex boundaries. Our method demonstrates\nsuperior performance against state-of-the-art methods through comprehensive\nexperiments on synthetic and real-world benchmarks. Code available at:\nhttps://github.com/yunshengtian/BE-CBO\n", "date": "2024-02-12", "categories": []}
{"id": "2405.08973", "title": "An adaptive approach to Bayesian Optimization with switching costs", "abstract": "  We investigate modifications to Bayesian Optimization for a\nresource-constrained setting of sequential experimental design where changes to\ncertain design variables of the search space incur a switching cost. This\nmodels the scenario where there is a trade-off between evaluating more while\nmaintaining the same setup, or switching and restricting the number of possible\nevaluations due to the incurred cost. We adapt two process-constrained batch\nalgorithms to this sequential problem formulation, and propose two new methods:\none cost-aware and one cost-ignorant. We validate and compare the algorithms\nusing a set of 7 scalable test functions in different dimensionalities and\nswitching-cost settings for 30 total configurations. Our proposed cost-aware\nhyperparameter-free algorithm yields comparable results to tuned\nprocess-constrained algorithms in all settings we considered, suggesting some\ndegree of robustness to varying landscape features and cost trade-offs. This\nmethod starts to outperform the other algorithms with increasing\nswitching-cost. Our work broadens out from other recent Bayesian Optimization\nstudies in resource-constrained settings that consider a batch setting only.\nWhile the contributions of this work are relevant to the general class of\nresource-constrained problems, they are particularly relevant to problems where\nadaptability to varying resource availability is of high importance\n", "date": "2024-05-14", "categories": []}
{"id": "2405.08674", "title": "Expensive Multi-Objective Bayesian Optimization Based on Diffusion\n  Models", "abstract": "  Multi-objective Bayesian optimization (MOBO) has shown promising performance\non various expensive multi-objective optimization problems (EMOPs). However,\neffectively modeling complex distributions of the Pareto optimal solutions is\ndifficult with limited function evaluations. Existing Pareto set learning\nalgorithms may exhibit considerable instability in such expensive scenarios,\nleading to significant deviations between the obtained solution set and the\nPareto set (PS). In this paper, we propose a novel Composite Diffusion Model\nbased Pareto Set Learning algorithm, namely CDM-PSL, for expensive MOBO.\nCDM-PSL includes both unconditional and conditional diffusion model for\ngenerating high-quality samples. Besides, we introduce an information entropy\nbased weighting method to balance different objectives of EMOPs. This method is\nintegrated with the guiding strategy, ensuring that all the objectives are\nappropriately balanced and given due consideration during the optimization\nprocess; Extensive experimental results on both synthetic benchmarks and\nreal-world problems demonstrates that our proposed algorithm attains superior\nperformance compared with various state-of-the-art MOBO algorithms.\n", "date": "2024-05-14", "categories": []}
{"id": "2311.06130", "title": "High-dimensional mixed-categorical Gaussian processes with application\n  to multidisciplinary design optimization for a green aircraft", "abstract": "  Recently, there has been a growing interest in mixed-categorical metamodels\nbased on Gaussian Process (GP) for Bayesian optimization. In this context,\ndifferent approaches can be used to build the mixed-categorical GP. Many of\nthese approaches involve a high number of hyperparameters; in fact, the more\ngeneral and precise the strategy used to build the GP, the greater the number\nof hyperparameters to estimate. This paper introduces an innovative dimension\nreduction algorithm that relies on partial least squares regression to reduce\nthe number of hyperparameters used to build a mixed-variable GP. Our goal is to\ngeneralize classical dimension reduction techniques commonly used within GP\n(for continuous inputs) to handle mixed-categorical inputs. The good potential\nof the proposed method is demonstrated in both structural and multidisciplinary\napplication contexts. The targeted applications include the analysis of a\ncantilever beam as well as the optimization of a green aircraft, resulting in a\nsignificant 439-kilogram reduction in fuel consumption during a single mission.\n", "date": "2023-11-10", "categories": []}
{"id": "2402.15347", "title": "Information-Theoretic Safe Bayesian Optimization", "abstract": "  We consider a sequential decision making task, where the goal is to optimize\nan unknown function without evaluating parameters that violate an a~priori\nunknown (safety) constraint. A common approach is to place a Gaussian process\nprior on the unknown functions and allow evaluations only in regions that are\nsafe with high probability. Most current methods rely on a discretization of\nthe domain and cannot be directly extended to the continuous case. Moreover,\nthe way in which they exploit regularity assumptions about the constraint\nintroduces an additional critical hyperparameter. In this paper, we propose an\ninformation-theoretic safe exploration criterion that directly exploits the GP\nposterior to identify the most informative safe parameters to evaluate. The\ncombination of this exploration criterion with a well known Bayesian\noptimization acquisition function yields a novel safe Bayesian optimization\nselection criterion. Our approach is naturally applicable to continuous domains\nand does not require additional explicit hyperparameters. We theoretically\nanalyze the method and show that we do not violate the safety constraint with\nhigh probability and that we learn about the value of the safe optimum up to\narbitrary precision. Empirical evaluations demonstrate improved data-efficiency\nand scalability.\n", "date": "2024-02-23", "categories": []}
{"id": "2305.20028", "title": "A Study of Bayesian Neural Network Surrogates for Bayesian Optimization", "abstract": "  Bayesian optimization is a highly efficient approach to optimizing objective\nfunctions which are expensive to query. These objectives are typically\nrepresented by Gaussian process (GP) surrogate models which are easy to\noptimize and support exact inference. While standard GP surrogates have been\nwell-established in Bayesian optimization, Bayesian neural networks (BNNs) have\nrecently become practical function approximators, with many benefits over\nstandard GPs such as the ability to naturally handle non-stationarity and learn\nrepresentations for high-dimensional data. In this paper, we study BNNs as\nalternatives to standard GP surrogates for optimization. We consider a variety\nof approximate inference procedures for finite-width BNNs, including\nhigh-quality Hamiltonian Monte Carlo, low-cost stochastic MCMC, and heuristics\nsuch as deep ensembles. We also consider infinite-width BNNs, linearized\nLaplace approximations, and partially stochastic models such as deep kernel\nlearning. We evaluate this collection of surrogate models on diverse problems\nwith varying dimensionality, number of objectives, non-stationarity, and\ndiscrete and continuous inputs. We find: (i) the ranking of methods is highly\nproblem dependent, suggesting the need for tailored inductive biases; (ii) HMC\nis the most successful approximate inference procedure for fully stochastic\nBNNs; (iii) full stochasticity may be unnecessary as deep kernel learning is\nrelatively competitive; (iv) deep ensembles perform relatively poorly; (v)\ninfinite-width BNNs are particularly promising, especially in high dimensions.\n", "date": "2023-05-31", "categories": []}
{"id": "2405.03092", "title": "Bayesian optimization for stable properties amid processing fluctuations\n  in sputter deposition", "abstract": "  We introduce a Bayesian optimization approach to guide the sputter deposition\nof molybdenum thin films, aiming to achieve desired residual stress and sheet\nresistance while minimizing susceptibility to stochastic fluctuations during\ndeposition. Thin films are pivotal in numerous technologies, including\nsemiconductors and optical devices, where their properties are critical.\nSputter deposition parameters, such as deposition power, vacuum chamber\npressure, and working distance, influence physical properties like residual\nstress and resistance. Excessive stress and high resistance can impair device\nperformance, necessitating the selection of optimal process parameters.\nFurthermore, these parameters should ensure the consistency and reliability of\nthin film properties, assisting in the reproducibility of the devices. However,\nexploring the multidimensional design space for process optimization is\nexpensive. Bayesian optimization is ideal for optimizing inputs/parameters of\ngeneral black-box functions without reliance on gradient information. We\nutilize Bayesian optimization to optimize deposition power and pressure using a\ncustom-built objective function incorporating observed stress and resistance\ndata. Additionally, we integrate prior knowledge of stress variation with\npressure into the objective function to prioritize films least affected by\nstochastic variations. Our findings demonstrate that Bayesian optimization\neffectively explores the design space and identifies optimal parameter\ncombinations meeting desired stress and resistance specifications.\n", "date": "2024-05-06", "categories": []}
{"id": "2405.00070", "title": "Bayesian-Guided Generation of Synthetic Microbiomes with Minimized\n  Pathogenicity", "abstract": "  Synthetic microbiomes offer new possibilities for modulating microbiota, to\naddress the barriers in multidtug resistance (MDR) research. We present a\nBayesian optimization approach to enable efficient searching over the space of\nsynthetic microbiome variants to identify candidates predictive of reduced MDR.\nMicrobiome datasets were encoded into a low-dimensional latent space using\nautoencoders. Sampling from this space allowed generation of synthetic\nmicrobiome signatures. Bayesian optimization was then implemented to select\nvariants for biological screening to maximize identification of designs with\nrestricted MDR pathogens based on minimal samples. Four acquisition functions\nwere evaluated: expected improvement, upper confidence bound, Thompson\nsampling, and probability of improvement. Based on each strategy, synthetic\nsamples were prioritized according to their MDR detection. Expected\nimprovement, upper confidence bound, and probability of improvement\nconsistently produced synthetic microbiome candidates with significantly fewer\nsearches than Thompson sampling. By combining deep latent space mapping and\nBayesian learning for efficient guided screening, this study demonstrated the\nfeasibility of creating bespoke synthetic microbiomes with customized MDR\nprofiles.\n", "date": "2024-04-29", "categories": []}
{"id": "2302.02399", "title": "Latent Space Bayesian Optimization with Latent Data Augmentation for\n  Enhanced Exploration", "abstract": "  Latent Space Bayesian Optimization (LSBO) combines generative models,\ntypically Variational Autoencoders (VAE), with Bayesian Optimization (BO) to\ngenerate de-novo objects of interest. However, LSBO faces challenges due to the\nmismatch between the objectives of BO and VAE, resulting in poor exploration\ncapabilities. In this paper, we propose novel contributions to enhance LSBO\nefficiency and overcome this challenge. We first introduce the concept of\nlatent consistency/inconsistency as a crucial problem in LSBO, arising from the\nVAE-BO mismatch. To address this, we propose the Latent Consistent\nAware-Acquisition Function (LCA-AF) that leverages consistent points in LSBO.\nAdditionally, we present LCA-VAE, a novel VAE method that creates a latent\nspace with increased consistent points through data augmentation in latent\nspace and penalization of latent inconsistencies. Combining LCA-VAE and LCA-AF,\nwe develop LCA-LSBO. Our approach achieves high sample-efficiency and effective\nexploration, emphasizing the significance of addressing latent consistency\nthrough the novel incorporation of data augmentation in latent space within\nLCA-VAE in LSBO. We showcase the performance of our proposal via de-novo image\ngeneration and de-novo chemical design tasks.\n", "date": "2023-02-05", "categories": []}
{"id": "2404.17997", "title": "Optimal Initialization of Batch Bayesian Optimization", "abstract": "  Field experiments and computer simulations are effective but time-consuming\nmethods of measuring the quality of engineered systems at different settings.\nTo reduce the total time required, experimenters may employ Bayesian\noptimization, which is parsimonious with measurements, and take measurements of\nmultiple settings simultaneously, in a batch. In practice, experimenters use\nvery few batches, thus, it is imperative that each batch be as informative as\npossible. Typically, the initial batch in a Batch Bayesian Optimization (BBO)\nis constructed from a quasi-random sample of settings values. We propose a\nbatch-design acquisition function, Minimal Terminal Variance (MTV), that\ndesigns a batch by optimization rather than random sampling. MTV adapts a\ndesign criterion function from Design of Experiments, called I-Optimality,\nwhich minimizes the variance of the post-evaluation estimates of quality,\nintegrated over the entire space of settings. MTV weights the integral by the\nprobability that a setting is optimal, making it able to design not only an\ninitial batch but all subsequent batches, as well. Applicability to both\ninitialization and subsequent batches is novel among acquisition functions.\nNumerical experiments on test functions and simulators show that MTV compares\nfavorably to other BBO methods.\n", "date": "2024-04-27", "categories": []}
{"id": "2404.17452", "title": "A Continuous Relaxation for Discrete Bayesian Optimization", "abstract": "  To optimize efficiently over discrete data and with only few available target\nobservations is a challenge in Bayesian optimization. We propose a continuous\nrelaxation of the objective function and show that inference and optimization\ncan be computationally tractable. We consider in particular the optimization\ndomain where very few observations and strict budgets exist; motivated by\noptimizing protein sequences for expensive to evaluate bio-chemical properties.\nThe advantages of our approach are two-fold: the problem is treated in the\ncontinuous setting, and available prior knowledge over sequences can be\nincorporated directly. More specifically, we utilize available and learned\ndistributions over the problem domain for a weighting of the Hellinger distance\nwhich yields a covariance function. We show that the resulting acquisition\nfunction can be optimized with both continuous or discrete optimization\nalgorithms and empirically assess our method on two bio-chemical sequence\noptimization tasks.\n", "date": "2024-04-26", "categories": []}
{"id": "2404.14433", "title": "KATO: Knowledge Alignment and Transfer for Transistor Sizing of\n  Different Design and Technology", "abstract": "  Automatic transistor sizing in circuit design continues to be a formidable\nchallenge. Despite that Bayesian optimization (BO) has achieved significant\nsuccess, it is circuit-specific, limiting the accumulation and transfer of\ndesign knowledge for broader applications. This paper proposes (1) efficient\nautomatic kernel construction, (2) the first transfer learning across different\ncircuits and technology nodes for BO, and (3) a selective transfer learning\nscheme to ensure only useful knowledge is utilized. These three novel\ncomponents are integrated into BO with Multi-objective Acquisition Ensemble\n(MACE) to form Knowledge Alignment and Transfer Optimization (KATO) to deliver\nstate-of-the-art performance: up to 2x simulation reduction and 1.2x design\nimprovement over the baselines.\n", "date": "2024-04-19", "categories": []}
{"id": "2404.14602", "title": "Adaptive Bayesian Optimization for High-Precision Motion Systems", "abstract": "  Controller tuning and parameter optimization are crucial in system design to\nimprove closed-loop system performance. Bayesian optimization has been\nestablished as an efficient model-free controller tuning and adaptation method.\nHowever, Bayesian optimization methods are computationally expensive and\ntherefore difficult to use in real-time critical scenarios. In this work, we\npropose a real-time purely data-driven, model-free approach for adaptive\ncontrol, by online tuning low-level controller parameters. We base our\nalgorithm on GoOSE, an algorithm for safe and sample-efficient Bayesian\noptimization, for handling performance and stability criteria. We introduce\nmultiple computational and algorithmic modifications for computational\nefficiency and parallelization of optimization steps. We further evaluate the\nalgorithm's performance on a real precision-motion system utilized in\nsemiconductor industry applications by modifying the payload and reference\nstepsize and comparing it to an interpolated constrained optimization-based\nbaseline approach.\n", "date": "2024-04-22", "categories": []}
{"id": "2311.14653", "title": "Data-driven Prior Learning for Bayesian Optimisation", "abstract": "  Transfer learning for Bayesian optimisation has generally assumed a strong\nsimilarity between optimisation tasks, with at least a subset having similar\noptimal inputs. This assumption can reduce computational costs, but it is\nviolated in a wide range of optimisation problems where transfer learning may\nnonetheless be useful. We replace this assumption with a weaker one only\nrequiring the shape of the optimisation landscape to be similar, and analyse\nthe recent method Prior Learning for Bayesian Optimisation - PLeBO - in this\nsetting. By learning priors for the hyperparameters of the Gaussian process\nsurrogate model we can better approximate the underlying function, especially\nfor few function evaluations. We validate the learned priors and compare to a\nbreadth of transfer learning approaches, using synthetic data and a recent air\npollution optimisation problem as benchmarks. We show that PLeBO and prior\ntransfer find good inputs in fewer evaluations.\n", "date": "2023-11-24", "categories": []}
{"id": "2404.12219", "title": "A Quadrature Approach for General-Purpose Batch Bayesian Optimization\n  via Probabilistic Lifting", "abstract": "  Parallelisation in Bayesian optimisation is a common strategy but faces\nseveral challenges: the need for flexibility in acquisition functions and\nkernel choices, flexibility dealing with discrete and continuous variables\nsimultaneously, model misspecification, and lastly fast massive\nparallelisation. To address these challenges, we introduce a versatile and\nmodular framework for batch Bayesian optimisation via probabilistic lifting\nwith kernel quadrature, called SOBER, which we present as a Python library\nbased on GPyTorch/BoTorch. Our framework offers the following unique benefits:\n(1) Versatility in downstream tasks under a unified approach. (2) A\ngradient-free sampler, which does not require the gradient of acquisition\nfunctions, offering domain-agnostic sampling (e.g., discrete and mixed\nvariables, non-Euclidean space). (3) Flexibility in domain prior distribution.\n(4) Adaptive batch size (autonomous determination of the optimal batch size).\n(5) Robustness against a misspecified reproducing kernel Hilbert space. (6)\nNatural stopping criterion.\n", "date": "2024-04-18", "categories": []}
{"id": "2404.10949", "title": "Human-Algorithm Collaborative Bayesian Optimization for Engineering\n  Systems", "abstract": "  Bayesian optimization has been successfully applied throughout Chemical\nEngineering for the optimization of functions that are expensive-to-evaluate,\nor where gradients are not easily obtainable. However, domain experts often\npossess valuable physical insights that are overlooked in fully automated\ndecision-making approaches, necessitating the inclusion of human input. In this\narticle we re-introduce the human back into the data-driven decision making\nloop by outlining an approach for collaborative Bayesian optimization. Our\nmethodology exploits the hypothesis that humans are more efficient at making\ndiscrete choices rather than continuous ones and enables experts to influence\ncritical early decisions. We apply high-throughput (batch) Bayesian\noptimization alongside discrete decision theory to enable domain experts to\ninfluence the selection of experiments. At every iteration we apply a\nmulti-objective approach that results in a set of alternate solutions that have\nboth high utility and are reasonably distinct. The expert then selects the\ndesired solution for evaluation from this set, allowing for the inclusion of\nexpert knowledge and improving accountability, whilst maintaining the\nadvantages of Bayesian optimization. We demonstrate our approach across a\nnumber of applied and numerical case studies including bioprocess optimization\nand reactor geometry design, demonstrating that even in the case of an\nuninformed practitioner our algorithm recovers the regret of standard Bayesian\noptimization. Through the inclusion of continuous expert opinion, our approach\nenables faster convergence, and improved accountability for Bayesian\noptimization in engineering systems.\n", "date": "2024-04-16", "categories": []}
{"id": "2403.04810", "title": "Restricted Bayesian Neural Network", "abstract": "  Modern deep learning tools are remarkably effective in addressing intricate\nproblems. However, their operation as black-box models introduces increased\nuncertainty in predictions. Additionally, they contend with various challenges,\nincluding the need for substantial storage space in large networks, issues of\noverfitting, underfitting, vanishing gradients, and more. This study explores\nthe concept of Bayesian Neural Networks, presenting a novel architecture\ndesigned to significantly alleviate the storage space complexity of a network.\nFurthermore, we introduce an algorithm adept at efficiently handling\nuncertainties, ensuring robust convergence values without becoming trapped in\nlocal optima, particularly when the objective function lacks perfect convexity.\n", "date": "2024-03-06", "categories": []}
{"id": "2404.00075", "title": "BEACON: Bayesian Experimental design Acceleration with Conditional\n  Normalizing flows $-$ a case study in optimal monitor well placement for\n  CO$_2$ sequestration", "abstract": "  CO$_2$ sequestration is a crucial engineering solution for mitigating climate\nchange. However, the uncertain nature of reservoir properties, necessitates\nrigorous monitoring of CO$_2$ plumes to prevent risks such as leakage, induced\nseismicity, or breaching licensed boundaries. To address this, project managers\nuse borehole wells for direct CO$_2$ and pressure monitoring at specific\nlocations. Given the high costs associated with drilling, it is crucial to\nstrategically place a limited number of wells to ensure maximally effective\nmonitoring within budgetary constraints. Our approach for selecting well\nlocations integrates fluid-flow solvers for forecasting plume trajectories with\ngenerative neural networks for plume inference uncertainty. Our methodology is\nextensible to three-dimensional domains and is developed within a Bayesian\nframework for optimal experimental design, ensuring scalability and\nmathematical optimality. We use a realistic case study to verify these claims\nby demonstrating our method's application in a large scale domain and optimal\nperformance as compared to baseline well placement.\n", "date": "2024-03-28", "categories": []}
{"id": "2403.18866", "title": "Graph Bayesian Optimization for Multiplex Influence Maximization", "abstract": "  Influence maximization (IM) is the problem of identifying a limited number of\ninitial influential users within a social network to maximize the number of\ninfluenced users. However, previous research has mostly focused on individual\ninformation propagation, neglecting the simultaneous and interactive\ndissemination of multiple information items. In reality, when users encounter a\npiece of information, such as a smartphone product, they often associate it\nwith related products in their minds, such as earphones or computers from the\nsame brand. Additionally, information platforms frequently recommend related\ncontent to users, amplifying this cascading effect and leading to multiplex\ninfluence diffusion.\n  This paper first formulates the Multiplex Influence Maximization (Multi-IM)\nproblem using multiplex diffusion models with an information association\nmechanism. In this problem, the seed set is a combination of influential users\nand information. To effectively manage the combinatorial complexity, we propose\nGraph Bayesian Optimization for Multi-IM (GBIM). The multiplex diffusion\nprocess is thoroughly investigated using a highly effective global kernelized\nattention message-passing module. This module, in conjunction with Bayesian\nlinear regression (BLR), produces a scalable surrogate model. A data\nacquisition module incorporating the exploration-exploitation trade-off is\ndeveloped to optimize the seed set further. Extensive experiments on synthetic\nand real-world datasets have proven our proposed framework effective. The code\nis available at https://github.com/zirui-yuan/GBIM.\n", "date": "2024-03-25", "categories": []}
{"id": "2403.08331", "title": "Bayesian Optimization that Limits Search Region to Lower Dimensions\n  Utilizing Local GPR", "abstract": "  Optimization of product and system characteristics is required in many\nfields, including design and control. Bayesian optimization (BO) is often used\nwhen there are high observing costs, because BO theoretically guarantees an\nupper bound on regret. However, computational costs increase exponentially with\nthe number of parameters to be optimized, decreasing search efficiency. We\npropose a BO that limits the search region to lower dimensions and utilizes\nlocal Gaussian process regression (LGPR) to scale the BO to higher dimensions.\nLGPR treats the low-dimensional search region as \"local,\" improving prediction\naccuracies there. The LGPR model is trained on a local subset of data specific\nto that region. This improves prediction accuracy and search efficiency and\nreduces the time complexity of matrix inversion in the Gaussian process\nregression. In evaluations with 20D Ackley and Rosenbrock functions, search\nefficiencies are equal to or higher than those of the compared methods,\nimproved by about 69% and 40% from the case without LGPR. We apply our method\nto an automatic design task for a power semiconductor device. We successfully\nreduce the specific on-resistance to 25% better than a conventional method and\n3.4% better than without LGPR.\n", "date": "2024-03-13", "categories": []}
{"id": "2403.16818", "title": "Multiple-Source Localization from a Single-Snapshot Observation Using\n  Graph Bayesian Optimization", "abstract": "  Due to the significance of its various applications, source localization has\ngarnered considerable attention as one of the most important means to confront\ndiffusion hazards. Multi-source localization from a single-snapshot observation\nis especially relevant due to its prevalence. However, the inherent\ncomplexities of this problem, such as limited information, interactions among\nsources, and dependence on diffusion models, pose challenges to resolution.\nCurrent methods typically utilize heuristics and greedy selection, and they are\nusually bonded with one diffusion model. Consequently, their effectiveness is\nconstrained. To address these limitations, we propose a simulation-based method\ntermed BOSouL. Bayesian optimization (BO) is adopted to approximate the results\nfor its sample efficiency. A surrogate function models uncertainty from the\nlimited information. It takes sets of nodes as the input instead of individual\nnodes. BOSouL can incorporate any diffusion model in the data acquisition\nprocess through simulations. Empirical studies demonstrate that its performance\nis robust across graph structures and diffusion models. The code is available\nat https://github.com/XGraph-Team/BOSouL.\n", "date": "2024-03-25", "categories": []}
{"id": "2403.14413", "title": "Model Uncertainty in Evolutionary Optimization and Bayesian\n  Optimization: A Comparative Analysis", "abstract": "  Black-box optimization problems, which are common in many real-world\napplications, require optimization through input-output interactions without\naccess to internal workings. This often leads to significant computational\nresources being consumed for simulations. Bayesian Optimization (BO) and\nSurrogate-Assisted Evolutionary Algorithm (SAEA) are two widely used\ngradient-free optimization techniques employed to address such challenges. Both\napproaches follow a similar iterative procedure that relies on surrogate models\nto guide the search process. This paper aims to elucidate the similarities and\ndifferences in the utilization of model uncertainty between these two methods,\nas well as the impact of model inaccuracies on algorithmic performance. A novel\nmodel-assisted strategy is introduced, which utilizes unevaluated solutions to\ngenerate offspring, leveraging the population-based search capabilities of\nevolutionary algorithm to enhance the effectiveness of model-assisted\noptimization. Experimental results demonstrate that the proposed approach\noutperforms mainstream Bayesian optimization algorithms in terms of accuracy\nand efficiency.\n", "date": "2024-03-21", "categories": []}
{"id": "2307.00618", "title": "Bounce: Reliable High-Dimensional Bayesian Optimization for\n  Combinatorial and Mixed Spaces", "abstract": "  Impactful applications such as materials discovery, hardware design, neural\narchitecture search, or portfolio optimization require optimizing\nhigh-dimensional black-box functions with mixed and combinatorial input spaces.\nWhile Bayesian optimization has recently made significant progress in solving\nsuch problems, an in-depth analysis reveals that the current state-of-the-art\nmethods are not reliable. Their performances degrade substantially when the\nunknown optima of the function do not have a certain structure. To fill the\nneed for a reliable algorithm for combinatorial and mixed spaces, this paper\nproposes Bounce that relies on a novel map of various variable types into\nnested embeddings of increasing dimensionality. Comprehensive experiments show\nthat Bounce reliably achieves and often even improves upon state-of-the-art\nperformance on a variety of high-dimensional problems.\n", "date": "2023-07-02", "categories": []}
{"id": "2403.12948", "title": "On Safety in Safe Bayesian Optimization", "abstract": "  Optimizing an unknown function under safety constraints is a central task in\nrobotics, biomedical engineering, and many other disciplines, and increasingly\nsafe Bayesian Optimization (BO) is used for this. Due to the safety critical\nnature of these applications, it is of utmost importance that theoretical\nsafety guarantees for these algorithms translate into the real world. In this\nwork, we investigate three safety-related issues of the popular class of\nSafeOpt-type algorithms. First, these algorithms critically rely on frequentist\nuncertainty bounds for Gaussian Process (GP) regression, but concrete\nimplementations typically utilize heuristics that invalidate all safety\nguarantees. We provide a detailed analysis of this problem and introduce\nReal-\\b{eta}-SafeOpt, a variant of the SafeOpt algorithm that leverages recent\nGP bounds and thus retains all theoretical guarantees. Second, we identify\nassuming an upper bound on the reproducing kernel Hilbert space (RKHS) norm of\nthe target function, a key technical assumption in SafeOpt-like algorithms, as\na central obstacle to real-world usage. To overcome this challenge, we\nintroduce the Lipschitz-only Safe Bayesian Optimization (LoSBO) algorithm,\nwhich guarantees safety without an assumption on the RKHS bound, and\nempirically show that this algorithm is not only safe, but also exhibits\nsuperior performance compared to the state-of-the-art on several function\nclasses. Third, SafeOpt and derived algorithms rely on a discrete search space,\nmaking them difficult to apply to higher-dimensional problems. To widen the\napplicability of these algorithms, we introduce Lipschitz-only GP-UCB\n(LoS-GP-UCB), a variant of LoSBO applicable to moderately high-dimensional\nproblems, while retaining safety.\n", "date": "2024-03-19", "categories": []}
{"id": "2403.07485", "title": "PMBO: Enhancing Black-Box Optimization through Multivariate Polynomial\n  Surrogates", "abstract": "  We introduce a surrogate-based black-box optimization method, termed\nPolynomial-model-based optimization (PMBO). The algorithm alternates polynomial\napproximation with Bayesian optimization steps, using Gaussian processes to\nmodel the error between the objective and its polynomial fit. We describe the\nalgorithmic design of PMBO and compare the results of the performance of PMBO\nwith several optimization methods for a set of analytic test functions.\n  The results show that PMBO outperforms the classic Bayesian optimization and\nis robust with respect to the choice of its correlation function family and its\nhyper-parameter setting, which, on the contrary, need to be carefully tuned in\nclassic Bayesian optimization. Remarkably, PMBO performs comparably with\nstate-of-the-art evolutionary algorithms such as the Covariance Matrix\nAdaptation -- Evolution Strategy (CMA-ES). This finding suggests that PMBO\nemerges as the pivotal choice among surrogate-based optimization methods when\naddressing low-dimensional optimization problems. Hereby, the simple nature of\npolynomials opens the opportunity for interpretation and analysis of the\ninferred surrogate model, providing a macroscopic perspective on the landscape\nof the objective function.\n", "date": "2024-03-12", "categories": []}
{"id": "2303.14877", "title": "Quantum approximate optimization via learning-based adaptive\n  optimization", "abstract": "  Combinatorial optimization problems are ubiquitous and computationally hard\nto solve in general. Quantum approximate optimization algorithm (QAOA), one of\nthe most representative quantum-classical hybrid algorithms, is designed to\nsolve combinatorial optimization problems by transforming the discrete\noptimization problem into a classical optimization problem over continuous\ncircuit parameters. QAOA objective landscape is notorious for pervasive local\nminima, and its viability significantly relies on the efficacy of the classical\noptimizer. In this work, we design double adaptive-region Bayesian optimization\n(DARBO) for QAOA. Our numerical results demonstrate that the algorithm greatly\noutperforms conventional optimizers in terms of speed, accuracy, and stability.\nWe also address the issues of measurement efficiency and the suppression of\nquantum noise by conducting the full optimization loop on a superconducting\nquantum processor as a proof of concept. This work helps to unlock the full\npower of QAOA and paves the way toward achieving quantum advantage in practical\nclassical tasks.\n", "date": "2023-03-27", "categories": []}
{"id": "2305.15572", "title": "The Behavior and Convergence of Local Bayesian Optimization", "abstract": "  A recent development in Bayesian optimization is the use of local\noptimization strategies, which can deliver strong empirical performance on\nhigh-dimensional problems compared to traditional global strategies. The \"folk\nwisdom\" in the literature is that the focus on local optimization sidesteps the\ncurse of dimensionality; however, little is known concretely about the expected\nbehavior or convergence of Bayesian local optimization routines. We first study\nthe behavior of the local approach, and find that the statistics of individual\nlocal solutions of Gaussian process sample paths are surprisingly good compared\nto what we would expect to recover from global methods. We then present the\nfirst rigorous analysis of such a Bayesian local optimization algorithm\nrecently proposed by M\\\"uller et al. (2021), and derive convergence rates in\nboth the noisy and noiseless settings.\n", "date": "2023-05-24", "categories": []}
{"id": "2402.03921", "title": "Large Language Models to Enhance Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is a powerful approach for optimizing complex and\nexpensive-to-evaluate black-box functions. Its importance is underscored in\nmany applications, notably including hyperparameter tuning, but its efficacy\ndepends on efficiently balancing exploration and exploitation. While there has\nbeen substantial progress in BO methods, striking this balance remains a\ndelicate process. In this light, we present LLAMBO, a novel approach that\nintegrates the capabilities of Large Language Models (LLM) within BO. At a high\nlevel, we frame the BO problem in natural language, enabling LLMs to\niteratively propose and evaluate promising solutions conditioned on historical\nevaluations. More specifically, we explore how combining contextual\nunderstanding, few-shot learning proficiency, and domain knowledge of LLMs can\nimprove model-based BO. Our findings illustrate that LLAMBO is effective at\nzero-shot warmstarting, and enhances surrogate modeling and candidate sampling,\nespecially in the early stages of search when observations are sparse. Our\napproach is performed in context and does not require LLM finetuning.\nAdditionally, it is modular by design, allowing individual components to be\nintegrated into existing BO frameworks, or function cohesively as an end-to-end\nmethod. We empirically validate LLAMBO's efficacy on the problem of\nhyperparameter tuning, highlighting strong empirical performance across a range\nof diverse benchmarks, proprietary, and synthetic tasks.\n", "date": "2024-02-06", "categories": []}
{"id": "2403.04629", "title": "Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI\n  Collaboration", "abstract": "  Bayesian optimization (BO) with Gaussian processes (GP) has become an\nindispensable algorithm for black box optimization problems. Not without a dash\nof irony, BO is often considered a black box itself, lacking ways to provide\nreasons as to why certain parameters are proposed to be evaluated. This is\nparticularly relevant in human-in-the-loop applications of BO, such as in\nrobotics. We address this issue by proposing ShapleyBO, a framework for\ninterpreting BO's proposals by game-theoretic Shapley values.They quantify each\nparameter's contribution to BO's acquisition function. Exploiting the linearity\nof Shapley values, we are further able to identify how strongly each parameter\ndrives BO's exploration and exploitation for additive acquisition functions\nlike the confidence bound. We also show that ShapleyBO can disentangle the\ncontributions to exploration into those that explore aleatoric and epistemic\nuncertainty. Moreover, our method gives rise to a ShapleyBO-assisted human\nmachine interface (HMI), allowing users to interfere with BO in case proposals\ndo not align with human reasoning. We demonstrate this HMI's benefits for the\nuse case of personalizing wearable robotic devices (assistive back exosuits) by\nhuman-in-the-loop BO. Results suggest human-BO teams with access to ShapleyBO\ncan achieve lower regret than teams without.\n", "date": "2024-03-07", "categories": []}
{"id": "2403.03816", "title": "Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box\n  Simulators with Noise Parameters", "abstract": "  The optimization of a black-box simulator over control parameters\n$\\mathbf{x}$ arises in a myriad of scientific applications. In such\napplications, the simulator often takes the form\n$f(\\mathbf{x},\\boldsymbol{\\theta})$, where $\\boldsymbol{\\theta}$ are parameters\nthat are uncertain in practice. Robust optimization aims to optimize the\nobjective $\\mathbb{E}[f(\\mathbf{x},\\boldsymbol{\\Theta})]$, where\n$\\boldsymbol{\\Theta} \\sim \\mathcal{P}$ is a random variable that models\nuncertainty on $\\boldsymbol{\\theta}$. For this, existing black-box methods\ntypically employ a two-stage approach for selecting the next point\n$(\\mathbf{x},\\boldsymbol{\\theta})$, where $\\mathbf{x}$ and\n$\\boldsymbol{\\theta}$ are optimized separately via different acquisition\nfunctions. As such, these approaches do not employ a joint acquisition over\n$(\\mathbf{x},\\boldsymbol{\\theta})$, and thus may fail to fully exploit\ncontrol-to-noise interactions for effective robust optimization. To address\nthis, we propose a new Bayesian optimization method called Targeted Variance\nReduction (TVR). The TVR leverages a novel joint acquisition function over\n$(\\mathbf{x},\\boldsymbol{\\theta})$, which targets variance reduction on the\nobjective within the desired region of improvement. Under a Gaussian process\nsurrogate on $f$, the TVR acquisition can be evaluated in closed form, and\nreveals an insightful exploration-exploitation-precision trade-off for robust\nblack-box optimization. The TVR can further accommodate a broad class of\nnon-Gaussian distributions on $\\mathcal{P}$ via a careful integration of\nnormalizing flows. We demonstrate the improved performance of TVR over the\nstate-of-the-art in a suite of numerical experiments and an application to the\nrobust design of automobile brake discs under operational uncertainty.\n", "date": "2024-03-06", "categories": []}
{"id": "2402.18337", "title": "Probabilistic Bayesian optimal experimental design using conditional\n  normalizing flows", "abstract": "  Bayesian optimal experimental design (OED) seeks to conduct the most\ninformative experiment under budget constraints to update the prior knowledge\nof a system to its posterior from the experimental data in a Bayesian\nframework. Such problems are computationally challenging because of (1)\nexpensive and repeated evaluation of some optimality criterion that typically\ninvolves a double integration with respect to both the system parameters and\nthe experimental data, (2) suffering from the curse-of-dimensionality when the\nsystem parameters and design variables are high-dimensional, (3) the\noptimization is combinatorial and highly non-convex if the design variables are\nbinary, often leading to non-robust designs. To make the solution of the\nBayesian OED problem efficient, scalable, and robust for practical\napplications, we propose a novel joint optimization approach. This approach\nperforms simultaneous (1) training of a scalable conditional normalizing flow\n(CNF) to efficiently maximize the expected information gain (EIG) of a jointly\nlearned experimental design (2) optimization of a probabilistic formulation of\nthe binary experimental design with a Bernoulli distribution. We demonstrate\nthe performance of our proposed method for a practical MRI data acquisition\nproblem, one of the most challenging Bayesian OED problems that has\nhigh-dimensional (320 $\\times$ 320) parameters at high image resolution,\nhigh-dimensional (640 $\\times$ 386) observations, and binary mask designs to\nselect the most informative observations.\n", "date": "2024-02-28", "categories": []}
{"id": "2402.17343", "title": "Enhanced Bayesian Optimization via Preferential Modeling of Abstract\n  Properties", "abstract": "  Experimental (design) optimization is a key driver in designing and\ndiscovering new products and processes. Bayesian Optimization (BO) is an\neffective tool for optimizing expensive and black-box experimental design\nprocesses. While Bayesian optimization is a principled data-driven approach to\nexperimental optimization, it learns everything from scratch and could greatly\nbenefit from the expertise of its human (domain) experts who often reason about\nsystems at different abstraction levels using physical properties that are not\nnecessarily directly measured (or measurable). In this paper, we propose a\nhuman-AI collaborative Bayesian framework to incorporate expert preferences\nabout unmeasured abstract properties into the surrogate modeling to further\nboost the performance of BO. We provide an efficient strategy that can also\nhandle any incorrect/misleading expert bias in preferential judgments. We\ndiscuss the convergence behavior of our proposed framework. Our experimental\nresults involving synthetic functions and real-world datasets show the\nsuperiority of our method against the baselines.\n", "date": "2024-02-27", "categories": []}
{"id": "2402.16237", "title": "Active Level Set Estimation for Continuous Search Space with Theoretical\n  Guarantee", "abstract": "  A common problem encountered in many real-world applications is level set\nestimation where the goal is to determine the region in the function domain\nwhere the function is above or below a given threshold. When the function is\nblack-box and expensive to evaluate, the level sets need to be found in a\nminimum set of function evaluations. Existing methods often assume a discrete\nsearch space with a finite set of data points for function evaluations and\nestimating the level sets. When applied to a continuous search space, these\nmethods often need to first discretize the space which leads to poor results\nwhile needing high computational time. While some methods cater for the\ncontinuous setting, they still lack a proper guarantee for theoretical\nconvergence. To address this problem, we propose a novel algorithm that does\nnot need any discretization and can directly work in continuous search spaces.\nOur method suggests points by constructing an acquisition function that is\ndefined as a measure of confidence of the function being higher or lower than\nthe given threshold. A theoretical analysis for the convergence of the\nalgorithm to an accurate solution is provided. On multiple synthetic and\nreal-world datasets, our algorithm successfully outperforms state-of-the-art\nmethods.\n", "date": "2024-02-26", "categories": []}
{"id": "2402.13402", "title": "Towards accelerating physical discovery via non-interactive and\n  interactive multi-fidelity Bayesian Optimization: Current challenges and\n  future opportunities", "abstract": "  Both computational and experimental material discovery bring forth the\nchallenge of exploring multidimensional and often non-differentiable parameter\nspaces, such as phase diagrams of Hamiltonians with multiple interactions,\ncomposition spaces of combinatorial libraries, processing spaces, and molecular\nembedding spaces. Often these systems are expensive or time-consuming to\nevaluate a single instance, and hence classical approaches based on exhaustive\ngrid or random search are too data intensive. This resulted in strong interest\ntowards active learning methods such as Bayesian optimization (BO) where the\nadaptive exploration occurs based on human learning (discovery) objective.\nHowever, classical BO is based on a predefined optimization target, and\npolicies balancing exploration and exploitation are purely data driven. In\npractical settings, the domain expert can pose prior knowledge on the system in\nform of partially known physics laws and often varies exploration policies\nduring the experiment. Here, we explore interactive workflows building on\nmulti-fidelity BO (MFBO), starting with classical (data-driven) MFBO, then\nstructured (physics-driven) sMFBO, and extending it to allow human in the loop\ninteractive iMFBO workflows for adaptive and domain expert aligned exploration.\nThese approaches are demonstrated over highly non-smooth multi-fidelity\nsimulation data generated from an Ising model, considering spin-spin\ninteraction as parameter space, lattice sizes as fidelity spaces, and the\nobjective as maximizing heat capacity. Detailed analysis and comparison show\nthe impact of physics knowledge injection and on-the-fly human decisions for\nimproved exploration, current challenges, and potential opportunities for\nalgorithm development with combining data, physics and real time human\ndecisions.\n", "date": "2024-02-20", "categories": []}
{"id": "2311.14645", "title": "A General Framework for User-Guided Bayesian Optimization", "abstract": "  The optimization of expensive-to-evaluate black-box functions is prevalent in\nvarious scientific disciplines. Bayesian optimization is an automatic, general\nand sample-efficient method to solve these problems with minimal knowledge of\nthe underlying function dynamics. However, the ability of Bayesian optimization\nto incorporate prior knowledge or beliefs about the function at hand in order\nto accelerate the optimization is limited, which reduces its appeal for\nknowledgeable practitioners with tight budgets. To allow domain experts to\ncustomize the optimization routine, we propose ColaBO, the first\nBayesian-principled framework for incorporating prior beliefs beyond the\ntypical kernel structure, such as the likely location of the optimizer or the\noptimal value. The generality of ColaBO makes it applicable across different\nMonte Carlo acquisition functions and types of user beliefs. We empirically\ndemonstrate ColaBO's ability to substantially accelerate optimization when the\nprior information is accurate, and to retain approximately default performance\nwhen it is misleading.\n", "date": "2023-11-24", "categories": []}
{"id": "2304.11005", "title": "Self-Correcting Bayesian Optimization through Bayesian Active Learning", "abstract": "  Gaussian processes are the model of choice in Bayesian optimization and\nactive learning. Yet, they are highly dependent on cleverly chosen\nhyperparameters to reach their full potential, and little effort is devoted to\nfinding good hyperparameters in the literature. We demonstrate the impact of\nselecting good hyperparameters for GPs and present two acquisition functions\nthat explicitly prioritize hyperparameter learning. Statistical distance-based\nActive Learning (SAL) considers the average disagreement between samples from\nthe posterior, as measured by a statistical distance. SAL outperforms the\nstate-of-the-art in Bayesian active learning on several test functions. We then\nintroduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to\nperform Bayesian optimization and active learning simultaneously. SCoreBO\nlearns the model hyperparameters at improved rates compared to vanilla BO,\nwhile outperforming the latest Bayesian optimization methods on traditional\nbenchmarks. Moreover, we demonstrate the importance of self-correction on\natypical Bayesian optimization tasks.\n", "date": "2023-04-21", "categories": []}
{"id": "2309.16597", "title": "Transfer Learning for Bayesian Optimization on Heterogeneous Search\n  Spaces", "abstract": "  Bayesian optimization (BO) is a popular black-box function optimization\nmethod, which makes sequential decisions based on a Bayesian model, typically a\nGaussian process (GP), of the function. To ensure the quality of the model,\ntransfer learning approaches have been developed to automatically design GP\npriors by learning from observations on \"training\" functions. These training\nfunctions are typically required to have the same domain as the \"test\" function\n(black-box function to be optimized). In this paper, we introduce MPHD, a model\npre-training method on heterogeneous domains, which uses a neural net mapping\nfrom domain-specific contexts to specifications of hierarchical GPs. MPHD can\nbe seamlessly integrated with BO to transfer knowledge across heterogeneous\nsearch spaces. Our theoretical and empirical results demonstrate the validity\nof MPHD and its superior performance on challenging black-box function\noptimization tasks.\n", "date": "2023-09-28", "categories": []}
{"id": "2310.05955", "title": "Bayesian Quality-Diversity approaches for constrained optimization\n  problems with mixed continuous, discrete and categorical variables", "abstract": "  Complex system design problems, such as those involved in aerospace\nengineering, require the use of numerically costly simulation codes in order to\npredict the performance of the system to be designed. In this context, these\ncodes are often embedded into an optimization process to provide the best\ndesign while satisfying the design constraints. Recently, new approaches,\ncalled Quality-Diversity, have been proposed in order to enhance the\nexploration of the design space and to provide a set of optimal diversified\nsolutions with respect to some feature functions. These functions are\ninteresting to assess trade-offs. Furthermore, complex design problems often\ninvolve mixed continuous, discrete, and categorical design variables allowing\nto take into account technological choices in the optimization problem.\nExisting Bayesian Quality-Diversity approaches suited for intensive\nhigh-fidelity simulations are not adapted to mixed variables constrained\noptimization problems. In order to overcome these limitations, a new\nQuality-Diversity methodology based on mixed variables Bayesian optimization\nstrategy is proposed in the context of limited simulation budget. Using adapted\ncovariance models and dedicated enrichment strategy for the Gaussian processes\nin Bayesian optimization, this approach allows to reduce the computational cost\nup to two orders of magnitude, with respect to classical Quality-Diversity\napproaches while dealing with discrete choices and the presence of constraints.\nThe performance of the proposed method is assessed on a benchmark of analytical\nproblems as well as on two aerospace system design problems highlighting its\nefficiency in terms of speed of convergence. The proposed approach provides\nvaluable trade-offs for decision-markers for complex system design.\n", "date": "2023-09-11", "categories": []}
{"id": "2302.03480", "title": "A Bayesian Optimization approach for calibrating large-scale\n  activity-based transport models", "abstract": "  The use of Agent-Based and Activity-Based modeling in transportation is\nrising due to the capability of addressing complex applications such as\ndisruptive trends (e.g., remote working and automation) or the design and\nassessment of disaggregated management strategies. Still, the broad adoption of\nlarge-scale disaggregate models is not materializing due to the inherently high\ncomplexity and computational needs. Activity-based models focused on behavioral\ntheory, for example, may involve hundreds of parameters that need to be\ncalibrated to match the detailed socio-economical characteristics of the\npopulation for any case study. This paper tackles this issue by proposing a\nnovel Bayesian Optimization approach incorporating a surrogate model in the\nform of an improved Random Forest, designed to automate the calibration process\nof the behavioral parameters. The proposed method is tested on a case study for\nthe city of Tallinn, Estonia, where the model to be calibrated consists of 477\nbehavioral parameters, using the SimMobility MT software. Satisfactory\nperformance is achieved in the major indicators defined for the calibration\nprocess: the error for the overall number of trips is equal to 4% and the\naverage error in the OD matrix is 15.92 vehicles per day.\n", "date": "2023-02-07", "categories": []}
{"id": "2305.19838", "title": "Relaxing the Additivity Constraints in Decentralized No-Regret\n  High-Dimensional Bayesian Optimization", "abstract": "  Bayesian Optimization (BO) is typically used to optimize an unknown function\n$f$ that is noisy and costly to evaluate, by exploiting an acquisition function\nthat must be maximized at each optimization step. Even if provably\nasymptotically optimal BO algorithms are efficient at optimizing\nlow-dimensional functions, scaling them to high-dimensional spaces remains an\nopen problem, often tackled by assuming an additive structure for $f$. By doing\nso, BO algorithms typically introduce additional restrictive assumptions on the\nadditive structure that reduce their applicability domain. This paper contains\ntwo main contributions: (i) we relax the restrictive assumptions on the\nadditive structure of $f$ without weakening the maximization guarantees of the\nacquisition function, and (ii) we address the over-exploration problem for\ndecentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically\noptimal decentralized BO algorithm that achieves very competitive performance\nagainst state-of-the-art BO algorithms, especially when the additive structure\nof $f$ comprises high-dimensional factors.\n", "date": "2023-05-31", "categories": []}
{"id": "2402.04885", "title": "A Unified Gaussian Process for Branching and Nested Hyperparameter\n  Optimization", "abstract": "  Choosing appropriate hyperparameters plays a crucial role in the success of\nneural networks as hyper-parameters directly control the behavior and\nperformance of the training algorithms. To obtain efficient tuning, Bayesian\noptimization methods based on Gaussian process (GP) models are widely used.\nDespite numerous applications of Bayesian optimization in deep learning, the\nexisting methodologies are developed based on a convenient but restrictive\nassumption that the tuning parameters are independent of each other. However,\ntuning parameters with conditional dependence are common in practice. In this\npaper, we focus on two types of them: branching and nested parameters. Nested\nparameters refer to those tuning parameters that exist only within a particular\nsetting of another tuning parameter, and a parameter within which other\nparameters are nested is called a branching parameter. To capture the\nconditional dependence between branching and nested parameters, a unified\nBayesian optimization framework is proposed. The sufficient conditions are\nrigorously derived to guarantee the validity of the kernel function, and the\nasymptotic convergence of the proposed optimization framework is proven under\nthe continuum-armed-bandit setting. Based on the new GP model, which accounts\nfor the dependent structure among input variables through a new kernel\nfunction, higher prediction accuracy and better optimization efficiency are\nobserved in a series of synthetic simulations and real data applications of\nneural networks. Sensitivity analysis is also performed to provide insights\ninto how changes in hyperparameter values affect prediction accuracy.\n", "date": "2024-01-19", "categories": []}
{"id": "2402.02687", "title": "Poisson Process for Bayesian Optimization", "abstract": "  BayesianOptimization(BO) is a sample-efficient black-box optimizer, and\nextensive methods have been proposed to build the absolute function response of\nthe black-box function through a probabilistic surrogate model, including\nTree-structured Parzen Estimator (TPE), random forest (SMAC), and Gaussian\nprocess (GP). However, few methods have been explored to estimate the relative\nrankings of candidates, which can be more robust to noise and have better\npracticality than absolute function responses, especially when the function\nresponses are intractable but preferences can be acquired. To this end, we\npropose a novel ranking-based surrogate model based on the Poisson process and\nintroduce an efficient BO framework, namely Poisson Process Bayesian\nOptimization (PoPBO). Two tailored acquisition functions are further derived\nfrom classic LCB and EI to accommodate it. Compared to the classic GP-BO\nmethod, our PoPBO has lower computation costs and better robustness to noise,\nwhich is verified by abundant experiments. The results on both simulated and\nreal-world benchmarks, including hyperparameter optimization (HPO) and neural\narchitecture search (NAS), show the effectiveness of PoPBO.\n", "date": "2024-02-05", "categories": []}
{"id": "2305.18435", "title": "Statistically Efficient Bayesian Sequential Experiment Design via\n  Reinforcement Learning with Cross-Entropy Estimators", "abstract": "  Reinforcement learning can learn amortised design policies for designing\nsequences of experiments. However, current amortised methods rely on estimators\nof expected information gain (EIG) that require an exponential number of\nsamples on the magnitude of the EIG to achieve an unbiased estimation. We\npropose the use of an alternative estimator based on the cross-entropy of the\njoint model distribution and a flexible proposal distribution. This proposal\ndistribution approximates the true posterior of the model parameters given the\nexperimental history and the design policy. Our method overcomes the\nexponential-sample complexity of previous approaches and provide more accurate\nestimates of high EIG values. More importantly, it allows learning of superior\ndesign policies, and is compatible with continuous and discrete design spaces,\nnon-differentiable likelihoods and even implicit probabilistic models.\n", "date": "2023-05-29", "categories": []}
{"id": "2402.03104", "title": "High-dimensional Bayesian Optimization via Covariance Matrix Adaptation\n  Strategy", "abstract": "  Bayesian Optimization (BO) is an effective method for finding the global\noptimum of expensive black-box functions. However, it is well known that\napplying BO to high-dimensional optimization problems is challenging. To\naddress this issue, a promising solution is to use a local search strategy that\npartitions the search domain into local regions with high likelihood of\ncontaining the global optimum, and then use BO to optimize the objective\nfunction within these regions. In this paper, we propose a novel technique for\ndefining the local regions using the Covariance Matrix Adaptation (CMA)\nstrategy. Specifically, we use CMA to learn a search distribution that can\nestimate the probabilities of data points being the global optimum of the\nobjective function. Based on this search distribution, we then define the local\nregions consisting of data points with high probabilities of being the global\noptimum. Our approach serves as a meta-algorithm as it can incorporate existing\nblack-box BO optimizers, such as BO, TuRBO, and BAxUS, to find the global\noptimum of the objective function within our derived local regions. We evaluate\nour proposed method on various benchmark synthetic and real-world problems. The\nresults demonstrate that our method outperforms existing state-of-the-art\ntechniques.\n", "date": "2024-02-05", "categories": []}
{"id": "2402.03243", "title": "PINN-BO: A Black-box Optimization Algorithm using Physics-Informed\n  Neural Networks", "abstract": "  Black-box optimization is a powerful approach for discovering global optima\nin noisy and expensive black-box functions, a problem widely encountered in\nreal-world scenarios. Recently, there has been a growing interest in leveraging\ndomain knowledge to enhance the efficacy of machine learning methods. Partial\nDifferential Equations (PDEs) often provide an effective means for elucidating\nthe fundamental principles governing the black-box functions. In this paper, we\npropose PINN-BO, a black-box optimization algorithm employing Physics-Informed\nNeural Networks that integrates the knowledge from Partial Differential\nEquations (PDEs) to improve the sample efficiency of the optimization. We\nanalyze the theoretical behavior of our algorithm in terms of regret bound\nusing advances in NTK theory and prove that the use of the PDE alongside the\nblack-box function evaluations, PINN-BO leads to a tighter regret bound. We\nperform several experiments on a variety of optimization tasks and show that\nour algorithm is more sample-efficient compared to existing methods.\n", "date": "2024-02-05", "categories": []}
{"id": "2310.15351", "title": "Random Exploration in Bayesian Optimization: Order-Optimal Regret and\n  Computational Efficiency", "abstract": "  We consider Bayesian optimization using Gaussian Process models, also\nreferred to as kernel-based bandit optimization. We study the methodology of\nexploring the domain using random samples drawn from a distribution. We show\nthat this random exploration approach achieves the optimal error rates. Our\nanalysis is based on novel concentration bounds in an infinite dimensional\nHilbert space established in this work, which may be of independent interest.\nWe further develop an algorithm based on random exploration with domain\nshrinking and establish its order-optimal regret guarantees under both\nnoise-free and noisy settings. In the noise-free setting, our analysis closes\nthe existing gap in regret performance and thereby resolves a COLT open\nproblem. The proposed algorithm also enjoys a computational advantage over\nprevailing methods due to the random exploration that obviates the expensive\noptimization of a non-convex acquisition function for choosing the query points\nat each iteration.\n", "date": "2023-10-23", "categories": []}
{"id": "2401.16373", "title": "Bayesian optimization as a flexible and efficient design framework for\n  sustainable process systems", "abstract": "  Bayesian optimization (BO) is a powerful technology for optimizing noisy\nexpensive-to-evaluate black-box functions, with a broad range of real-world\napplications in science, engineering, economics, manufacturing, and beyond. In\nthis paper, we provide an overview of recent developments, challenges, and\nopportunities in BO for design of next-generation process systems. After\ndescribing several motivating applications, we discuss how advanced BO methods\nhave been developed to more efficiently tackle important problems in these\napplications. We conclude the paper with a summary of challenges and\nopportunities related to improving the quality of the probabilistic model, the\nchoice of internal optimization procedure used to select the next sample point,\nand the exploitation of problem structure to improve sample efficiency.\n", "date": "2024-01-29", "categories": []}
{"id": "2401.14544", "title": "Bayesian Optimization through Gaussian Cox Process Models for\n  Spatio-temporal Data", "abstract": "  Bayesian optimization (BO) has established itself as a leading strategy for\nefficiently optimizing expensive-to-evaluate functions. Existing BO methods\nmostly rely on Gaussian process (GP) surrogate models and are not applicable to\n(doubly-stochastic) Gaussian Cox processes, where the observation process is\nmodulated by a latent intensity function modeled as a GP. In this paper, we\npropose a novel maximum a posteriori inference of Gaussian Cox processes. It\nleverages the Laplace approximation and change of kernel technique to transform\nthe problem into a new reproducing kernel Hilbert space, where it becomes more\ntractable computationally. It enables us to obtain both a functional posterior\nof the latent intensity function and the covariance of the posterior, thus\nextending existing works that often focus on specific link functions or\nestimating the posterior mean. Using the result, we propose a BO framework\nbased on the Gaussian Cox process model and further develop a Nystr\\\"om\napproximation for efficient computation. Extensive evaluations on various\nsynthetic and real-world datasets demonstrate significant improvement over\nstate-of-the-art inference solutions for Gaussian Cox processes, as well as\neffective BO with a wide range of acquisition functions designed through the\nunderlying Gaussian Cox process model.\n", "date": "2024-01-25", "categories": []}
{"id": "2302.08298", "title": "Unleashing the Potential of Acquisition Functions in High-Dimensional\n  Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is widely used to optimize expensive-to-evaluate\nblack-box functions.BO first builds a surrogate model to represent the\nobjective function and assesses its uncertainty. It then decides where to\nsample by maximizing an acquisition function (AF) based on the surrogate model.\nHowever, when dealing with high-dimensional problems, finding the global\nmaximum of the AF becomes increasingly challenging. In such cases, the\ninitialization of the AF maximizer plays a pivotal role, as an inadequate setup\ncan severely hinder the effectiveness of the AF.\n  This paper investigates a largely understudied problem concerning the impact\nof AF maximizer initialization on exploiting AFs' capability. Our large-scale\nempirical study shows that the widely used random initialization strategy often\nfails to harness the potential of an AF. In light of this, we propose a better\ninitialization approach by employing multiple heuristic optimizers to leverage\nthe historical data of black-box optimization to generate initial points for\nthe AF maximize. We evaluate our approach with a range of heavily studied\nsynthetic functions and real-world applications. Experimental results show that\nour techniques, while simple, can significantly enhance the standard BO and\noutperform state-of-the-art methods by a large margin in most test cases.\n", "date": "2023-02-16", "categories": []}
{"id": "2312.08891", "title": "High-Dimensional Bayesian Optimisation with Large-Scale Constraints --\n  An Application to Aeroelastic Tailoring", "abstract": "  Design optimisation potentially leads to lightweight aircraft structures with\nlower environmental impact. Due to the high number of design variables and\nconstraints, these problems are ordinarily solved using gradient-based\noptimisation methods, leading to a local solution in the design space while the\nglobal space is neglected. Bayesian Optimisation is a promising path towards\nsample-efficient, global optimisation based on probabilistic surrogate models.\nWhile Bayesian optimisation methods have demonstrated their strength for\nproblems with a low number of design variables, the scalability to\nhigh-dimensional problems while incorporating large-scale constraints is still\nlacking. Especially in aeroelastic tailoring where directional stiffness\nproperties are embodied into the structural design of aircraft, to control\naeroelastic deformations and to increase the aerodynamic and structural\nperformance, the safe operation of the system needs to be ensured by involving\nconstraints resulting from different analysis disciplines. Hence, a global\ndesign space search becomes even more challenging. The present study attempts\nto tackle the problem by using high-dimensional Bayesian Optimisation in\ncombination with a dimensionality reduction approach to solve the optimisation\nproblem occurring in aeroelastic tailoring, presenting a novel approach for\nhigh-dimensional problems with large-scale constraints. Experiments on\nwell-known benchmark cases with black-box constraints show that the proposed\napproach can incorporate large-scale constraints.\n", "date": "2023-12-14", "categories": []}
{"id": "2206.01409", "title": "Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable\n  Bayesian Optimization", "abstract": "  This paper presents a new type of hybrid model for Bayesian optimization (BO)\nadept at managing mixed variables, encompassing both quantitative (continuous\nand integer) and qualitative (categorical) types. Our proposed new hybrid\nmodels (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for\ncategorical variables with Gaussian Processes (GP) for continuous ones. hybridM\nleverages the upper confidence bound tree search (UCTS) for MCTS strategy,\nshowcasing the tree architecture's integration into Bayesian optimization. Our\ninnovations, including dynamic online kernel selection in the surrogate\nmodeling phase and a unique UCTS search strategy, position our hybrid models as\nan advancement in mixed-variable surrogate models. Numerical experiments\nunderscore the superiority of hybrid models, highlighting their potential in\nBayesian optimization.\n", "date": "2022-06-03", "categories": []}
{"id": "2401.05716", "title": "Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature\n  and Bayesian Optimization", "abstract": "  In this paper, we study the problem of estimating the normalizing constant\n$\\int e^{-\\lambda f(x)}dx$ through queries to the black-box function $f$, where\n$f$ belongs to a reproducing kernel Hilbert space (RKHS), and $\\lambda$ is a\nproblem parameter. We show that to estimate the normalizing constant within a\nsmall relative error, the level of difficulty depends on the value of\n$\\lambda$: When $\\lambda$ approaches zero, the problem is similar to Bayesian\nquadrature (BQ), while when $\\lambda$ approaches infinity, the problem is\nsimilar to Bayesian optimization (BO). More generally, the problem varies\nbetween BQ and BO. We find that this pattern holds true even when the function\nevaluations are noisy, bringing new aspects to this topic. Our findings are\nsupported by both algorithm-independent lower bounds and algorithmic upper\nbounds, as well as simulation studies conducted on a variety of benchmark\nfunctions.\n", "date": "2024-01-11", "categories": []}
{"id": "2401.02650", "title": "Improving sample efficiency of high dimensional Bayesian optimization\n  with MCMC", "abstract": "  Sequential optimization methods are often confronted with the curse of\ndimensionality in high-dimensional spaces. Current approaches under the\nGaussian process framework are still burdened by the computational complexity\nof tracking Gaussian process posteriors and need to partition the optimization\nproblem into small regions to ensure exploration or assume an underlying\nlow-dimensional structure. With the idea of transiting the candidate points\ntowards more promising positions, we propose a new method based on Markov Chain\nMonte Carlo to efficiently sample from an approximated posterior. We provide\ntheoretical guarantees of its convergence in the Gaussian process Thompson\nsampling setting. We also show experimentally that both the Metropolis-Hastings\nand the Langevin Dynamics version of our algorithm outperform state-of-the-art\nmethods in high-dimensional sequential optimization and reinforcement learning\nbenchmarks.\n", "date": "2024-01-05", "categories": []}
{"id": "2310.00077", "title": "Optimizing with Low Budgets: a Comparison on the Black-box Optimization\n  Benchmarking Suite and OpenAI Gym", "abstract": "  The growing ubiquity of machine learning (ML) has led it to enter various\nareas of computer science, including black-box optimization (BBO). Recent\nresearch is particularly concerned with Bayesian optimization (BO). BO-based\nalgorithms are popular in the ML community, as they are used for hyperparameter\noptimization and more generally for algorithm configuration. However, their\nefficiency decreases as the dimensionality of the problem and the budget of\nevaluations increase. Meanwhile, derivative-free optimization methods have\nevolved independently in the optimization community. Therefore, we urge to\nunderstand whether cross-fertilization is possible between the two communities,\nML and BBO, i.e., whether algorithms that are heavily used in ML also work well\nin BBO and vice versa. Comparative experiments often involve rather small\nbenchmarks and show visible problems in the experimental setup, such as poor\ninitialization of baselines, overfitting due to problem-specific setting of\nhyperparameters, and low statistical significance.\n  With this paper, we update and extend a comparative study presented by Hutter\net al. in 2013. We compare BBO tools for ML with more classical heuristics,\nfirst on the well-known BBOB benchmark suite from the COCO environment and then\non Direct Policy Search for OpenAI Gym, a reinforcement learning benchmark. Our\nresults confirm that BO-based optimizers perform well on both benchmarks when\nbudgets are limited, albeit with a higher computational cost, while they are\noften outperformed by algorithms from other families when the evaluation budget\nbecomes larger. We also show that some algorithms from the BBO community\nperform surprisingly well on ML tasks.\n", "date": "2023-09-29", "categories": []}
{"id": "2401.01398", "title": "Accelerating Black-Box Molecular Property Optimization by Adaptively\n  Learning Sparse Subspaces", "abstract": "  Molecular property optimization (MPO) problems are inherently challenging\nsince they are formulated over discrete, unstructured spaces and the labeling\nprocess involves expensive simulations or experiments, which fundamentally\nlimits the amount of available data. Bayesian optimization (BO) is a powerful\nand popular framework for efficient optimization of noisy, black-box objective\nfunctions (e.g., measured property values), thus is a potentially attractive\nframework for MPO. To apply BO to MPO problems, one must select a structured\nmolecular representation that enables construction of a probabilistic surrogate\nmodel. Many molecular representations have been developed, however, they are\nall high-dimensional, which introduces important challenges in the BO process\n-- mainly because the curse of dimensionality makes it difficult to define and\nperform inference over a suitable class of surrogate models. This challenge has\nbeen recently addressed by learning a lower-dimensional encoding of a SMILE or\ngraph representation of a molecule in an unsupervised manner and then\nperforming BO in the encoded space. In this work, we show that such methods\nhave a tendency to \"get stuck,\" which we hypothesize occurs since the mapping\nfrom the encoded space to property values is not necessarily well-modeled by a\nGaussian process. We argue for an alternative approach that combines numerical\nmolecular descriptors with a sparse axis-aligned Gaussian process model, which\nis capable of rapidly identifying sparse subspaces that are most relevant to\nmodeling the unknown property function. We demonstrate that our proposed method\nsubstantially outperforms existing MPO methods on a variety of benchmark and\nreal-world problems. Specifically, we show that our method can routinely find\nnear-optimal molecules out of a set of more than $>100$k alternatives within\n100 or fewer expensive queries.\n", "date": "2024-01-02", "categories": []}
{"id": "2309.02842", "title": "Random Postprocessing for Combinatorial Bayesian Optimization", "abstract": "  Model-based sequential approaches to discrete \"black-box\" optimization,\nincluding Bayesian optimization techniques, often access the same points\nmultiple times for a given objective function in interest, resulting in many\nsteps to find the global optimum. Here, we numerically study the effect of a\npostprocessing method on Bayesian optimization that strictly prohibits\nduplicated samples in the dataset. We find the postprocessing method\nsignificantly reduces the number of sequential steps to find the global\noptimum, especially when the acquisition function is of maximum a posterior\nestimation. Our results provide a simple but general strategy to solve the slow\nconvergence of Bayesian optimization for high-dimensional problems.\n", "date": "2023-09-06", "categories": []}
{"id": "2312.16983", "title": "PG-LBO: Enhancing High-Dimensional Bayesian Optimization with\n  Pseudo-Label and Gaussian Process Guidance", "abstract": "  Variational Autoencoder based Bayesian Optimization (VAE-BO) has demonstrated\nits excellent performance in addressing high-dimensional structured\noptimization problems. However, current mainstream methods overlook the\npotential of utilizing a pool of unlabeled data to construct the latent space,\nwhile only concentrating on designing sophisticated models to leverage the\nlabeled data. Despite their effective usage of labeled data, these methods\noften require extra network structures, additional procedure, resulting in\ncomputational inefficiency. To address this issue, we propose a novel method to\neffectively utilize unlabeled data with the guidance of labeled data.\nSpecifically, we tailor the pseudo-labeling technique from semi-supervised\nlearning to explicitly reveal the relative magnitudes of optimization objective\nvalues hidden within the unlabeled data. Based on this technique, we assign\nappropriate training weights to unlabeled data to enhance the construction of a\ndiscriminative latent space. Furthermore, we treat the VAE encoder and the\nGaussian Process (GP) in Bayesian optimization as a unified deep kernel\nlearning process, allowing the direct utilization of labeled data, which we\nterm as Gaussian Process guidance. This directly and effectively integrates the\ngoal of improving GP accuracy into the VAE training, thereby guiding the\nconstruction of the latent space. The extensive experiments demonstrate that\nour proposed method outperforms existing VAE-BO algorithms in various\noptimization scenarios. Our code will be published at\nhttps://github.com/TaicaiChen/PG-LBO.\n", "date": "2023-12-28", "categories": []}
{"id": "2312.03212", "title": "Constrained Bayesian Optimization Under Partial Observations: Balanced\n  Improvements and Provable Convergence", "abstract": "  The partially observable constrained optimization problems (POCOPs) impede\ndata-driven optimization techniques since an infeasible solution of POCOPs can\nprovide little information about the objective as well as the constraints. We\nendeavor to design an efficient and provable method for expensive POCOPs under\nthe framework of constrained Bayesian optimization. Our method consists of two\nkey components. Firstly, we present an improved design of the acquisition\nfunctions that introduces balanced exploration during optimization. We\nrigorously study the convergence properties of this design to demonstrate its\neffectiveness. Secondly, we propose a Gaussian process embedding different\nlikelihoods as the surrogate model for a partially observable constraint. This\nmodel leads to a more accurate representation of the feasible regions compared\nto traditional classification-based models. Our proposed method is empirically\nstudied on both synthetic and real-world problems. The results demonstrate the\ncompetitiveness of our method for solving POCOPs.\n", "date": "2023-12-06", "categories": []}
{"id": "2305.15930", "title": "End-to-End Meta-Bayesian Optimisation with Transformer Neural Processes", "abstract": "  Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of\nBayesian optimisation by leveraging data from related tasks. While previous\nmethods successfully meta-learn either a surrogate model or an acquisition\nfunction independently, joint training of both components remains an open\nchallenge. This paper proposes the first end-to-end differentiable meta-BO\nframework that generalises neural processes to learn acquisition functions via\ntransformer architectures. We enable this end-to-end framework with\nreinforcement learning (RL) to tackle the lack of labelled acquisition data.\nEarly on, we notice that training transformer-based neural processes from\nscratch with RL is challenging due to insufficient supervision, especially when\nrewards are sparse. We formalise this claim with a combinatorial analysis\nshowing that the widely used notion of regret as a reward signal exhibits a\nlogarithmic sparsity pattern in trajectory lengths. To tackle this problem, we\naugment the RL objective with an auxiliary task that guides part of the\narchitecture to learn a valid probabilistic model as an inductive bias. We\ndemonstrate that our method achieves state-of-the-art regret results against\nvarious baselines in experiments on standard hyperparameter optimisation tasks\nand also outperforms others in the real-world problems of mixed-integer\nprogramming tuning, antibody design, and logic synthesis for electronic design\nautomation.\n", "date": "2023-05-25", "categories": []}
{"id": "2312.10423", "title": "Stochastic Bayesian Optimization with Unknown Continuous Context\n  Distribution via Kernel Density Estimation", "abstract": "  Bayesian optimization (BO) is a sample-efficient method and has been widely\nused for optimizing expensive black-box functions. Recently, there has been a\nconsiderable interest in BO literature in optimizing functions that are\naffected by context variable in the environment, which is uncontrollable by\ndecision makers. In this paper, we focus on the optimization of functions'\nexpectations over continuous context variable, subject to an unknown\ndistribution. To address this problem, we propose two algorithms that employ\nkernel density estimation to learn the probability density function (PDF) of\ncontinuous context variable online. The first algorithm is simpler, which\ndirectly optimizes the expectation under the estimated PDF. Considering that\nthe estimated PDF may have high estimation error when the true distribution is\ncomplicated, we further propose the second algorithm that optimizes the\ndistributionally robust objective. Theoretical results demonstrate that both\nalgorithms have sub-linear Bayesian cumulative regret on the expectation\nobjective. Furthermore, we conduct numerical experiments to empirically\ndemonstrate the effectiveness of our algorithms.\n", "date": "2023-12-16", "categories": []}
{"id": "2209.04587", "title": "Multipoint-BAX: A New Approach for Efficiently Tuning Particle\n  Accelerator Emittance via Virtual Objectives", "abstract": "  Although beam emittance is critical for the performance of high-brightness\naccelerators, optimization is often time limited as emittance calculations,\ncommonly done via quadrupole scans, are typically slow. Such calculations are a\ntype of $\\textit{multipoint query}$, i.e. each query requires multiple\nsecondary measurements. Traditional black-box optimizers such as Bayesian\noptimization are slow and inefficient when dealing with such objectives as they\nmust acquire the full series of measurements, but return only the emittance,\nwith each query. We propose a new information-theoretic algorithm,\nMultipoint-BAX, for black-box optimization on multipoint queries, which queries\nand models individual beam-size measurements using techniques from Bayesian\nAlgorithm Execution (BAX). Our method avoids the slow multipoint query on the\naccelerator by acquiring points through a $\\textit{virtual objective}$, i.e.\ncalculating the emittance objective from a fast learned model rather than\ndirectly from the accelerator. We use Multipoint-BAX to minimize emittance at\nthe Linac Coherent Light Source (LCLS) and the Facility for Advanced\nAccelerator Experimental Tests II (FACET-II). In simulation, our method is\n20$\\times$ faster and more robust to noise compared to existing methods. In\nlive tests, it matched the hand-tuned emittance at FACET-II and achieved a 24%\nlower emittance than hand-tuning at LCLS. Our method represents a conceptual\nshift for optimizing multipoint queries, and we anticipate that it can be\nreadily adapted to similar problems in particle accelerators and other\nscientific instruments.\n", "date": "2022-09-10", "categories": []}
{"id": "2312.12633", "title": "Long-run Behaviour of Multi-fidelity Bayesian Optimisation", "abstract": "  Multi-fidelity Bayesian Optimisation (MFBO) has been shown to generally\nconverge faster than single-fidelity Bayesian Optimisation (SFBO) (Poloczek et\nal. (2017)). Inspired by recent benchmark papers, we are investigating the\nlong-run behaviour of MFBO, based on observations in the literature that it\nmight under-perform in certain scenarios (Mikkola et al. (2023), Eggensperger\net al. (2021)). An under-performance of MBFO in the long-run could\nsignificantly undermine its application to many research tasks, especially when\nwe are not able to identify when the under-performance begins. We create a\nsimple benchmark study, showcase empirical results and discuss scenarios and\npossible reasons of under-performance.\n", "date": "2023-12-19", "categories": []}
{"id": "2312.11318", "title": "Domain Invariant Learning for Gaussian Processes and Bayesian\n  Exploration", "abstract": "  Out-of-distribution (OOD) generalization has long been a challenging problem\nthat remains largely unsolved. Gaussian processes (GP), as popular\nprobabilistic model classes, especially in the small data regime, presume\nstrong OOD generalization abilities. Surprisingly, their OOD generalization\nabilities have been under-explored before compared with other lines of GP\nresearch. In this paper, we identify that GP is not free from the problem and\npropose a domain invariant learning algorithm for Gaussian processes (DIL-GP)\nwith a min-max optimization on the likelihood. DIL-GP discovers the\nheterogeneity in the data and forces invariance across partitioned subsets of\ndata. We further extend the DIL-GP to improve Bayesian optimization's\nadaptability on changing environments. Numerical experiments demonstrate the\nsuperiority of DIL-GP for predictions on several synthetic and real-world\ndatasets. We further demonstrate the effectiveness of the DIL-GP Bayesian\noptimization method on a PID parameters tuning experiment for a quadrotor. The\nfull version and source code are available at:\nhttps://github.com/Billzxl/DIL-GP.\n", "date": "2023-12-18", "categories": []}
{"id": "2308.09888", "title": "On Estimating the Gradient of the Expected Information Gain in Bayesian\n  Experimental Design", "abstract": "  Bayesian Experimental Design (BED), which aims to find the optimal\nexperimental conditions for Bayesian inference, is usually posed as to optimize\nthe expected information gain (EIG). The gradient information is often needed\nfor efficient EIG optimization, and as a result the ability to estimate the\ngradient of EIG is essential for BED problems. The primary goal of this work is\nto develop methods for estimating the gradient of EIG, which, combined with the\nstochastic gradient descent algorithms, result in efficient optimization of\nEIG. Specifically, we first introduce a posterior expected representation of\nthe EIG gradient with respect to the design variables. Based on this, we\npropose two methods for estimating the EIG gradient, UEEG-MCMC that leverages\nposterior samples generated through Markov Chain Monte Carlo (MCMC) to estimate\nthe EIG gradient, and BEEG-AP that focuses on achieving high simulation\nefficiency by repeatedly using parameter samples. Theoretical analysis and\nnumerical studies illustrate that UEEG-MCMC is robust agains the actual EIG\nvalue, while BEEG-AP is more efficient when the EIG value to be optimized is\nsmall. Moreover, both methods show superior performance compared to several\npopular benchmarks in our numerical experiments.\n", "date": "2023-08-19", "categories": []}
{"id": "2312.08021", "title": "Improving search relevance of Azure Cognitive Search by Bayesian\n  optimization", "abstract": "  Azure Cognitive Search (ACS) has emerged as a major contender in \"Search as a\nService\" cloud products in recent years. However, one of the major challenges\nfor ACS users is to improve the relevance of the search results for their\nspecific usecases. In this paper, we propose a novel method to find the optimal\nACS configuration that maximizes search relevance for a specific usecase\n(product search, document search...) The proposed solution improves key online\nmarketplace metrics such as click through rates (CTR) by formulating the search\nrelevance problem as hyperparameter tuning. We have observed significant\nimprovements in real-world search call to action (CTA) rate in multiple\nmarketplaces by introducing optimized weights generated from the proposed\napproach.\n", "date": "2023-12-13", "categories": []}
{"id": "2210.12496", "title": "Bayesian Optimization with Conformal Prediction Sets", "abstract": "  Bayesian optimization is a coherent, ubiquitous approach to decision-making\nunder uncertainty, with applications including multi-arm bandits, active\nlearning, and black-box optimization. Bayesian optimization selects decisions\n(i.e. objective function queries) with maximal expected utility with respect to\nthe posterior distribution of a Bayesian model, which quantifies reducible,\nepistemic uncertainty about query outcomes. In practice, subjectively\nimplausible outcomes can occur regularly for two reasons: 1) model\nmisspecification and 2) covariate shift. Conformal prediction is an uncertainty\nquantification method with coverage guarantees even for misspecified models and\na simple mechanism to correct for covariate shift. We propose conformal\nBayesian optimization, which directs queries towards regions of search space\nwhere the model predictions have guaranteed validity, and investigate its\nbehavior on a suite of black-box optimization tasks and tabular ranking tasks.\nIn many cases we find that query coverage can be significantly improved without\nharming sample-efficiency.\n", "date": "2022-10-22", "categories": []}
{"id": "2306.09803", "title": "Framework and Benchmarks for Combinatorial and Mixed-variable Bayesian\n  Optimization", "abstract": "  This paper introduces a modular framework for Mixed-variable and\nCombinatorial Bayesian Optimization (MCBO) to address the lack of systematic\nbenchmarking and standardized evaluation in the field. Current MCBO papers\noften introduce non-diverse or non-standard benchmarks to evaluate their\nmethods, impeding the proper assessment of different MCBO primitives and their\ncombinations. Additionally, papers introducing a solution for a single MCBO\nprimitive often omit benchmarking against baselines that utilize the same\nmethods for the remaining primitives. This omission is primarily due to the\nsignificant implementation overhead involved, resulting in a lack of controlled\nassessments and an inability to showcase the merits of a contribution\neffectively. To overcome these challenges, our proposed framework enables an\neffortless combination of Bayesian Optimization components, and provides a\ndiverse set of synthetic and real-world benchmarking tasks. Leveraging this\nflexibility, we implement 47 novel MCBO algorithms and benchmark them against\nseven existing MCBO solvers and five standard black-box optimization algorithms\non ten tasks, conducting over 4000 experiments. Our findings reveal a superior\ncombination of MCBO primitives outperforming existing approaches and illustrate\nthe significance of model fit and the use of a trust region. We make our MCBO\nlibrary available under the MIT license at\n\\url{https://github.com/huawei-noah/HEBO/tree/master/MCBO}.\n", "date": "2023-06-16", "categories": []}
{"id": "2312.03466", "title": "Search Strategies for Self-driving Laboratories with Pending Experiments", "abstract": "  Self-driving laboratories (SDLs) consist of multiple stations that perform\nmaterial synthesis and characterisation tasks. To minimize station downtime and\nmaximize experimental throughput, it is practical to run experiments in\nasynchronous parallel, in which multiple experiments are being performed at\nonce in different stages. Asynchronous parallelization of experiments, however,\nintroduces delayed feedback (i.e. \"pending experiments\"), which is known to\nreduce Bayesian optimiser performance. Here, we build a simulator for a\nmulti-stage SDL and compare optimisation strategies for dealing with delayed\nfeedback and asynchronous parallelized operation. Using data from a real SDL,\nwe build a ground truth Bayesian optimisation simulator from 177 previously run\nexperiments for maximizing the conductivity of functional coatings. We then\ncompare search strategies such as expected improvement, noisy expected\nimprovement, 4-mode exploration and random sampling. We evaluate their\nperformance in terms of amount of delay and problem dimensionality. Our\nsimulation results showcase the trade-off between the asynchronous parallel\noperation and delayed feedback.\n", "date": "2023-12-06", "categories": []}
{"id": "2206.14115", "title": "Quantum Neural Architecture Search with Quantum Circuits Metric and\n  Bayesian Optimization", "abstract": "  Quantum neural networks are promising for a wide range of applications in the\nNoisy Intermediate-Scale Quantum era. As such, there is an increasing demand\nfor automatic quantum neural architecture search. We tackle this challenge by\ndesigning a quantum circuits metric for Bayesian optimization with Gaussian\nprocess. To this goal, we propose a new quantum gates distance that\ncharacterizes the gates' action over every quantum state and provide a\ntheoretical perspective on its geometrical properties. Our approach\nsignificantly outperforms the benchmark on three empirical quantum machine\nlearning problems including training a quantum generative adversarial network,\nsolving combinatorial optimization in the MaxCut problem, and simulating\nquantum Fourier transform. Our method can be extended to characterize behaviors\nof various quantum machine learning models.\n", "date": "2022-06-28", "categories": []}
{"id": "2312.02852", "title": "Expert-guided Bayesian Optimisation for Human-in-the-loop Experimental\n  Design of Known Systems", "abstract": "  Domain experts often possess valuable physical insights that are overlooked\nin fully automated decision-making processes such as Bayesian optimisation. In\nthis article we apply high-throughput (batch) Bayesian optimisation alongside\nanthropological decision theory to enable domain experts to influence the\nselection of optimal experiments. Our methodology exploits the hypothesis that\nhumans are better at making discrete choices than continuous ones and enables\nexperts to influence critical early decisions. At each iteration we solve an\naugmented multi-objective optimisation problem across a number of alternate\nsolutions, maximising both the sum of their utility function values and the\ndeterminant of their covariance matrix, equivalent to their total variability.\nBy taking the solution at the knee point of the Pareto front, we return a set\nof alternate solutions at each iteration that have both high utility values and\nare reasonably distinct, from which the expert selects one for evaluation. We\ndemonstrate that even in the case of an uninformed practitioner, our algorithm\nrecovers the regret of standard Bayesian optimisation.\n", "date": "2023-12-05", "categories": []}
{"id": "2312.01692", "title": "Risk-Controlling Model Selection via Guided Bayesian Optimization", "abstract": "  Adjustable hyperparameters of machine learning models typically impact\nvarious key trade-offs such as accuracy, fairness, robustness, or inference\ncost. Our goal in this paper is to find a configuration that adheres to\nuser-specified limits on certain risks while being useful with respect to other\nconflicting metrics. We solve this by combining Bayesian Optimization (BO) with\nrigorous risk-controlling procedures, where our core idea is to steer BO\ntowards an efficient testing strategy. Our BO method identifies a set of Pareto\noptimal configurations residing in a designated region of interest. The\nresulting candidates are statistically verified and the best-performing\nconfiguration is selected with guaranteed risk levels. We demonstrate the\neffectiveness of our approach on a range of tasks with multiple desiderata,\nincluding low error rates, equitable predictions, handling spurious\ncorrelations, managing rate and distortion in generative models, and reducing\ncomputational costs.\n", "date": "2023-12-04", "categories": []}
{"id": "2312.00622", "title": "Practical Path-based Bayesian Optimization", "abstract": "  There has been a surge in interest in data-driven experimental design with\napplications to chemical engineering and drug manufacturing. Bayesian\noptimization (BO) has proven to be adaptable to such cases, since we can model\nthe reactions of interest as expensive black-box functions. Sometimes, the cost\nof this black-box functions can be separated into two parts: (a) the cost of\nthe experiment itself, and (b) the cost of changing the input parameters. In\nthis short paper, we extend the SnAKe algorithm to deal with both types of\ncosts simultaneously. We further propose extensions to the case of a maximum\nallowable input change, as well as to the multi-objective setting.\n", "date": "2023-12-01", "categories": []}
{"id": "2302.14545", "title": "Modern Bayesian Experimental Design", "abstract": "  Bayesian experimental design (BED) provides a powerful and general framework\nfor optimizing the design of experiments. However, its deployment often poses\nsubstantial computational challenges that can undermine its practical use. In\nthis review, we outline how recent advances have transformed our ability to\novercome these challenges and thus utilize BED effectively, before discussing\nsome key areas for future development in the field.\n", "date": "2023-02-28", "categories": []}
{"id": "2311.11254", "title": "BOIS: Bayesian Optimization of Interconnected Systems", "abstract": "  Bayesian optimization (BO) has proven to be an effective paradigm for the\nglobal optimization of expensive-to-sample systems. One of the main advantages\nof BO is its use of Gaussian processes (GPs) to characterize model uncertainty\nwhich can be leveraged to guide the learning and search process. However, BO\ntypically treats systems as black-boxes and this limits the ability to exploit\nstructural knowledge (e.g., physics and sparse interconnections). Composite\nfunctions of the form $f(x, y(x))$, wherein GP modeling is shifted from the\nperformance function $f$ to an intermediate function $y$, offer an avenue for\nexploiting structural knowledge. However, the use of composite functions in a\nBO framework is complicated by the need to generate a probability density for\n$f$ from the Gaussian density of $y$ calculated by the GP (e.g., when $f$ is\nnonlinear it is not possible to obtain a closed-form expression). Previous work\nhas handled this issue using sampling techniques; these are easy to implement\nand flexible but are computationally intensive. In this work, we introduce a\nnew paradigm which allows for the efficient use of composite functions in BO;\nthis uses adaptive linearizations of $f$ to obtain closed-form expressions for\nthe statistical moments of the composite function. We show that this simple\napproach (which we call BOIS) enables the exploitation of structural knowledge,\nsuch as that arising in interconnected systems as well as systems that embed\nmultiple GP models and combinations of physics and GP models. Using a chemical\nprocess optimization case study, we benchmark the effectiveness of BOIS against\nstandard BO and sampling approaches. Our results indicate that BOIS achieves\nperformance gains and accurately captures the statistics of composite\nfunctions.\n", "date": "2023-11-19", "categories": []}
{"id": "2311.15162", "title": "Domain Knowledge Injection in Bayesian Search for New Materials", "abstract": "  In this paper we propose DKIBO, a Bayesian optimization (BO) algorithm that\naccommodates domain knowledge to tune exploration in the search space. Bayesian\noptimization has recently emerged as a sample-efficient optimizer for many\nintractable scientific problems. While various existing BO frameworks allow the\ninput of prior beliefs to accelerate the search by narrowing down the space,\nincorporating such knowledge is not always straightforward and can often\nintroduce bias and lead to poor performance. Here we propose a simple approach\nto incorporate structural knowledge in the acquisition function by utilizing an\nadditional deterministic surrogate model to enrich the approximation power of\nthe Gaussian process. This is suitably chosen according to structural\ninformation of the problem at hand and acts a corrective term towards a\nbetter-informed sampling. We empirically demonstrate the practical utility of\nthe proposed method by successfully injecting domain knowledge in a materials\ndesign task. We further validate our method's performance on different\nexperimental settings and ablation analyses.\n", "date": "2023-11-26", "categories": []}
{"id": "2301.11588", "title": "Bounding Box-based Multi-objective Bayesian Optimization of Risk\n  Measures under Input Uncertainty", "abstract": "  In this study, we propose a novel multi-objective Bayesian optimization\n(MOBO) method to efficiently identify the Pareto front (PF) defined by risk\nmeasures for black-box functions under the presence of input uncertainty (IU).\nExisting BO methods for Pareto optimization in the presence of IU are\nrisk-specific or without theoretical guarantees, whereas our proposed method\naddresses general risk measures and has theoretical guarantees. The basic idea\nof the proposed method is to assume a Gaussian process (GP) model for the\nblack-box function and to construct high-probability bounding boxes for the\nrisk measures using the GP model. Furthermore, in order to reduce the\nuncertainty of non-dominated bounding boxes, we propose a method of selecting\nthe next evaluation point using a maximin distance defined by the maximum value\nof a quasi distance based on bounding boxes. As theoretical analysis, we prove\nthat the algorithm can return an arbitrary-accurate solution in a finite number\nof iterations with high probability, for various risk measures such as Bayes\nrisk, worst-case risk, and value-at-risk. We also give a theoretical analysis\nthat takes into account approximation errors because there exist non-negligible\napproximation errors (e.g., finite approximation of PFs and sampling-based\napproximation of bounding boxes) in practice. We confirm that the proposed\nmethod outperforms compared with existing methods not only in the setting with\nIU but also in the setting of ordinary MOBO through numerical experiments.\n", "date": "2023-01-27", "categories": []}
{"id": "2311.13460", "title": "Multi-Objective Bayesian Optimization with Active Preference Learning", "abstract": "  There are a lot of real-world black-box optimization problems that need to\noptimize multiple criteria simultaneously. However, in a multi-objective\noptimization (MOO) problem, identifying the whole Pareto front requires the\nprohibitive search cost, while in many practical scenarios, the decision maker\n(DM) only needs a specific solution among the set of the Pareto optimal\nsolutions. We propose a Bayesian optimization (BO) approach to identifying the\nmost preferred solution in the MOO with expensive objective functions, in which\na Bayesian preference model of the DM is adaptively estimated by an interactive\nmanner based on the two types of supervisions called the pairwise preference\nand improvement request. To explore the most preferred solution, we define an\nacquisition function in which the uncertainty both in the objective functions\nand the DM preference is incorporated. Further, to minimize the interaction\ncost with the DM, we also propose an active learning strategy for the\npreference estimation. We empirically demonstrate the effectiveness of our\nproposed method through the benchmark function optimization and the\nhyper-parameter optimization problems for machine learning models.\n", "date": "2023-11-22", "categories": []}
{"id": "2210.01071", "title": "New Paradigms for Exploiting Parallel Experiments in Bayesian\n  Optimization", "abstract": "  Bayesian optimization (BO) is one of the most effective methods for\nclosed-loop experimental design and black-box optimization. However, a key\nlimitation of BO is that it is an inherently sequential algorithm (one\nexperiment is proposed per round) and thus cannot directly exploit\nhigh-throughput (parallel) experiments. Diverse modifications to the BO\nframework have been proposed in the literature to enable exploitation of\nparallel experiments but such approaches are limited in the degree of\nparallelization that they can achieve and can lead to redundant experiments\n(thus wasting resources and potentially compromising performance). In this\nwork, we present new parallel BO paradigms that exploit the structure of the\nsystem to partition the design space. Specifically, we propose an approach that\npartitions the design space by following the level sets of the performance\nfunction and an approach that exploits partially-separable structures of the\nperformance function found. We conduct extensive numerical experiments using a\nreactor case study to benchmark the effectiveness of these approaches against a\nvariety of state-of-the-art parallel algorithms reported in the literature. Our\ncomputational results show that our approaches significantly reduce the\nrequired search time and increase the probability of finding a global (rather\nthan local) solution.\n", "date": "2022-10-03", "categories": []}
{"id": "2310.18288", "title": "Sustainable Concrete via Bayesian Optimization", "abstract": "  Eight percent of global carbon dioxide emissions can be attributed to the\nproduction of cement, the main component of concrete, which is also the\ndominant source of CO2 emissions in the construction of data centers. The\ndiscovery of lower-carbon concrete formulae is therefore of high significance\nfor sustainability. However, experimenting with new concrete formulae is time\nconsuming and labor intensive, as one usually has to wait to record the\nconcrete's 28-day compressive strength, a quantity whose measurement can by its\ndefinition not be accelerated. This provides an opportunity for experimental\ndesign methodology like Bayesian Optimization (BO) to accelerate the search for\nstrong and sustainable concrete formulae. Herein, we 1) propose modeling steps\nthat make concrete strength amenable to be predicted accurately by a Gaussian\nprocess model with relatively few measurements, 2) formulate the search for\nsustainable concrete as a multi-objective optimization problem, and 3) leverage\nthe proposed model to carry out multi-objective BO with real-world strength\nmeasurements of the algorithmically proposed mixes. Our experimental results\nshow improved trade-offs between the mixtures' global warming potential (GWP)\nand their associated compressive strengths, compared to mixes based on current\nindustry practices. Our methods are open-sourced at\ngithub.com/facebookresearch/SustainableConcrete.\n", "date": "2023-10-27", "categories": []}
{"id": "2310.20258", "title": "Advancing Bayesian Optimization via Learning Correlated Latent Space", "abstract": "  Bayesian optimization is a powerful method for optimizing black-box functions\nwith limited function evaluations. Recent works have shown that optimization in\na latent space through deep generative models such as variational autoencoders\nleads to effective and efficient Bayesian optimization for structured or\ndiscrete data. However, as the optimization does not take place in the input\nspace, it leads to an inherent gap that results in potentially suboptimal\nsolutions. To alleviate the discrepancy, we propose Correlated latent space\nBayesian Optimization (CoBO), which focuses on learning correlated latent\nspaces characterized by a strong correlation between the distances in the\nlatent space and the distances within the objective function. Specifically, our\nmethod introduces Lipschitz regularization, loss weighting, and trust region\nrecoordination to minimize the inherent gap around the promising areas. We\ndemonstrate the effectiveness of our approach on several optimization tasks in\ndiscrete data, such as molecule design and arithmetic expression fitting, and\nachieve high performance within a small budget.\n", "date": "2023-10-31", "categories": []}
{"id": "2311.09591", "title": "Accelerating material discovery with a threshold-driven hybrid\n  acquisition policy-based Bayesian optimization", "abstract": "  Advancements in materials play a crucial role in technological progress.\nHowever, the process of discovering and developing materials with desired\nproperties is often impeded by substantial experimental costs, extensive\nresource utilization, and lengthy development periods. To address these\nchallenges, modern approaches often employ machine learning (ML) techniques\nsuch as Bayesian Optimization (BO), which streamline the search for optimal\nmaterials by iteratively selecting experiments that are most likely to yield\nbeneficial results. However, traditional BO methods, while beneficial, often\nstruggle with balancing the trade-off between exploration and exploitation,\nleading to sub-optimal performance in material discovery processes. This paper\nintroduces a novel Threshold-Driven UCB-EI Bayesian Optimization (TDUE-BO)\nmethod, which dynamically integrates the strengths of Upper Confidence Bound\n(UCB) and Expected Improvement (EI) acquisition functions to optimize the\nmaterial discovery process. Unlike the classical BO, our method focuses on\nefficiently navigating the high-dimensional material design space (MDS).\nTDUE-BO begins with an exploration-focused UCB approach, ensuring a\ncomprehensive initial sweep of the MDS. As the model gains confidence,\nindicated by reduced uncertainty, it transitions to the more exploitative EI\nmethod, focusing on promising areas identified earlier. The UCB-to-EI switching\npolicy dictated guided through continuous monitoring of the model uncertainty\nduring each step of sequential sampling results in navigating through the MDS\nmore efficiently while ensuring rapid convergence. The effectiveness of TDUE-BO\nis demonstrated through its application on three different material datasets,\nshowing significantly better approximation and optimization performance over\nthe EI and UCB-based BO methods in terms of the RMSE scores and convergence\nefficiency, respectively.\n", "date": "2023-11-16", "categories": []}
{"id": "2302.09184", "title": "Rapid Design of Top-Performing Metal-Organic Frameworks with Qualitative\n  Representations of Building Blocks", "abstract": "  Data-driven materials design often encounters challenges where systems\nrequire or possess qualitative (categorical) information. Metal-organic\nframeworks (MOFs) are an example of such material systems. The representation\nof MOFs through different building blocks makes it a challenge for designers to\nincorporate qualitative information into design optimization. Furthermore, the\nlarge number of potential building blocks leads to a combinatorial challenge,\nwith millions of possible MOFs that could be explored through time consuming\nphysics-based approaches. In this work, we integrated Latent Variable Gaussian\nProcess (LVGP) and Multi-Objective Batch-Bayesian Optimization (MOBBO) to\nidentify top-performing MOFs adaptively, autonomously, and efficiently without\nany human intervention. Our approach provides three main advantages: (i) no\nspecific physical descriptors are required and only building blocks that\nconstruct the MOFs are used in global optimization through qualitative\nrepresentations, (ii) the method is application and property independent, and\n(iii) the latent variable approach provides an interpretable model of\nqualitative building blocks with physical justification. To demonstrate the\neffectiveness of our method, we considered a design space with more than 47,000\nMOF candidates. By searching only ~1% of the design space, LVGP-MOBBO was able\nto identify all MOFs on the Pareto front and more than 97% of the 50\ntop-performing designs for the CO$_2$ working capacity and CO$_2$/N$_2$\nselectivity properties. Finally, we compared our approach with the Random\nForest algorithm and demonstrated its efficiency, interpretability, and\nrobustness.\n", "date": "2023-02-17", "categories": []}
{"id": "2306.12370", "title": "PriorBand: Practical Hyperparameter Optimization in the Age of Deep\n  Learning", "abstract": "  Hyperparameters of Deep Learning (DL) pipelines are crucial for their\ndownstream performance. While a large number of methods for Hyperparameter\nOptimization (HPO) have been developed, their incurred costs are often\nuntenable for modern DL. Consequently, manual experimentation is still the most\nprevalent approach to optimize hyperparameters, relying on the researcher's\nintuition, domain knowledge, and cheap preliminary explorations. To resolve\nthis misalignment between HPO algorithms and DL researchers, we propose\nPriorBand, an HPO algorithm tailored to DL, able to utilize both expert beliefs\nand cheap proxy tasks. Empirically, we demonstrate PriorBand's efficiency\nacross a range of DL benchmarks and show its gains under informative expert\ninput and robustness against poor expert beliefs\n", "date": "2023-06-21", "categories": []}
{"id": "2310.05166", "title": "A Corrected Expected Improvement Acquisition Function Under Noisy\n  Observations", "abstract": "  Sequential maximization of expected improvement (EI) is one of the most\nwidely used policies in Bayesian optimization because of its simplicity and\nability to handle noisy observations. In particular, the improvement function\noften uses the best posterior mean as the best incumbent in noisy settings.\nHowever, the uncertainty associated with the incumbent solution is often\nneglected in many analytic EI-type methods: a closed-form acquisition function\nis derived in the noise-free setting, but then applied to the setting with\nnoisy observations. To address this limitation, we propose a modification of EI\nthat corrects its closed-form expression by incorporating the covariance\ninformation provided by the Gaussian Process (GP) model. This acquisition\nfunction specializes to the classical noise-free result, and we argue should\nreplace that formula in Bayesian optimization software packages, tutorials, and\ntextbooks. This enhanced acquisition provides good generality for noisy and\nnoiseless settings. We show that our method achieves a sublinear convergence\nrate on the cumulative regret bound under heteroscedastic observation noise.\nOur empirical results demonstrate that our proposed acquisition function can\noutperform EI in the presence of noisy observations on benchmark functions for\nblack-box optimization, as well as on parameter search for neural network model\ncompression.\n", "date": "2023-10-08", "categories": []}
{"id": "2310.03912", "title": "RTDK-BO: High Dimensional Bayesian Optimization with Reinforced\n  Transformer Deep kernels", "abstract": "  Bayesian Optimization (BO), guided by Gaussian process (GP) surrogates, has\nproven to be an invaluable technique for efficient, high-dimensional, black-box\noptimization, a critical problem inherent to many applications such as\nindustrial design and scientific computing. Recent contributions have\nintroduced reinforcement learning (RL) to improve the optimization performance\non both single function optimization and \\textit{few-shot} multi-objective\noptimization. However, even few-shot techniques fail to exploit similarities\nshared between closely related objectives. In this paper, we combine recent\ndevelopments in Deep Kernel Learning (DKL) and attention-based Transformer\nmodels to improve the modeling powers of GP surrogates with meta-learning. We\npropose a novel method for improving meta-learning BO surrogates by\nincorporating attention mechanisms into DKL, empowering the surrogates to adapt\nto contextual information gathered during the BO process. We combine this\nTransformer Deep Kernel with a learned acquisition function trained with\ncontinuous Soft Actor-Critic Reinforcement Learning to aid in exploration. This\nReinforced Transformer Deep Kernel (RTDK-BO) approach yields state-of-the-art\nresults in continuous high-dimensional optimization problems.\n", "date": "2023-10-05", "categories": []}
{"id": "2310.20145", "title": "Efficient Robust Bayesian Optimization for Arbitrary Uncertain Inputs", "abstract": "  Bayesian Optimization (BO) is a sample-efficient optimization algorithm\nwidely employed across various applications. In some challenging BO tasks,\ninput uncertainty arises due to the inevitable randomness in the optimization\nprocess, such as machining errors, execution noise, or contextual variability.\nThis uncertainty deviates the input from the intended value before evaluation,\nresulting in significant performance fluctuations in the final result. In this\npaper, we introduce a novel robust Bayesian Optimization algorithm, AIRBO,\nwhich can effectively identify a robust optimum that performs consistently well\nunder arbitrary input uncertainty. Our method directly models the uncertain\ninputs of arbitrary distributions by empowering the Gaussian Process with the\nMaximum Mean Discrepancy (MMD) and further accelerates the posterior inference\nvia Nystrom approximation. Rigorous theoretical regret bound is established\nunder MMD estimation error and extensive experiments on synthetic functions and\nreal problems demonstrate that our approach can handle various input\nuncertainties and achieve state-of-the-art performance.\n", "date": "2023-10-31", "categories": []}
{"id": "2311.02119", "title": "Safe Sequential Optimization for Switching Environments", "abstract": "  We consider the problem of designing a sequential decision making agent to\nmaximize an unknown time-varying function which switches with time. At each\nstep, the agent receives an observation of the function's value at a point\ndecided by the agent. The observation could be corrupted by noise. The agent is\nalso constrained to take safe decisions with high probability, i.e., the chosen\npoints should have a function value greater than a threshold. For this\nswitching environment, we propose a policy called Adaptive-SafeOpt and evaluate\nits performance via simulations. The policy incorporates Bayesian optimization\nand change point detection for the safe sequential optimization problem. We\nobserve that a major challenge in adapting to the switching change is to\nidentify safe decisions when the change point is detected and prevent\nattraction to local optima.\n", "date": "2023-11-03", "categories": []}
{"id": "2311.01195", "title": "Batch Bayesian Optimization for Replicable Experimental Design", "abstract": "  Many real-world experimental design problems (a) evaluate multiple\nexperimental conditions in parallel and (b) replicate each condition multiple\ntimes due to large and heteroscedastic observation noise. Given a fixed total\nbudget, this naturally induces a trade-off between evaluating more unique\nconditions while replicating each of them fewer times vs. evaluating fewer\nunique conditions and replicating each more times. Moreover, in these problems,\npractitioners may be risk-averse and hence prefer an input with both good\naverage performance and small variability. To tackle both challenges, we\npropose the Batch Thompson Sampling for Replicable Experimental Design\n(BTS-RED) framework, which encompasses three algorithms. Our BTS-RED-Known and\nBTS-RED-Unknown algorithms, for, respectively, known and unknown noise\nvariance, choose the number of replications adaptively rather than\ndeterministically such that an input with a larger noise variance is replicated\nmore times. As a result, despite the noise heteroscedasticity, both algorithms\nenjoy a theoretical guarantee and are asymptotically no-regret. Our\nMean-Var-BTS-RED algorithm aims at risk-averse optimization and is also\nasymptotically no-regret. We also show the effectiveness of our algorithms in\ntwo practical real-world applications: precision agriculture and AutoML.\n", "date": "2023-11-02", "categories": []}
{"id": "2306.05304", "title": "Bayesian Optimisation of Functions on Graphs", "abstract": "  The increasing availability of graph-structured data motivates the task of\noptimising over functions defined on the node set of graphs. Traditional graph\nsearch algorithms can be applied in this case, but they may be\nsample-inefficient and do not make use of information about the function\nvalues; on the other hand, Bayesian optimisation is a class of promising\nblack-box solvers with superior sample efficiency, but it has been scarcely\nbeen applied to such novel setups. To fill this gap, we propose a novel\nBayesian optimisation framework that optimises over functions defined on\ngeneric, large-scale and potentially unknown graphs. Through the learning of\nsuitable kernels on graphs, our framework has the advantage of adapting to the\nbehaviour of the target function. The local modelling approach further\nguarantees the efficiency of our method. Extensive experiments on both\nsynthetic and real-world graphs demonstrate the effectiveness of the proposed\noptimisation framework.\n", "date": "2023-06-08", "categories": []}
{"id": "2310.12526", "title": "Parallel Bayesian Optimization Using Satisficing Thompson Sampling for\n  Time-Sensitive Black-Box Optimization", "abstract": "  Bayesian optimization (BO) is widely used for black-box optimization\nproblems, and have been shown to perform well in various real-world tasks.\nHowever, most of the existing BO methods aim to learn the optimal solution,\nwhich may become infeasible when the parameter space is extremely large or the\nproblem is time-sensitive. In these contexts, switching to a satisficing\nsolution that requires less information can result in better performance. In\nthis work, we focus on time-sensitive black-box optimization problems and\npropose satisficing Thompson sampling-based parallel Bayesian optimization\n(STS-PBO) approaches, including synchronous and asynchronous versions. We shift\nthe target from an optimal solution to a satisficing solution that is easier to\nlearn. The rate-distortion theory is introduced to construct a loss function\nthat balances the amount of information that needs to be learned with\nsub-optimality, and the Blahut-Arimoto algorithm is adopted to compute the\ntarget solution that reaches the minimum information rate under the distortion\nlimit at each step. Both discounted and undiscounted Bayesian cumulative regret\nbounds are theoretically derived for the proposed STS-PBO approaches. The\neffectiveness of the proposed methods is demonstrated on a fast-charging design\nproblem of Lithium-ion batteries. The results are accordant with theoretical\nanalyses, and show that our STS-PBO methods outperform both sequential\ncounterparts and parallel BO with traditional Thompson sampling in both\nsynchronous and asynchronous settings.\n", "date": "2023-10-19", "categories": []}
{"id": "2310.11749", "title": "Estimating Material Properties of Interacting Objects Using Sum-GP-UCB", "abstract": "  Robots need to estimate the material and dynamic properties of objects from\nobservations in order to simulate them accurately. We present a Bayesian\noptimization approach to identifying the material property parameters of\nobjects based on a set of observations. Our focus is on estimating these\nproperties based on observations of scenes with different sets of interacting\nobjects. We propose an approach that exploits the structure of the reward\nfunction by modeling the reward for each observation separately and using only\nthe parameters of the objects in that scene as inputs. The resulting\nlower-dimensional models generalize better over the parameter space, which in\nturn results in a faster optimization. To speed up the optimization process\nfurther, and reduce the number of simulation runs needed to find good parameter\nvalues, we also propose partial evaluations of the reward function, wherein the\nselected parameters are only evaluated on a subset of real world evaluations.\nThe approach was successfully evaluated on a set of scenes with a wide range of\nobject interactions, and we showed that our method can effectively perform\nincremental learning without resetting the rewards of the gathered\nobservations.\n", "date": "2023-10-18", "categories": []}
{"id": "2310.08751", "title": "Constrained Bayesian Optimization with Adaptive Active Learning of\n  Unknown Constraints", "abstract": "  Optimizing objectives under constraints, where both the objectives and\nconstraints are black box functions, is a common scenario in real-world\napplications such as scientific experimental design, design of medical\ntherapies, and industrial process optimization. One popular approach to\nhandling these complex scenarios is Bayesian Optimization (BO). In terms of\ntheoretical behavior, BO is relatively well understood in the unconstrained\nsetting, where its principles have been well explored and validated. However,\nwhen it comes to constrained Bayesian optimization (CBO), the existing\nframework often relies on heuristics or approximations without the same level\nof theoretical guarantees.\n  In this paper, we delve into the theoretical and practical aspects of\nconstrained Bayesian optimization, where the objective and constraints can be\nindependently evaluated and are subject to noise. By recognizing that both the\nobjective and constraints can help identify high-confidence regions of interest\n(ROI), we propose an efficient CBO framework that intersects the ROIs\nidentified from each aspect to determine the general ROI. The ROI, coupled with\na novel acquisition function that adaptively balances the optimization of the\nobjective and the identification of feasible regions, enables us to derive\nrigorous theoretical justifications for its performance. We showcase the\nefficiency and robustness of our proposed CBO framework through empirical\nevidence and discuss the fundamental challenge of deriving practical regret\nbounds for CBO algorithms.\n", "date": "2023-10-12", "categories": []}
{"id": "2310.05456", "title": "Ensemble-based Hybrid Optimization of Bayesian Neural Networks and\n  Traditional Machine Learning Algorithms", "abstract": "  This research introduces a novel methodology for optimizing Bayesian Neural\nNetworks (BNNs) by synergistically integrating them with traditional machine\nlearning algorithms such as Random Forests (RF), Gradient Boosting (GB), and\nSupport Vector Machines (SVM). Feature integration solidifies these results by\nemphasizing the second-order conditions for optimality, including stationarity\nand positive definiteness of the Hessian matrix. Conversely, hyperparameter\ntuning indicates a subdued impact in improving Expected Improvement (EI),\nrepresented by EI(x). Overall, the ensemble method stands out as a robust,\nalgorithmically optimized approach.\n", "date": "2023-10-09", "categories": []}
{"id": "2304.14420", "title": "Network Cascade Vulnerability using Constrained Bayesian Optimization", "abstract": "  Measures of power grid vulnerability are often assessed by the amount of\ndamage an adversary can exact on the network. However, the cascading impact of\nsuch attacks is often overlooked, even though cascades are one of the primary\ncauses of large-scale blackouts. This paper explores modifications of\ntransmission line protection settings as candidates for adversarial attacks,\nwhich can remain undetectable as long as the network equilibrium state remains\nunaltered. This forms the basis of a black-box function in a Bayesian\noptimization procedure, where the objective is to find protection settings that\nmaximize network degradation due to cascading. Notably, our proposed method is\nagnostic to the choice of the cascade simulator and its underlying assumptions.\nNumerical experiments reveal that, against conventional wisdom, maximally\nmisconfiguring the protection settings of all network lines does not cause the\nmost cascading. More surprisingly, even when the degree of misconfiguration is\nlimited due to resource constraints, it is still possible to find settings that\nproduce cascades comparable in severity to instances where there are no\nresource constraints.\n", "date": "2023-04-27", "categories": []}
{"id": "2310.03515", "title": "High-dimensional Bayesian Optimization with Group Testing", "abstract": "  Bayesian optimization is an effective method for optimizing\nexpensive-to-evaluate black-box functions. High-dimensional problems are\nparticularly challenging as the surrogate model of the objective suffers from\nthe curse of dimensionality, which makes accurate modeling difficult. We\npropose a group testing approach to identify active variables to facilitate\nefficient optimization in these domains. The proposed algorithm, Group Testing\nBayesian Optimization (GTBO), first runs a testing phase where groups of\nvariables are systematically selected and tested on whether they influence the\nobjective. To that end, we extend the well-established theory of group testing\nto functions of continuous ranges. In the second phase, GTBO guides\noptimization by placing more importance on the active dimensions. By exploiting\nthe axis-aligned subspace assumption, GTBO is competitive against\nstate-of-the-art methods on several synthetic and real-world high-dimensional\noptimization tasks. Furthermore, GTBO aids in the discovery of active\nparameters in applications, thereby enhancing practitioners' understanding of\nthe problem at hand.\n", "date": "2023-10-05", "categories": []}
{"id": "2310.01455", "title": "Shaping of Magnetic Field Coils in Fusion Reactors using Bayesian\n  Optimisation", "abstract": "  Nuclear fusion using magnetic confinement holds promise as a viable method\nfor sustainable energy. However, most fusion devices have been experimental and\nas we move towards energy reactors, we are entering into a new paradigm of\nengineering. Curating a design for a fusion reactor is a high-dimensional\nmulti-output optimisation process. Through this work we demonstrate a\nproof-of-concept of an AI-driven strategy to help explore the design search\nspace and identify optimum parameters. By utilising a Multi-Output Bayesian\nOptimisation scheme, our strategy is capable of identifying the Pareto front\nassociated with the optimisation of the toroidal field coil shape of a tokamak.\nThe optimisation helps to identify design parameters that would minimise the\ncosts incurred while maximising the plasma stability by way of minimising\nmagnetic ripples.\n", "date": "2023-10-02", "categories": []}
{"id": "2310.00758", "title": "Data-driven adaptive building thermal controller tuning with\n  constraints: A primal-dual contextual Bayesian optimization approach", "abstract": "  We study the problem of tuning the parameters of a room temperature\ncontroller to minimize its energy consumption, subject to the constraint that\nthe daily cumulative thermal discomfort of the occupants is below a given\nthreshold. We formulate it as an online constrained black-box optimization\nproblem where, on each day, we observe some relevant environmental context and\nadaptively select the controller parameters. In this paper, we propose to use a\ndata-driven Primal-Dual Contextual Bayesian Optimization (PDCBO) approach to\nsolve this problem. In a simulation case study on a single room, we apply our\nalgorithm to tune the parameters of a Proportional Integral (PI) heating\ncontroller and the pre-heating time. Our results show that PDCBO can save up to\n4.7% energy consumption compared to other state-of-the-art Bayesian\noptimization-based methods while keeping the daily thermal discomfort below the\ngiven tolerable threshold on average. Additionally, PDCBO can automatically\ntrack time-varying tolerable thresholds while existing methods fail to do so.\nWe then study an alternative constrained tuning problem where we aim to\nminimize the thermal discomfort with a given energy budget. With this\nformulation, PDCBO reduces the average discomfort by up to 63% compared to\nstate-of-the-art safe optimization methods while keeping the average daily\nenergy consumption below the required threshold.\n", "date": "2023-10-01", "categories": []}
{"id": "2212.10538", "title": "HyperBO+: Pre-training a universal prior for Bayesian optimization with\n  hierarchical Gaussian processes", "abstract": "  Bayesian optimization (BO), while proved highly effective for many black-box\nfunction optimization tasks, requires practitioners to carefully select priors\nthat well model their functions of interest. Rather than specifying by hand,\nresearchers have investigated transfer learning based methods to automatically\nlearn the priors, e.g. multi-task BO (Swersky et al., 2013), few-shot BO\n(Wistuba and Grabocka, 2021) and HyperBO (Wang et al., 2022). However, those\nprior learning methods typically assume that the input domains are the same for\nall tasks, weakening their ability to use observations on functions with\ndifferent domains or generalize the learned priors to BO on different search\nspaces. In this work, we present HyperBO+: a pre-training approach for\nhierarchical Gaussian processes that enables the same prior to work universally\nfor Bayesian optimization on functions with different domains. We propose a\ntwo-step pre-training method and analyze its appealing asymptotic properties\nand benefits to BO both theoretically and empirically. On real-world\nhyperparameter tuning tasks that involve multiple search spaces, we demonstrate\nthat HyperBO+ is able to generalize to unseen search spaces and achieves lower\nregrets than competitive baselines.\n", "date": "2022-12-20", "categories": []}
{"id": "2207.00479", "title": "Asynchronous Decentralized Bayesian Optimization for Large Scale\n  Hyperparameter Optimization", "abstract": "  Bayesian optimization (BO) is a promising approach for hyperparameter\noptimization of deep neural networks (DNNs), where each model training can take\nminutes to hours. In BO, a computationally cheap surrogate model is employed to\nlearn the relationship between parameter configurations and their performance\nsuch as accuracy. Parallel BO methods often adopt single manager/multiple\nworkers strategies to evaluate multiple hyperparameter configurations\nsimultaneously. Despite significant hyperparameter evaluation time, the\noverhead in such centralized schemes prevents these methods to scale on a large\nnumber of workers. We present an asynchronous-decentralized BO, wherein each\nworker runs a sequential BO and asynchronously communicates its results through\nshared storage. We scale our method without loss of computational efficiency\nwith above 95% of worker's utilization to 1,920 parallel workers (full\nproduction queue of the Polaris supercomputer) and demonstrate improvement in\nmodel accuracy as well as faster convergence on the CANDLE benchmark from the\nExascale computing project.\n", "date": "2022-07-01", "categories": []}
{"id": "2309.14936", "title": "Parallel Multi-Objective Hyperparameter Optimization with Uniform\n  Normalization and Bounded Objectives", "abstract": "  Machine learning (ML) methods offer a wide range of configurable\nhyperparameters that have a significant influence on their performance. While\naccuracy is a commonly used performance objective, in many settings, it is not\nsufficient. Optimizing the ML models with respect to multiple objectives such\nas accuracy, confidence, fairness, calibration, privacy, latency, and memory\nconsumption is becoming crucial. To that end, hyperparameter optimization, the\napproach to systematically optimize the hyperparameters, which is already\nchallenging for a single objective, is even more challenging for multiple\nobjectives. In addition, the differences in objective scales, the failures, and\nthe presence of outlier values in objectives make the problem even harder. We\npropose a multi-objective Bayesian optimization (MoBO) algorithm that addresses\nthese problems through uniform objective normalization and randomized weights\nin scalarization. We increase the efficiency of our approach by imposing\nconstraints on the objective to avoid exploring unnecessary configurations\n(e.g., insufficient accuracy). Finally, we leverage an approach to parallelize\nthe MoBO which results in a 5x speed-up when using 16x more workers.\n", "date": "2023-09-26", "categories": []}
{"id": "2303.01682", "title": "Neural-BO: A Black-box Optimization Algorithm using Deep Neural Networks", "abstract": "  Bayesian Optimization (BO) is an effective approach for global optimization\nof black-box functions when function evaluations are expensive. Most prior\nworks use Gaussian processes to model the black-box function, however, the use\nof kernels in Gaussian processes leads to two problems: first, the kernel-based\nmethods scale poorly with the number of data points and second, kernel methods\nare usually not effective on complex structured high dimensional data due to\ncurse of dimensionality. Therefore, we propose a novel black-box optimization\nalgorithm where the black-box function is modeled using a neural network. Our\nalgorithm does not need a Bayesian neural network to estimate predictive\nuncertainty and is therefore computationally favorable. We analyze the\ntheoretical behavior of our algorithm in terms of regret bound using advances\nin NTK theory showing its efficient convergence. We perform experiments with\nboth synthetic and real-world optimization tasks and show that our algorithm is\nmore sample efficient compared to existing methods.\n", "date": "2023-03-03", "categories": []}
{"id": "2304.06104", "title": "Primal-Dual Contextual Bayesian Optimization for Control System Online\n  Optimization with Time-Average Constraints", "abstract": "  This paper studies the problem of online performance optimization of\nconstrained closed-loop control systems, where both the objective and the\nconstraints are unknown black-box functions affected by exogenous time-varying\ncontextual disturbances. A primal-dual contextual Bayesian optimization\nalgorithm is proposed that achieves sublinear cumulative regret with respect to\nthe dynamic optimal solution under certain regularity conditions. Furthermore,\nthe algorithm achieves zero time-average constraint violation, ensuring that\nthe average value of the constraint function satisfies the desired constraint.\nThe method is applied to both sampled instances from Gaussian processes and a\ncontinuous stirred tank reactor parameter tuning problem; simulation results\nshow that the method simultaneously provides close-to-optimal performance and\nmaintains constraint feasibility on average. This contrasts current\nstate-of-the-art methods, which either suffer from large cumulative regret or\nsevere constraint violations for the case studies presented.\n", "date": "2023-04-12", "categories": []}
{"id": "2302.07260", "title": "Scalable Bayesian optimization with high-dimensional outputs using\n  randomized prior networks", "abstract": "  Several fundamental problems in science and engineering consist of global\noptimization tasks involving unknown high-dimensional (black-box) functions\nthat map a set of controllable variables to the outcomes of an expensive\nexperiment. Bayesian Optimization (BO) techniques are known to be effective in\ntackling global optimization problems using a relatively small number objective\nfunction evaluations, but their performance suffers when dealing with\nhigh-dimensional outputs. To overcome the major challenge of dimensionality,\nhere we propose a deep learning framework for BO and sequential decision making\nbased on bootstrapped ensembles of neural architectures with randomized priors.\nUsing appropriate architecture choices, we show that the proposed framework can\napproximate functional relationships between design variables and quantities of\ninterest, even in cases where the latter take values in high-dimensional vector\nspaces or even infinite-dimensional function spaces. In the context of BO, we\naugmented the proposed probabilistic surrogates with re-parameterized Monte\nCarlo approximations of multiple-point (parallel) acquisition functions, as\nwell as methodological extensions for accommodating black-box constraints and\nmulti-fidelity information sources. We test the proposed framework against\nstate-of-the-art methods for BO and demonstrate superior performance across\nseveral challenging tasks with high-dimensional outputs, including a\nconstrained multi-fidelity optimization task involving shape optimization of\nrotor blades in turbo-machinery.\n", "date": "2023-02-14", "categories": []}
{"id": "2309.05784", "title": "Grey-box Bayesian Optimization for Sensor Placement in Assisted Living\n  Environments", "abstract": "  Optimizing the configuration and placement of sensors is crucial for reliable\nfall detection, indoor localization, and activity recognition in assisted\nliving spaces. We propose a novel, sample-efficient approach to find a\nhigh-quality sensor placement in an arbitrary indoor space based on grey-box\nBayesian optimization and simulation-based evaluation. Our key technical\ncontribution lies in capturing domain-specific knowledge about the spatial\ndistribution of activities and incorporating it into the iterative selection of\nquery points in Bayesian optimization. Considering two simulated indoor\nenvironments and a real-world dataset containing human activities and sensor\ntriggers, we show that our proposed method performs better compared to\nstate-of-the-art black-box optimization techniques in identifying high-quality\nsensor placements, leading to accurate activity recognition in terms of\nF1-score, while also requiring a significantly lower (51.3% on average) number\nof expensive function queries.\n", "date": "2023-09-11", "categories": []}
{"id": "2309.04510", "title": "Decreasing the Computing Time of Bayesian Optimization using\n  Generalizable Memory Pruning", "abstract": "  Bayesian optimization (BO) suffers from long computing times when processing\nhighly-dimensional or large data sets. These long computing times are a result\nof the Gaussian process surrogate model having a polynomial time complexity\nwith the number of experiments. Running BO on high-dimensional or massive data\nsets becomes intractable due to this time complexity scaling, in turn,\nhindering experimentation. Alternative surrogate models have been developed to\nreduce the computing utilization of the BO procedure, however, these methods\nrequire mathematical alteration of the inherit surrogate function, pigeonholing\nuse into only that function. In this paper, we demonstrate a generalizable BO\nwrapper of memory pruning and bounded optimization, capable of being used with\nany surrogate model and acquisition function. Using this memory pruning\napproach, we show a decrease in wall-clock computing times per experiment of BO\nfrom a polynomially increasing pattern to a sawtooth pattern that has a\nnon-increasing trend without sacrificing convergence performance. Furthermore,\nwe illustrate the generalizability of the approach across two unique data sets,\ntwo unique surrogate models, and four unique acquisition functions. All model\nimplementations are run on the MIT Supercloud state-of-the-art computing\nhardware.\n", "date": "2023-09-08", "categories": []}
{"id": "2208.13771", "title": "Fast Bayesian Optimization of Needle-in-a-Haystack Problems using\n  Zooming Memory-Based Initialization (ZoMBI)", "abstract": "  Needle-in-a-Haystack problems exist across a wide range of applications\nincluding rare disease prediction, ecological resource management, fraud\ndetection, and material property optimization. A Needle-in-a-Haystack problem\narises when there is an extreme imbalance of optimum conditions relative to the\nsize of the dataset. For example, only $0.82\\%$ out of $146$k total materials\nin the open-access Materials Project database have a negative Poisson's ratio.\nHowever, current state-of-the-art optimization algorithms are not designed with\nthe capabilities to find solutions to these challenging multidimensional\nNeedle-in-a-Haystack problems, resulting in slow convergence to a global\noptimum or pigeonholing into a local minimum. In this paper, we present a\nZooming Memory-Based Initialization algorithm, entitled ZoMBI. ZoMBI actively\nextracts knowledge from the previously best-performing evaluated experiments to\niteratively zoom in the sampling search bounds towards the global optimum\n\"needle\" and then prunes the memory of low-performing historical experiments to\naccelerate compute times by reducing the algorithm time complexity from\n$O(n^3)$ to $O(\\phi^3)$ for $\\phi$ forward experiments per activation, which\ntrends to a constant $O(1)$ over several activations. Additionally, ZoMBI\nimplements two custom adaptive acquisition functions to further guide the\nsampling of new experiments toward the global optimum. We validate the\nalgorithm's optimization performance on three real-world datasets exhibiting\nNeedle-in-a-Haystack and further stress-test the algorithm's performance on an\nadditional 174 analytical datasets. The ZoMBI algorithm demonstrates compute\ntime speed-ups of 400x compared to traditional Bayesian optimization as well as\nefficiently discovering optima in under 100 experiments that are up to 3x more\nhighly optimized than those discovered by similar methods MiP-EGO, TuRBO, and\nHEBO.\n", "date": "2022-08-26", "categories": []}
{"id": "2309.02771", "title": "On the Effects of Heterogeneous Errors on Multi-fidelity Bayesian\n  Optimization", "abstract": "  Bayesian optimization (BO) is a sequential optimization strategy that is\nincreasingly employed in a wide range of areas including materials design. In\nreal world applications, acquiring high-fidelity (HF) data through physical\nexperiments or HF simulations is the major cost component of BO. To alleviate\nthis bottleneck, multi-fidelity (MF) methods are used to forgo the sole\nreliance on the expensive HF data and reduce the sampling costs by querying\ninexpensive low-fidelity (LF) sources whose data are correlated with HF\nsamples. However, existing multi-fidelity BO (MFBO) methods operate under the\nfollowing two assumptions that rarely hold in practical applications: (1) LF\nsources provide data that are well correlated with the HF data on a global\nscale, and (2) a single random process can model the noise in the fused data.\nThese assumptions dramatically reduce the performance of MFBO when LF sources\nare only locally correlated with the HF source or when the noise variance\nvaries across the data sources. In this paper, we dispense with these incorrect\nassumptions by proposing an MF emulation method that (1) learns a noise model\nfor each data source, and (2) enables MFBO to leverage highly biased LF sources\nwhich are only locally correlated with the HF source. We illustrate the\nperformance of our method through analytical examples and engineering problems\non materials design.\n", "date": "2023-09-06", "categories": []}
{"id": "2309.00663", "title": "Polynomial-Model-Based Optimization for Blackbox Objectives", "abstract": "  For a wide range of applications the structure of systems like Neural\nNetworks or complex simulations, is unknown and approximation is costly or even\nimpossible. Black-box optimization seeks to find optimal (hyper-) parameters\nfor these systems such that a pre-defined objective function is minimized.\nPolynomial-Model-Based Optimization (PMBO) is a novel blackbox optimizer that\nfinds the minimum by fitting a polynomial surrogate to the objective function.\n  Motivated by Bayesian optimization the model is iteratively updated according\nto the acquisition function Expected Improvement, thus balancing the\nexploitation and exploration rate and providing an uncertainty estimate of the\nmodel. PMBO is benchmarked against other state-of-the-art algorithms for a\ngiven set of artificial, analytical functions. PMBO competes successfully with\nthose algorithms and even outperforms all of them in some cases. As the results\nsuggest, we believe PMBO is the pivotal choice for solving blackbox\noptimization tasks occurring in a wide range of disciplines.\n", "date": "2023-09-01", "categories": []}
{"id": "2309.02287", "title": "Optimal Observation-Intervention Trade-Off in Optimisation Problems with\n  Causal Structure", "abstract": "  We consider the problem of optimising an expensive-to-evaluate grey-box\nobjective function, within a finite budget, where known side-information exists\nin the form of the causal structure between the design variables. Standard\nblack-box optimisation ignores the causal structure, often making it\ninefficient and expensive. The few existing methods that consider the causal\nstructure are myopic and do not fully accommodate the observation-intervention\ntrade-off that emerges when estimating causal effects. In this paper, we show\nthat the observation-intervention trade-off can be formulated as a non-myopic\noptimal stopping problem which permits an efficient solution. We give\ntheoretical results detailing the structure of the optimal stopping times and\ndemonstrate the generality of our approach by showing that it can be integrated\nwith existing causal Bayesian optimisation algorithms. Experimental results\nshow that our formulation can enhance existing algorithms on real and synthetic\nbenchmarks.\n", "date": "2023-09-05", "categories": []}
{"id": "2304.12666", "title": "Bayesian Optimization Meets Self-Distillation", "abstract": "  Bayesian optimization (BO) has contributed greatly to improving model\nperformance by suggesting promising hyperparameter configurations iteratively\nbased on observations from multiple training trials. However, only partial\nknowledge (i.e., the measured performances of trained models and their\nhyperparameter configurations) from previous trials is transferred. On the\nother hand, Self-Distillation (SD) only transfers partial knowledge learned by\nthe task model itself. To fully leverage the various knowledge gained from all\ntraining trials, we propose the BOSS framework, which combines BO and SD. BOSS\nsuggests promising hyperparameter configurations through BO and carefully\nselects pre-trained models from previous trials for SD, which are otherwise\nabandoned in the conventional BO process. BOSS achieves significantly better\nperformance than both BO and SD in a wide range of tasks including general\nimage classification, learning with noisy labels, semi-supervised learning, and\nmedical image analysis tasks.\n", "date": "2023-04-25", "categories": []}
{"id": "2308.08666", "title": "BREATHE: Second-Order Gradients and Heteroscedastic Emulation based\n  Design Space Exploration", "abstract": "  Researchers constantly strive to explore larger and more complex search\nspaces in various scientific studies and physical experiments. However, such\ninvestigations often involve sophisticated simulators or time-consuming\nexperiments that make exploring and observing new design samples challenging.\nPrevious works that target such applications are typically sample-inefficient\nand restricted to vector search spaces. To address these limitations, this work\nproposes a constrained multi-objective optimization (MOO) framework, called\nBREATHE, that searches not only traditional vector-based design spaces but also\ngraph-based design spaces to obtain best-performing graphs. It leverages\nsecond-order gradients and actively trains a heteroscedastic surrogate model\nfor sample-efficient optimization. In a single-objective vector optimization\napplication, it leads to 64.1% higher performance than the next-best baseline,\nrandom forest regression. In graph-based search, BREATHE outperforms the\nnext-best baseline, i.e., a graphical version of Gaussian-process-based\nBayesian optimization, with up to 64.9% higher performance. In a MOO task, it\nachieves up to 21.9$\\times$ higher hypervolume than the state-of-the-art\nmethod, multi-objective Bayesian optimization (MOBOpt). BREATHE also\noutperforms the baseline methods on most standard MOO benchmark applications.\n", "date": "2023-08-16", "categories": []}
{"id": "2308.09612", "title": "Constrained Bayesian Optimization Using a Lagrange Multiplier Applied to\n  Power Transistor Design", "abstract": "  We propose a novel constrained Bayesian Optimization (BO) algorithm\noptimizing the design process of Laterally-Diffused Metal-Oxide-Semiconductor\n(LDMOS) transistors while realizing a target Breakdown Voltage (BV). We convert\nthe constrained BO problem into a conventional BO problem using a Lagrange\nmultiplier. Instead of directly optimizing the traditional Figure-of-Merit\n(FOM), we set the Lagrangian as the objective function of BO. This adaptive\nobjective function with a changeable Lagrange multiplier can address\nconstrained BO problems which have constraints that require costly evaluations,\nwithout the need for additional surrogate models to approximate constraints.\nOur algorithm enables a device designer to set the target BV in the design\nspace, and obtain a device that satisfies the optimized FOM and the target BV\nconstraint automatically. Utilizing this algorithm, we have also explored the\nphysical limits of the FOM for our devices in 30 - 50 V range within the\ndefined design space.\n", "date": "2023-08-18", "categories": []}
{"id": "2308.08291", "title": "Robust Bayesian Satisficing", "abstract": "  Distributional shifts pose a significant challenge to achieving robustness in\ncontemporary machine learning. To overcome this challenge, robust satisficing\n(RS) seeks a robust solution to an unspecified distributional shift while\nachieving a utility above a desired threshold. This paper focuses on the\nproblem of RS in contextual Bayesian optimization when there is a discrepancy\nbetween the true and reference distributions of the context. We propose a novel\nrobust Bayesian satisficing algorithm called RoBOS for noisy black-box\noptimization. Our algorithm guarantees sublinear lenient regret under certain\nassumptions on the amount of distribution shift. In addition, we define a\nweaker notion of regret called robust satisficing regret, in which our\nalgorithm achieves a sublinear upper bound independent of the amount of\ndistribution shift. To demonstrate the effectiveness of our method, we apply it\nto various learning problems and compare it to other approaches, such as\ndistributionally robust optimization.\n", "date": "2023-08-16", "categories": []}
{"id": "2302.08612", "title": "Robust expected improvement for Bayesian optimization", "abstract": "  Bayesian Optimization (BO) links Gaussian Process (GP) surrogates with\nsequential design toward optimizing expensive-to-evaluate black-box functions.\nExample design heuristics, or so-called acquisition functions, like expected\nimprovement (EI), balance exploration and exploitation to furnish global\nsolutions under stringent evaluation budgets. However, they fall short when\nsolving for robust optima, meaning a preference for solutions in a wider domain\nof attraction. Robust solutions are useful when inputs are imprecisely\nspecified, or where a series of solutions is desired. A common mathematical\nprogramming technique in such settings involves an adversarial objective,\nbiasing a local solver away from ``sharp'' troughs. Here we propose a surrogate\nmodeling and active learning technique called robust expected improvement (REI)\nthat ports adversarial methodology into the BO/GP framework. After describing\nthe methods, we illustrate and draw comparisons to several competitors on\nbenchmark synthetic exercises and real problems of varying complexity.\n", "date": "2023-02-16", "categories": []}
{"id": "2308.04660", "title": "Efficient Bayesian Optimization with Deep Kernel Learning and\n  Transformer Pre-trained on Multiple Heterogeneous Datasets", "abstract": "  Bayesian optimization (BO) is widely adopted in black-box optimization\nproblems and it relies on a surrogate model to approximate the black-box\nresponse function. With the increasing number of black-box optimization tasks\nsolved and even more to solve, the ability to learn from multiple prior tasks\nto jointly pre-train a surrogate model is long-awaited to further boost\noptimization efficiency. In this paper, we propose a simple approach to\npre-train a surrogate, which is a Gaussian process (GP) with a kernel defined\non deep features learned from a Transformer-based encoder, using datasets from\nprior tasks with possibly heterogeneous input spaces. In addition, we provide a\nsimple yet effective mix-up initialization strategy for input tokens\ncorresponding to unseen input variables and therefore accelerate new tasks'\nconvergence. Experiments on both synthetic and real benchmark problems\ndemonstrate the effectiveness of our proposed pre-training and transfer BO\nstrategy over existing methods.\n", "date": "2023-08-09", "categories": []}
{"id": "2210.06635", "title": "A Bayesian Optimization Framework for Finding Local Optima in Expensive\n  Multi-Modal Functions", "abstract": "  Bayesian optimization (BO) is a popular global optimization scheme for\nsample-efficient optimization in domains with expensive function evaluations.\nThe existing BO techniques are capable of finding a single global optimum\nsolution. However, finding a set of global and local optimum solutions is\ncrucial in a wide range of real-world problems, as implementing some of the\noptimal solutions might not be feasible due to various practical restrictions\n(e.g., resource limitation, physical constraints, etc.). In such domains, if\nmultiple solutions are known, the implementation can be quickly switched to\nanother solution, and the best possible system performance can still be\nobtained. This paper develops a multimodal BO framework to effectively find a\nset of local/global solutions for expensive-to-evaluate multimodal objective\nfunctions. We consider the standard BO setting with Gaussian process regression\nrepresenting the objective function. We analytically derive the joint\ndistribution of the objective function and its first-order derivatives. This\njoint distribution is used in the body of the BO acquisition functions to\nsearch for local optima during the optimization process. We introduce variants\nof the well-known BO acquisition functions to the multimodal setting and\ndemonstrate the performance of the proposed framework in locating a set of\nlocal optimum solutions using multiple optimization problems.\n", "date": "2022-10-13", "categories": []}
{"id": "2308.01743", "title": "Finding the Optimum Design of Large Gas Engines Prechambers Using CFD\n  and Bayesian Optimization", "abstract": "  The turbulent jet ignition concept using prechambers is a promising solution\nto achieve stable combustion at lean conditions in large gas engines, leading\nto high efficiency at low emission levels. Due to the wide range of design and\noperating parameters for large gas engine prechambers, the preferred method for\nevaluating different designs is computational fluid dynamics (CFD), as testing\nin test bed measurement campaigns is time-consuming and expensive. However, the\nsignificant computational time required for detailed CFD simulations due to the\ncomplexity of solving the underlying physics also limits its applicability. In\noptimization settings similar to the present case, i.e., where the evaluation\nof the objective function(s) is computationally costly, Bayesian optimization\nhas largely replaced classical design-of-experiment. Thus, the present study\ndeals with the computationally efficient Bayesian optimization of large gas\nengine prechambers design using CFD simulation. Reynolds-averaged-Navier-Stokes\nsimulations are used to determine the target values as a function of the\nselected prechamber design parameters. The results indicate that the chosen\nstrategy is effective to find a prechamber design that achieves the desired\ntarget values.\n", "date": "2023-08-03", "categories": []}
{"id": "2306.05150", "title": "Bayesian Optimization of Expensive Nested Grey-Box Functions", "abstract": "  We consider the problem of optimizing a grey-box objective function, i.e.,\nnested function composed of both black-box and white-box functions. A general\nformulation for such grey-box problems is given, which covers the existing\ngrey-box optimization formulations as special cases. We then design an\noptimism-driven algorithm to solve it. Under certain regularity assumptions,\nour algorithm achieves similar regret bound as that for the standard black-box\nBayesian optimization algorithm, up to a constant multiplicative term depending\non the Lipschitz constants of the functions considered. We further extend our\nmethod to the constrained case and discuss special cases. For the commonly used\nkernel functions, the regret bounds allow us to derive a convergence rate to\nthe optimal solution. Experimental results show that our grey-box optimization\nmethod empirically improves the speed of finding the global optimal solution\nsignificantly, as compared to the standard black-box optimization algorithm.\n", "date": "2023-06-08", "categories": []}
{"id": "2307.16625", "title": "Adversarial Causal Bayesian Optimization", "abstract": "  In Causal Bayesian Optimization (CBO), an agent intervenes on an unknown\nstructural causal model to maximize a downstream reward variable. In this\npaper, we consider the generalization where other agents or external events\nalso intervene on the system, which is key for enabling adaptiveness to\nnon-stationarities such as weather changes, market forces, or adversaries. We\nformalize this generalization of CBO as Adversarial Causal Bayesian\nOptimization (ACBO) and introduce the first algorithm for ACBO with bounded\nregret: Causal Bayesian Optimization with Multiplicative Weights (CBO-MW). Our\napproach combines a classical online learning strategy with causal modeling of\nthe rewards. To achieve this, it computes optimistic counterfactual reward\nestimates by propagating uncertainty through the causal graph. We derive regret\nbounds for CBO-MW that naturally depend on graph-related quantities. We further\npropose a scalable implementation for the case of combinatorial interventions\nand submodular rewards. Empirically, CBO-MW outperforms non-causal and\nnon-adversarial Bayesian optimization methods on synthetic environments and\nenvironments based on real-word data. Our experiments include a realistic\ndemonstration of how CBO-MW can be used to learn users' demand patterns in a\nshared mobility system and reposition vehicles in strategic areas.\n", "date": "2023-07-31", "categories": []}
{"id": "2308.00285", "title": "Predictive Modeling through Hyper-Bayesian Optimization", "abstract": "  Model selection is an integral problem of model based optimization techniques\nsuch as Bayesian optimization (BO). Current approaches often treat model\nselection as an estimation problem, to be periodically updated with\nobservations coming from the optimization iterations. In this paper, we propose\nan alternative way to achieve both efficiently. Specifically, we propose a\nnovel way of integrating model selection and BO for the single goal of reaching\nthe function optima faster. The algorithm moves back and forth between BO in\nthe model space and BO in the function space, where the goodness of the\nrecommended model is captured by a score function and fed back, capturing how\nwell the model helped convergence in the function space. The score function is\nderived in such a way that it neutralizes the effect of the moving nature of\nthe BO in the function space, thus keeping the model selection problem\nstationary. This back and forth leads to quick convergence for both model\nselection and BO in the function space. In addition to improved sample\nefficiency, the framework outputs information about the black-box function.\nConvergence is proved, and experimental results show significant improvement\ncompared to standard BO.\n", "date": "2023-08-01", "categories": []}
{"id": "2305.03824", "title": "No-Regret Constrained Bayesian Optimization of Noisy and Expensive\n  Hybrid Models using Differentiable Quantile Function Approximations", "abstract": "  This paper investigates the problem of efficient constrained global\noptimization of hybrid models that are a composition of a known white-box\nfunction and an expensive multi-output black-box function subject to noisy\nobservations, which often arises in real-world science and engineering\napplications. We propose a novel method, Constrained Upper Quantile Bound\n(CUQB), to solve such problems that directly exploits the composite structure\nof the objective and constraint functions that we show leads substantially\nimproved sampling efficiency. CUQB is a conceptually simple, deterministic\napproach that avoid constraint approximations used by previous methods.\nAlthough the CUQB acquisition function is not available in closed form, we\npropose a novel differentiable sample average approximation that enables it to\nbe efficiently maximized. We further derive bounds on the cumulative regret and\nconstraint violation under a non-parametric Bayesian representation of the\nblack-box function. Since these bounds depend sublinearly on the number of\niterations under some regularity assumptions, we establis bounds on the\nconvergence rate to the optimal solution of the original constrained problem.\nIn contrast to most existing methods, CUQB further incorporates a simple\ninfeasibility detection scheme, which we prove triggers in a finite number of\niterations when the original problem is infeasible (with high probability given\nthe Bayesian model). Numerical experiments on several test problems, including\nenvironmental model calibration and real-time optimization of a reactor system,\nshow that CUQB significantly outperforms traditional Bayesian optimization in\nboth constrained and unconstrained cases. Furthermore, compared to other\nstate-of-the-art methods that exploit composite structure, CUQB achieves\ncompetitive empirical performance while also providing substantially improved\ntheoretical guarantees.\n", "date": "2023-05-05", "categories": []}
{"id": "2307.13371", "title": "Learning Regions of Interest for Bayesian Optimization with Adaptive\n  Level-Set Estimation", "abstract": "  We study Bayesian optimization (BO) in high-dimensional and non-stationary\nscenarios. Existing algorithms for such scenarios typically require extensive\nhyperparameter tuning, which limits their practical effectiveness. We propose a\nframework, called BALLET, which adaptively filters for a high-confidence region\nof interest (ROI) as a superlevel-set of a nonparametric probabilistic model\nsuch as a Gaussian process (GP). Our approach is easy to tune, and is able to\nfocus on local region of the optimization space that can be tackled by existing\nBO methods. The key idea is to use two probabilistic models: a coarse GP to\nidentify the ROI, and a localized GP for optimization within the ROI. We show\ntheoretically that BALLET can efficiently shrink the search space, and can\nexhibit a tighter regret bound than standard BO without ROI filtering. We\ndemonstrate empirically the effectiveness of BALLET on both synthetic and\nreal-world optimization tasks.\n", "date": "2023-07-25", "categories": []}
{"id": "2305.17535", "title": "PFNs4BO: In-Context Learning for Bayesian Optimization", "abstract": "  In this paper, we use Prior-data Fitted Networks (PFNs) as a flexible\nsurrogate for Bayesian Optimization (BO). PFNs are neural processes that are\ntrained to approximate the posterior predictive distribution (PPD) through\nin-context learning on any prior distribution that can be efficiently sampled\nfrom. We describe how this flexibility can be exploited for surrogate modeling\nin BO. We use PFNs to mimic a naive Gaussian process (GP), an advanced GP, and\na Bayesian Neural Network (BNN). In addition, we show how to incorporate\nfurther information into the prior, such as allowing hints about the position\nof optima (user priors), ignoring irrelevant dimensions, and performing\nnon-myopic BO by learning the acquisition function. The flexibility underlying\nthese extensions opens up vast possibilities for using PFNs for BO. We\ndemonstrate the usefulness of PFNs for BO in a large-scale evaluation on\nartificial GP samples and three different hyperparameter optimization testbeds:\nHPO-B, Bayesmark, and PD1. We publish code alongside trained models at\ngithub.com/automl/PFNs4BO.\n", "date": "2023-05-27", "categories": []}
{"id": "2302.14015", "title": "CO-BED: Information-Theoretic Contextual Optimization via Bayesian\n  Experimental Design", "abstract": "  We formalize the problem of contextual optimization through the lens of\nBayesian experimental design and propose CO-BED -- a general, model-agnostic\nframework for designing contextual experiments using information-theoretic\nprinciples. After formulating a suitable information-based objective, we employ\nblack-box variational methods to simultaneously estimate it and optimize the\ndesigns in a single stochastic gradient scheme. In addition, to accommodate\ndiscrete actions within our framework, we propose leveraging continuous\nrelaxation schemes, which can naturally be integrated into our variational\nobjective. As a result, CO-BED provides a general and automated solution to a\nwide range of contextual optimization problems. We illustrate its effectiveness\nin a number of experiments, where CO-BED demonstrates competitive performance\neven when compared to bespoke, model-specific alternatives.\n", "date": "2023-02-27", "categories": []}
{"id": "2304.08309", "title": "Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization", "abstract": "  The linearized-Laplace approximation (LLA) has been shown to be effective and\nefficient in constructing Bayesian neural networks. It is theoretically\ncompelling since it can be seen as a Gaussian process posterior with the mean\nfunction given by the neural network's maximum-a-posteriori predictive function\nand the covariance function induced by the empirical neural tangent kernel.\nHowever, while its efficacy has been studied in large-scale tasks like image\nclassification, it has not been studied in sequential decision-making problems\nlike Bayesian optimization where Gaussian processes -- with simple mean\nfunctions and kernels such as the radial basis function -- are the de-facto\nsurrogate models. In this work, we study the usefulness of the LLA in Bayesian\noptimization and highlight its strong performance and flexibility. However, we\nalso present some pitfalls that might arise and a potential problem with the\nLLA when the search space is unbounded.\n", "date": "2023-04-17", "categories": []}
{"id": "2301.11832", "title": "SOBER: Highly Parallel Bayesian Optimization and Bayesian Quadrature\n  over Discrete and Mixed Spaces", "abstract": "  Batch Bayesian optimisation and Bayesian quadrature have been shown to be\nsample-efficient methods of performing optimisation and quadrature where\nexpensive-to-evaluate objective functions can be queried in parallel. However,\ncurrent methods do not scale to large batch sizes -- a frequent desideratum in\npractice (e.g. drug discovery or simulation-based inference). We present a\nnovel algorithm, SOBER, which permits scalable and diversified batch global\noptimisation and quadrature with arbitrary acquisition functions and kernels\nover discrete and mixed spaces. The key to our approach is to reformulate batch\nselection for global optimisation as a quadrature problem, which relaxes\nacquisition function maximisation (non-convex) to kernel recombination\n(convex). Bridging global optimisation and quadrature can efficiently solve\nboth tasks by balancing the merits of exploitative Bayesian optimisation and\nexplorative Bayesian quadrature. We show that SOBER outperforms 11 competitive\nbaselines on 12 synthetic and diverse real-world tasks.\n", "date": "2023-01-27", "categories": []}
{"id": "2306.04262", "title": "Self-Adjusting Weighted Expected Improvement for Bayesian Optimization", "abstract": "  Bayesian Optimization (BO) is a class of surrogate-based, sample-efficient\nalgorithms for optimizing black-box problems with small evaluation budgets. The\nBO pipeline itself is highly configurable with many different design choices\nregarding the initial design, surrogate model, and acquisition function (AF).\nUnfortunately, our understanding of how to select suitable components for a\nproblem at hand is very limited. In this work, we focus on the definition of\nthe AF, whose main purpose is to balance the trade-off between exploring\nregions with high uncertainty and those with high promise for good solutions.\nWe propose Self-Adjusting Weighted Expected Improvement (SAWEI), where we let\nthe exploration-exploitation trade-off self-adjust in a data-driven manner,\nbased on a convergence criterion for BO. On the noise-free black-box BBOB\nfunctions of the COCO benchmarking platform, our method exhibits a favorable\nany-time performance compared to handcrafted baselines and serves as a robust\ndefault choice for any problem structure. The suitability of our method also\ntransfers to HPOBench. With SAWEI, we are a step closer to on-the-fly,\ndata-driven, and robust BO designs that automatically adjust their sampling\nbehavior to the problem at hand.\n", "date": "2023-06-07", "categories": []}
{"id": "2211.01561", "title": "Benefits of Monotonicity in Safe Exploration with Gaussian Processes", "abstract": "  We consider the problem of sequentially maximising an unknown function over a\nset of actions while ensuring that every sampled point has a function value\nbelow a given safety threshold. We model the function using kernel-based and\nGaussian process methods, while differing from previous works in our assumption\nthat the function is monotonically increasing with respect to a \\emph{safety\nvariable}. This assumption is motivated by various practical applications such\nas adaptive clinical trial design and robotics. Taking inspiration from the\n\\textsc{\\sffamily GP-UCB} and \\textsc{\\sffamily SafeOpt} algorithms, we propose\nan algorithm, monotone safe {\\sffamily UCB} (\\textsc{\\sffamily M-SafeUCB}) for\nthis task. We show that \\textsc{\\sffamily M-SafeUCB} enjoys theoretical\nguarantees in terms of safety, a suitably-defined regret notion, and\napproximately finding the entire safe boundary. In addition, we illustrate that\nthe monotonicity assumption yields significant benefits in terms of the\nguarantees obtained, as well as algorithmic simplicity and efficiency. We\nsupport our theoretical findings by performing empirical evaluations on a\nvariety of functions, including a simulated clinical trial experiment.\n", "date": "2022-11-03", "categories": []}
{"id": "2306.10815", "title": "Practical First-Order Bayesian Optimization Algorithms", "abstract": "  First Order Bayesian Optimization (FOBO) is a sample efficient sequential\napproach to find the global maxima of an expensive-to-evaluate black-box\nobjective function by suitably querying for the function and its gradient\nevaluations. Such methods assume Gaussian process (GP) models for both, the\nfunction and its gradient, and use them to construct an acquisition function\nthat identifies the next query point. In this paper, we propose a class of\npractical FOBO algorithms that efficiently utilizes the information from the\ngradient GP to identify potential query points with zero gradients. We\nconstruct a multi-level acquisition function where in the first step, we\noptimize a lower level acquisition function with multiple restarts to identify\npotential query points with zero gradient value. We then use the upper level\nacquisition function to rank these query points based on their function values\nto potentially identify the global maxima. As a final step, the potential point\nof maxima is chosen as the actual query point. We validate the performance of\nour proposed algorithms on several test functions and show that our algorithms\noutperform state-of-the-art FOBO algorithms. We also illustrate the application\nof our algorithms in finding optimal set of hyper-parameters in machine\nlearning and in learning the optimal policy in reinforcement learning tasks.\n", "date": "2023-06-19", "categories": []}
{"id": "2306.08055", "title": "Tune As You Scale: Hyperparameter Optimization For Compute Efficient\n  Training", "abstract": "  Hyperparameter tuning of deep learning models can lead to order-of-magnitude\nperformance gains for the same amount of compute. Despite this, systematic\ntuning is uncommon, particularly for large models, which are expensive to\nevaluate and tend to have many hyperparameters, necessitating difficult\njudgment calls about tradeoffs, budgets, and search bounds. To address these\nissues and propose a practical method for robustly tuning large models, we\npresent Cost-Aware Pareto Region Bayesian Search (CARBS), a Bayesian\noptimization algorithm that performs local search around the performance-cost\nPareto frontier. CARBS does well even in unbounded search spaces with many\nhyperparameters, learns scaling relationships so that it can tune models even\nas they are scaled up, and automates much of the \"black magic\" of tuning. Among\nour results, we effectively solve the entire ProcGen benchmark just by tuning a\nsimple baseline (PPO, as provided in the original ProcGen paper). We also\nreproduce the model size vs. training tokens scaling result from the Chinchilla\nproject (Hoffmann et al. 2022), while simultaneously discovering scaling laws\nfor every other hyperparameter, via an easy automated process that uses\nsignificantly less compute and is applicable to any deep learning problem (not\njust language models).\n", "date": "2023-06-13", "categories": []}
{"id": "2305.20011", "title": "Constrained Causal Bayesian Optimization", "abstract": "  We propose constrained causal Bayesian optimization (cCBO), an approach for\nfinding interventions in a known causal graph that optimize a target variable\nunder some constraints. cCBO first reduces the search space by exploiting the\ngraph structure and, if available, an observational dataset; and then solves\nthe restricted optimization problem by modelling target and constraint\nquantities using Gaussian processes and by sequentially selecting interventions\nvia a constrained expected improvement acquisition function. We propose\ndifferent surrogate models that enable to integrate observational and\ninterventional data while capturing correlation among effects with increasing\nlevels of sophistication. We evaluate cCBO on artificial and real-world causal\ngraphs showing successful trade off between fast convergence and percentage of\nfeasible interventions.\n", "date": "2023-05-31", "categories": []}
{"id": "2210.00762", "title": "Meta-Learning Priors for Safe Bayesian Optimization", "abstract": "  In robotics, optimizing controller parameters under safety constraints is an\nimportant challenge. Safe Bayesian optimization (BO) quantifies uncertainty in\nthe objective and constraints to safely guide exploration in such settings.\nHand-designing a suitable probabilistic model can be challenging, however. In\nthe presence of unknown safety constraints, it is crucial to choose reliable\nmodel hyper-parameters to avoid safety violations. Here, we propose a\ndata-driven approach to this problem by meta-learning priors for safe BO from\noffline data. We build on a meta-learning algorithm, F-PACOH, capable of\nproviding reliable uncertainty quantification in settings of data scarcity. As\ncore contribution, we develop a novel framework for choosing safety-compliant\npriors in a data-riven manner via empirical uncertainty metrics and a frontier\nsearch algorithm. On benchmark functions and a high-precision motion system, we\ndemonstrate that our meta-learned priors accelerate the convergence of safe BO\napproaches while maintaining safety.\n", "date": "2022-10-03", "categories": []}
{"id": "2302.01511", "title": "Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian\n  Regret Bounds", "abstract": "  Gaussian process upper confidence bound (GP-UCB) is a theoretically promising\napproach for black-box optimization; however, the confidence parameter $\\beta$\nis considerably large in the theorem and chosen heuristically in practice.\nThen, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which\nfollows the Gamma distribution, to mitigate the impact of manually specifying\n$\\beta$. This study first generalizes the regret analysis of RGP-UCB to a wider\nclass of distributions, including the Gamma distribution. Furthermore, we\npropose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential\ndistribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not\nrequire an increase in the confidence parameter in terms of the number of\niterations, which avoids over-exploration in the later iterations. Finally, we\ndemonstrate the effectiveness of IRGP-UCB through extensive experiments.\n", "date": "2023-02-03", "categories": []}
{"id": "2302.01513", "title": "Towards Practical Preferential Bayesian Optimization with Skew Gaussian\n  Processes", "abstract": "  We study preferential Bayesian optimization (BO) where reliable feedback is\nlimited to pairwise comparison called duels. An important challenge in\npreferential BO, which uses the preferential Gaussian process (GP) model to\nrepresent flexible preference structure, is that the posterior distribution is\na computationally intractable skew GP. The most widely used approach for\npreferential BO is Gaussian approximation, which ignores the skewness of the\ntrue posterior. Alternatively, Markov chain Monte Carlo (MCMC) based\npreferential BO is also proposed. In this work, we first verify the accuracy of\nGaussian approximation, from which we reveal the critical problem that the\npredictive probability of duels can be inaccurate. This observation motivates\nus to improve the MCMC-based estimation for skew GP, for which we show the\npractical efficiency of Gibbs sampling and derive the low variance MC\nestimator. However, the computational time of MCMC can still be a bottleneck in\npractice. Towards building a more practical preferential BO, we develop a new\nmethod that achieves both high computational efficiency and low sample\ncomplexity, and then demonstrate its effectiveness through extensive numerical\nexperiments.\n", "date": "2023-02-03", "categories": []}
{"id": "2305.18630", "title": "Identification of stormwater control strategies and their associated\n  uncertainties using Bayesian Optimization", "abstract": "  Dynamic control is emerging as an effective methodology for operating\nstormwater systems under stress from rapidly evolving weather patterns.\nInformed by rainfall predictions and real-time sensor measurements, control\nassets in the stormwater network can be dynamically configured to tune the\nbehavior of the stormwater network to reduce the risk of urban flooding,\nequalize flows to the water reclamation facilities, and protect the receiving\nwater bodies. However, developing such control strategies requires significant\nhuman and computational resources, and a methodology does not yet exist for\nquantifying the risks associated with implementing these control strategies. To\naddress these challenges, in this paper, we introduce a Bayesian\nOptimization-based approach for identifying stormwater control strategies and\nestimating the associated uncertainties. We evaluate the efficacy of this\napproach in identifying viable control strategies in a simulated environment on\nreal-world inspired combined and separated stormwater networks. We demonstrate\nthe computational efficiency of the proposed approach by comparing it against a\nGenetic algorithm. Furthermore, we extend the Bayesian Optimization-based\napproach to quantify the uncertainty associated with the identified control\nstrategies and evaluate it on a synthetic stormwater network. To our knowledge,\nthis is the first-ever stormwater control methodology that quantifies\nuncertainty associated with the identified control actions. This Bayesian\noptimization-based stormwater control methodology is an off-the-shelf control\napproach that can be applied to control any stormwater network as long we have\naccess to the rainfall predictions, and there exists a model for simulating the\nbehavior of the stormwater network.\n", "date": "2023-05-29", "categories": []}
{"id": "2305.19267", "title": "Parallelized Acquisition for Active Learning using Monte Carlo Sampling", "abstract": "  Bayesian inference remains one of the most important tool-kits for any\nscientist, but increasingly expensive likelihood functions are required for\never-more complex experiments, raising the cost of generating a Monte Carlo\nsample of the posterior. Recent attention has been directed towards the use of\nemulators of the posterior based on Gaussian Process (GP) regression combined\nwith active sampling to achieve comparable precision with far fewer costly\nlikelihood evaluations. Key to this approach is the batched acquisition of\nproposals, so that the true posterior can be evaluated in parallel. This is\nusually achieved via sequential maximization of the highly multimodal\nacquisition function. Unfortunately, this approach parallelizes poorly and is\nprone to getting stuck in local maxima. Our approach addresses this issue by\ngenerating nearly-optimal batches of candidates using an almost-embarrassingly\nparallel Nested Sampler on the mean prediction of the GP. The resulting\nnearly-sorted Monte Carlo sample is used to generate a batch of candidates\nranked according to their sequentially conditioned acquisition function values\nat little cost. The final sample can also be used for inferring marginal\nquantities. Our proposed implementation (NORA) demonstrates comparable accuracy\nto sequential conditioned acquisition optimization and efficient\nparallelization in various synthetic and cosmological inference problems.\n", "date": "2023-05-30", "categories": []}
{"id": "2301.12844", "title": "Are Random Decompositions all we need in High Dimensional Bayesian\n  Optimisation?", "abstract": "  Learning decompositions of expensive-to-evaluate black-box functions promises\nto scale Bayesian optimisation (BO) to high-dimensional problems. However, the\nsuccess of these techniques depends on finding proper decompositions that\naccurately represent the black-box. While previous works learn those\ndecompositions based on data, we investigate data-independent decomposition\nsampling rules in this paper. We find that data-driven learners of\ndecompositions can be easily misled towards local decompositions that do not\nhold globally across the search space. Then, we formally show that a random\ntree-based decomposition sampler exhibits favourable theoretical guarantees\nthat effectively trade off maximal information gain and functional mismatch\nbetween the actual black-box and its surrogate as provided by the\ndecomposition. Those results motivate the development of the random\ndecomposition upper-confidence bound algorithm (RDUCB) that is straightforward\nto implement - (almost) plug-and-play - and, surprisingly, yields significant\nempirical gains compared to the previous state-of-the-art on a comprehensive\nset of benchmarks. We also confirm the plug-and-play nature of our modelling\ncomponent by integrating our method with HEBO, showing improved practical gains\nin the highest dimensional tasks from Bayesmark.\n", "date": "2023-01-30", "categories": []}
{"id": "2305.17444", "title": "Query-Efficient Black-Box Red Teaming via Bayesian Optimization", "abstract": "  The deployment of large-scale generative models is often restricted by their\npotential risk of causing harm to users in unpredictable ways. We focus on the\nproblem of black-box red teaming, where a red team generates test cases and\ninteracts with the victim model to discover a diverse set of failures with\nlimited query access. Existing red teaming methods construct test cases based\non human supervision or language model (LM) and query all test cases in a\nbrute-force manner without incorporating any information from past evaluations,\nresulting in a prohibitively large number of queries. To this end, we propose\nBayesian red teaming (BRT), novel query-efficient black-box red teaming methods\nbased on Bayesian optimization, which iteratively identify diverse positive\ntest cases leading to model failures by utilizing the pre-defined user input\npool and the past evaluations. Experimental results on various user input pools\ndemonstrate that our method consistently finds a significantly larger number of\ndiverse positive test cases under the limited query budget than the baseline\nmethods. The source code is available at\nhttps://github.com/snu-mllab/Bayesian-Red-Teaming.\n", "date": "2023-05-27", "categories": []}
{"id": "2302.14510", "title": "Bayesian Kernelized Tensor Factorization as Surrogate for Bayesian\n  Optimization", "abstract": "  Bayesian optimization (BO) primarily uses Gaussian processes (GP) as the key\nsurrogate model, mostly with a simple stationary and separable kernel function\nsuch as the squared-exponential kernel with automatic relevance determination\n(SE-ARD). However, such simple kernel specifications are deficient in learning\nfunctions with complex features, such as being nonstationary, nonseparable, and\nmultimodal. Approximating such functions using a local GP, even in a\nlow-dimensional space, requires a large number of samples, not to mention in a\nhigh-dimensional setting. In this paper, we propose to use Bayesian Kernelized\nTensor Factorization (BKTF) -- as a new surrogate model -- for BO in a\n$D$-dimensional Cartesian product space. Our key idea is to approximate the\nunderlying $D$-dimensional solid with a fully Bayesian low-rank tensor CP\ndecomposition, in which we place GP priors on the latent basis functions for\neach dimension to encode local consistency and smoothness. With this\nformulation, information from each sample can be shared not only with neighbors\nbut also across dimensions. Although BKTF no longer has an analytical\nposterior, we can still efficiently approximate the posterior distribution\nthrough Markov chain Monte Carlo (MCMC) and obtain prediction and full\nuncertainty quantification (UQ). We conduct numerical experiments on both\nstandard BO test functions and machine learning hyperparameter tuning problems,\nand our results show that BKTF offers a flexible and highly effective approach\nfor characterizing complex functions with UQ, especially in cases where the\ninitial sample size and budget are severely limited.\n", "date": "2023-02-28", "categories": []}
{"id": "2303.15212", "title": "Deep Ranking Ensembles for Hyperparameter Optimization", "abstract": "  Automatically optimizing the hyperparameters of Machine Learning algorithms\nis one of the primary open questions in AI. Existing work in Hyperparameter\nOptimization (HPO) trains surrogate models for approximating the response\nsurface of hyperparameters as a regression task. In contrast, we hypothesize\nthat the optimal strategy for training surrogates is to preserve the ranks of\nthe performances of hyperparameter configurations as a Learning to Rank\nproblem. As a result, we present a novel method that meta-learns neural network\nsurrogates optimized for ranking the configurations' performances while\nmodeling their uncertainty via ensembling. In a large-scale experimental\nprotocol comprising 12 baselines, 16 HPO search spaces and 86 datasets/tasks,\nwe demonstrate that our method achieves new state-of-the-art results in HPO.\n", "date": "2023-03-27", "categories": []}
{"id": "2301.04344", "title": "Robust Bayesian Target Value Optimization", "abstract": "  We consider the problem of finding an input to a stochastic black box\nfunction such that the scalar output of the black box function is as close as\npossible to a target value in the sense of the expected squared error. While\nthe optimization of stochastic black boxes is classic in (robust) Bayesian\noptimization, the current approaches based on Gaussian processes predominantly\nfocus either on i) maximization/minimization rather than target value\noptimization or ii) on the expectation, but not the variance of the output,\nignoring output variations due to stochasticity in uncontrollable environmental\nvariables. In this work, we fill this gap and derive acquisition functions for\ncommon criteria such as the expected improvement, the probability of\nimprovement, and the lower confidence bound, assuming that aleatoric effects\nare Gaussian with known variance. Our experiments illustrate that this setting\nis compatible with certain extensions of Gaussian processes, and show that the\nthus derived acquisition functions can outperform classical Bayesian\noptimization even if the latter assumptions are violated. An industrial use\ncase in billet forging is presented.\n", "date": "2023-01-11", "categories": []}
{"id": "2305.08624", "title": "Mastering the exploration-exploitation trade-off in Bayesian\n  Optimization", "abstract": "  Gaussian Process based Bayesian Optimization is a well-known sample efficient\nsequential strategy for globally optimizing black-box, expensive, and\nmulti-extremal functions. The role of the Gaussian Process is to provide a\nprobabilistic approximation of the unknown function, depending on the\nsequentially collected observations, while an acquisition function drives the\nchoice of the next solution to evaluate, balancing between exploration and\nexploitation, depending on the current Gaussian Process model. Despite the huge\neffort of the scientific community in defining effective\nexploration-exploitation mechanisms, we are still far away from the master\nacquisition function. This paper merges the most relevant results and insights\nfrom both algorithmic and human search strategies to propose a novel\nacquisition function, mastering the trade-off between explorative and\nexploitative choices, adaptively. We compare the proposed acquisition function\non a number of test functions and against different state-of-the-art ones,\nwhich are instead based on prefixed or random scheduling between exploration\nand exploitation. A Pareto analysis is performed with respect to two\n(antagonistic) goals: convergence to the optimum and exploration capability.\nResults empirically prove that the proposed acquisition function is almost\nalways Pareto optimal and also the most balanced trade-off between the two\ngoals.\n", "date": "2023-05-15", "categories": []}
{"id": "2210.10953", "title": "Discovering Many Diverse Solutions with Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is a popular approach for sample-efficient\noptimization of black-box objective functions. While BO has been successfully\napplied to a wide range of scientific applications, traditional approaches to\nsingle-objective BO only seek to find a single best solution. This can be a\nsignificant limitation in situations where solutions may later turn out to be\nintractable. For example, a designed molecule may turn out to violate\nconstraints that can only be reasonably evaluated after the optimization\nprocess has concluded. To address this issue, we propose Rank-Ordered Bayesian\nOptimization with Trust-regions (ROBOT) which aims to find a portfolio of\nhigh-performing solutions that are diverse according to a user-specified\ndiversity metric. We evaluate ROBOT on several real-world applications and show\nthat it can discover large sets of high-performing diverse solutions while\nrequiring few additional function evaluations compared to finding a single best\nsolution.\n", "date": "2022-10-20", "categories": []}
{"id": "2303.11954", "title": "Bayesian Optimization for Function Compositions with Applications to\n  Dynamic Pricing", "abstract": "  Bayesian Optimization (BO) is used to find the global optima of black box\nfunctions. In this work, we propose a practical BO method of function\ncompositions where the form of the composition is known but the constituent\nfunctions are expensive to evaluate. By assuming an independent Gaussian\nprocess (GP) model for each of the constituent black-box function, we propose\nExpected Improvement (EI) and Upper Confidence Bound (UCB) based BO algorithms\nand demonstrate their ability to outperform not just vanilla BO but also the\ncurrent state-of-art algorithms. We demonstrate a novel application of the\nproposed methods to dynamic pricing in revenue management when the underlying\ndemand function is expensive to evaluate.\n", "date": "2023-03-21", "categories": []}
{"id": "2304.11251", "title": "Machine Learning and the Future of Bayesian Computation", "abstract": "  Bayesian models are a powerful tool for studying complex data, allowing the\nanalyst to encode rich hierarchical dependencies and leverage prior\ninformation. Most importantly, they facilitate a complete characterization of\nuncertainty through the posterior distribution. Practical posterior computation\nis commonly performed via MCMC, which can be computationally infeasible for\nhigh dimensional models with many observations. In this article we discuss the\npotential to improve posterior computation using ideas from machine learning.\nConcrete future directions are explored in vignettes on normalizing flows,\nBayesian coresets, distributed Bayesian inference, and variational inference.\n", "date": "2023-04-21", "categories": []}
{"id": "2304.10051", "title": "HyperTuner: A Cross-Layer Multi-Objective Hyperparameter Auto-Tuning\n  Framework for Data Analytic Services", "abstract": "  Hyper-parameters optimization (HPO) is vital for machine learning models.\nBesides model accuracy, other tuning intentions such as model training time and\nenergy consumption are also worthy of attention from data analytic service\nproviders. Hence, it is essential to take both model hyperparameters and system\nparameters into consideration to execute cross-layer multi-objective\nhyperparameter auto-tuning. Towards this challenging target, we propose\nHyperTuner in this paper. To address the formulated high-dimensional black-box\nmulti-objective optimization problem, HyperTuner first conducts multi-objective\nparameter importance ranking with its MOPIR algorithm and then leverages the\nproposed ADUMBO algorithm to find the Pareto-optimal configuration set. During\neach iteration, ADUMBO selects the most promising configuration from the\ngenerated Pareto candidate set via maximizing a new well-designed metric, which\ncan adaptively leverage the uncertainty as well as the predicted mean across\nall the surrogate models along with the iteration times. We evaluate HyperTuner\non our local distributed TensorFlow cluster and experimental results show that\nit is always able to find a better Pareto configuration front superior in both\nconvergence and diversity compared with the other four baseline algorithms.\nBesides, experiments with different training datasets, different optimization\nobjectives and different machine learning platforms verify that HyperTuner can\nwell adapt to various data analytic service scenarios.\n", "date": "2023-04-20", "categories": []}
{"id": "2304.09278", "title": "A Data Driven Sequential Learning Framework to Accelerate and Optimize\n  Multi-Objective Manufacturing Decisions", "abstract": "  Manufacturing advanced materials and products with a specific property or\ncombination of properties is often warranted. To achieve that it is crucial to\nfind out the optimum recipe or processing conditions that can generate the\nideal combination of these properties. Most of the time, a sufficient number of\nexperiments are needed to generate a Pareto front. However, manufacturing\nexperiments are usually costly and even conducting a single experiment can be a\ntime-consuming process. So, it's critical to determine the optimal location for\ndata collection to gain the most comprehensive understanding of the process.\nSequential learning is a promising approach to actively learn from the ongoing\nexperiments, iteratively update the underlying optimization routine, and adapt\nthe data collection process on the go. This paper presents a novel data-driven\nBayesian optimization framework that utilizes sequential learning to\nefficiently optimize complex systems with multiple conflicting objectives.\nAdditionally, this paper proposes a novel metric for evaluating multi-objective\ndata-driven optimization approaches. This metric considers both the quality of\nthe Pareto front and the amount of data used to generate it. The proposed\nframework is particularly beneficial in practical applications where acquiring\ndata can be expensive and resource intensive. To demonstrate the effectiveness\nof the proposed algorithm and metric, the algorithm is evaluated on a\nmanufacturing dataset. The results indicate that the proposed algorithm can\nachieve the actual Pareto front while processing significantly less data. It\nimplies that the proposed data-driven framework can lead to similar\nmanufacturing decisions with reduced costs and time.\n", "date": "2023-04-18", "categories": []}
{"id": "2304.07949", "title": "Metrics for Bayesian Optimal Experiment Design under Model\n  Misspecification", "abstract": "  The conventional approach to Bayesian decision-theoretic experiment design\ninvolves searching over possible experiments to select a design that maximizes\nthe expected value of a specified utility function. The expectation is over the\njoint distribution of all unknown variables implied by the statistical model\nthat will be used to analyze the collected data. The utility function defines\nthe objective of the experiment where a common utility function is the\ninformation gain. This article introduces an expanded framework for this\nprocess, where we go beyond the traditional Expected Information Gain criteria\nand introduce the Expected General Information Gain which measures robustness\nto the model discrepancy and Expected Discriminatory Information as a criterion\nto quantify how well an experiment can detect model discrepancy. The\nfunctionality of the framework is showcased through its application to a\nscenario involving a linearized spring mass damper system and an F-16 model\nwhere the model discrepancy is taken into account while doing Bayesian optimal\nexperiment design.\n", "date": "2023-04-17", "categories": []}
{"id": "2207.04994", "title": "Uncertainty-Aware Mixed-Variable Machine Learning for Materials Design", "abstract": "  Data-driven design shows the promise of accelerating materials discovery but\nis challenging due to the prohibitive cost of searching the vast design space\nof chemistry, structure, and synthesis methods. Bayesian Optimization (BO)\nemploys uncertainty-aware machine learning models to select promising designs\nto evaluate, hence reducing the cost. However, BO with mixed numerical and\ncategorical variables, which is of particular interest in materials design, has\nnot been well studied. In this work, we survey frequentist and Bayesian\napproaches to uncertainty quantification of machine learning with mixed\nvariables. We then conduct a systematic comparative study of their performances\nin BO using a popular representative model from each group, the random\nforest-based Lolo model (frequentist) and the latent variable Gaussian process\nmodel (Bayesian). We examine the efficacy of the two models in the optimization\nof mathematical functions, as well as properties of structural and functional\nmaterials, where we observe performance differences as related to problem\ndimensionality and complexity. By investigating the machine learning models'\npredictive and uncertainty estimation capabilities, we provide interpretations\nof the observed performance differences. Our results provide practical guidance\non choosing between frequentist and Bayesian uncertainty-aware machine learning\nmodels for mixed-variable BO in materials design.\n", "date": "2022-07-11", "categories": []}
{"id": "2208.02704", "title": "Bayesian Optimization with Informative Covariance", "abstract": "  Bayesian optimization is a methodology for global optimization of unknown and\nexpensive objectives. It combines a surrogate Bayesian regression model with an\nacquisition function to decide where to evaluate the objective. Typical\nregression models are given by Gaussian processes with stationary covariance\nfunctions. However, these functions are unable to express prior input-dependent\ninformation, including possible locations of the optimum. The ubiquity of\nstationary models has led to the common practice of exploiting prior\ninformation via informative mean functions. In this paper, we highlight that\nthese models can perform poorly, especially in high dimensions. We propose\nnovel informative covariance functions for optimization, leveraging\nnonstationarity to encode preferences for certain regions of the search space\nand adaptively promote local exploration during optimization. We demonstrate\nthat the proposed functions can increase the sample efficiency of Bayesian\noptimization in high dimensions, even under weak prior information.\n", "date": "2022-08-04", "categories": []}
{"id": "2303.15746", "title": "qEUBO: A Decision-Theoretic Acquisition Function for Preferential\n  Bayesian Optimization", "abstract": "  Preferential Bayesian optimization (PBO) is a framework for optimizing a\ndecision maker's latent utility function using preference feedback. This work\nintroduces the expected utility of the best option (qEUBO) as a novel\nacquisition function for PBO. When the decision maker's responses are\nnoise-free, we show that qEUBO is one-step Bayes optimal and thus equivalent to\nthe popular knowledge gradient acquisition function. We also show that qEUBO\nenjoys an additive constant approximation guarantee to the one-step\nBayes-optimal policy when the decision maker's responses are corrupted by\nnoise. We provide an extensive evaluation of qEUBO and demonstrate that it\noutperforms the state-of-the-art acquisition functions for PBO across many\nsettings. Finally, we show that, under sufficient regularity conditions,\nqEUBO's Bayesian simple regret converges to zero at a rate $o(1/n)$ as the\nnumber of queries, $n$, goes to infinity. In contrast, we show that simple\nregret under qEI, a popular acquisition function for standard BO often used for\nPBO, can fail to converge to zero. Enjoying superior performance, simple\ncomputation, and a grounded decision-theoretic justification, qEUBO is a\npromising acquisition function for PBO.\n", "date": "2023-03-28", "categories": []}
{"id": "2303.13034", "title": "Preference-Aware Constrained Multi-Objective Bayesian Optimization", "abstract": "  This paper addresses the problem of constrained multi-objective optimization\nover black-box objective functions with practitioner-specified preferences over\nthe objectives when a large fraction of the input space is infeasible (i.e.,\nviolates constraints). This problem arises in many engineering design problems\nincluding analog circuits and electric power system design. Our overall goal is\nto approximate the optimal Pareto set over the small fraction of feasible input\ndesigns. The key challenges include the huge size of the design space, multiple\nobjectives and large number of constraints, and the small fraction of feasible\ninput designs which can be identified only after performing expensive\nsimulations. We propose a novel and efficient preference-aware constrained\nmulti-objective Bayesian optimization approach referred to as PAC-MOO to\naddress these challenges. The key idea is to learn surrogate models for both\noutput objectives and constraints, and select the candidate input for\nevaluation in each iteration that maximizes the information gained about the\noptimal constrained Pareto front while factoring in the preferences over\nobjectives. Our experiments on two real-world analog circuit design\noptimization problems demonstrate the efficacy of PAC-MOO over prior methods.\n", "date": "2023-03-23", "categories": []}
{"id": "2211.02218", "title": "Fully Bayesian inference for latent variable Gaussian process models", "abstract": "  Real engineering and scientific applications often involve one or more\nqualitative inputs. Standard Gaussian processes (GPs), however, cannot directly\naccommodate qualitative inputs. The recently introduced latent variable\nGaussian process (LVGP) overcomes this issue by first mapping each qualitative\nfactor to underlying latent variables (LVs), and then uses any standard GP\ncovariance function over these LVs. The LVs are estimated similarly to the\nother GP hyperparameters through maximum likelihood estimation, and then\nplugged into the prediction expressions. However, this plug-in approach will\nnot account for uncertainty in estimation of the LVs, which can be significant\nespecially with limited training data. In this work, we develop a fully\nBayesian approach for the LVGP model and for visualizing the effects of the\nqualitative inputs via their LVs. We also develop approximations for scaling up\nLVGPs and fully Bayesian inference for the LVGP hyperparameters. We conduct\nnumerical studies comparing plug-in inference against fully Bayesian inference\nover a few engineering models and material design applications. In contrast to\nprevious studies on standard GP modeling that have largely concluded that a\nfully Bayesian treatment offers limited improvements, our results show that for\nLVGP modeling it offers significant improvements in prediction accuracy and\nuncertainty quantification over the plug-in approach.\n", "date": "2022-11-04", "categories": []}
{"id": "2302.14732", "title": "Constrained Bayesian Optimization for Automatic Underwater Vehicle Hull\n  Design", "abstract": "  Automatic underwater vehicle hull Design optimization is a complex\nengineering process for generating a UUV hull with optimized properties on a\ngiven requirement. First, it involves the integration of involved\ncomputationally complex engineering simulation tools. Second, it needs\nintegration of a sample efficient optimization framework with the integrated\ntoolchain. To this end, we integrated the CAD tool called FreeCAD with CFD tool\nopenFoam for automatic design evaluation. For optimization, we chose Bayesian\noptimization (BO), which is a well-known technique developed for optimizing\ntime-consuming expensive engineering simulations and has proven to be very\nsample efficient in a variety of problems, including hyper-parameter tuning and\nexperimental design. During the optimization process, we can handle infeasible\ndesign as constraints integrated into the optimization process. By integrating\ndomain-specific toolchain with AI-based optimization, we executed the automatic\ndesign optimization of underwater vehicle hull design. For empirical\nevaluation, we took two different use cases of real-world underwater vehicle\ndesign to validate the execution of our tool.\n", "date": "2023-02-28", "categories": []}
{"id": "2211.10257", "title": "Model-based Causal Bayesian Optimization", "abstract": "  How should we intervene on an unknown structural equation model to maximize a\ndownstream variable of interest? This setting, also known as causal Bayesian\noptimization (CBO), has important applications in medicine, ecology, and\nmanufacturing. Standard Bayesian optimization algorithms fail to effectively\nleverage the underlying causal structure. Existing CBO approaches assume\nnoiseless measurements and do not come with guarantees. We propose the\nmodel-based causal Bayesian optimization algorithm (MCBO) that learns a full\nsystem model instead of only modeling intervention-reward pairs. MCBO\npropagates epistemic uncertainty about the causal mechanisms through the graph\nand trades off exploration and exploitation via the optimism principle. We\nbound its cumulative regret, and obtain the first non-asymptotic bounds for\nCBO. Unlike in standard Bayesian optimization, our acquisition function cannot\nbe evaluated in closed form, so we show how the reparameterization trick can be\nused to apply gradient-based optimizers. The resulting practical implementation\nof MCBO compares favorably with state-of-the-art approaches empirically.\n", "date": "2022-11-18", "categories": []}
{"id": "2303.05694", "title": "Gaussian Max-Value Entropy Search for Multi-Agent Bayesian Optimization", "abstract": "  We study the multi-agent Bayesian optimization (BO) problem, where multiple\nagents maximize a black-box function via iterative queries. We focus on Entropy\nSearch (ES), a sample-efficient BO algorithm that selects queries to maximize\nthe mutual information about the maximum of the black-box function. One of the\nmain challenges of ES is that calculating the mutual information requires\ncomputationally-costly approximation techniques. For multi-agent BO problems,\nthe computational cost of ES is exponential in the number of agents. To address\nthis challenge, we propose the Gaussian Max-value Entropy Search, a multi-agent\nBO algorithm with favorable sample and computational efficiency. The key to our\nidea is to use a normal distribution to approximate the function maximum and\ncalculate its mutual information accordingly. The resulting approximation\nallows queries to be cast as the solution of a closed-form optimization problem\nwhich, in turn, can be solved via a modified gradient ascent algorithm and\nscaled to a large number of agents. We demonstrate the effectiveness of\nGaussian max-value Entropy Search through numerical experiments on standard\ntest functions and real-robot experiments on the source-seeking problem.\nResults show that the proposed algorithm outperforms the multi-agent BO\nbaselines in the numerical experiments and can stably seek the source with a\nlimited number of noisy observations on real robots.\n", "date": "2023-03-10", "categories": []}
{"id": "2303.01774", "title": "Bayesian Optimization over High-Dimensional Combinatorial Spaces via\n  Dictionary-based Embeddings", "abstract": "  We consider the problem of optimizing expensive black-box functions over\nhigh-dimensional combinatorial spaces which arises in many science,\nengineering, and ML applications. We use Bayesian Optimization (BO) and propose\na novel surrogate modeling approach for efficiently handling a large number of\nbinary and categorical parameters. The key idea is to select a number of\ndiscrete structures from the input space (the dictionary) and use them to\ndefine an ordinal embedding for high-dimensional combinatorial structures. This\nallows us to use existing Gaussian process models for continuous spaces. We\ndevelop a principled approach based on binary wavelets to construct\ndictionaries for binary spaces, and propose a randomized construction method\nthat generalizes to categorical spaces. We provide theoretical justification to\nsupport the effectiveness of the dictionary-based embeddings. Our experiments\non diverse real-world benchmarks demonstrate the effectiveness of our proposed\nsurrogate modeling approach over state-of-the-art BO methods.\n", "date": "2023-03-03", "categories": []}
{"id": "2302.13360", "title": "Guiding the Sequential Experiments in Autonomous Experimentation\n  Platforms through EI-based Bayesian Optimization and Bayesian Model Averaging", "abstract": "  Autonomous Experimentation Platforms (AEPs) are advanced manufacturing\nplatforms that, under intelligent control, can sequentially search the material\ndesign space (MDS) and identify parameters with the desired properties. At the\nheart of the intelligent control of these AEPs is the policy guiding the\nsequential experiments, which is to choose the location to carry out the next\nexperiment. In such cases, a balance between exploitation and exploration must\nbe achieved. A Bayesian Optimization (BO) framework with Expected Improvement\nbased (EI-based) acquisition function can effectively search the MDS and guide\nwhere to conduct the next experiments so that the underlying relationship can\nbe identified with a smaller number of experiments. The traditional BO\nframework tries to optimize a black box objective function in a sequential\nmanner by relying on a single model. However, this single-model approach does\nnot account for model uncertainty. Bayesian Model Averaging (BMA) addresses\nthis issue by working with multiple models and thus considering the uncertainty\nin the models. In this work, we first apply the conventional BO algorithm with\nthe most popular EI-based experiment policy in a real-life fatigue dataset for\nsteel to predict the fatigue strength of steel. Afterward, we apply BMA to the\nsame dataset by working with a set of predictive models and compare the\nperformance of BMA with the traditional BO algorithm, which relies on a single\nmodel for approximation. We compare the results in terms of RMSE and find that\nBMA performs better than EI-based BO in the prediction task by considering the\nmodel uncertainty in its framework.\n", "date": "2023-02-26", "categories": []}
{"id": "2210.13937", "title": "Multi-Fidelity Bayesian Optimization with Unreliable Information Sources", "abstract": "  Bayesian optimization (BO) is a powerful framework for optimizing black-box,\nexpensive-to-evaluate functions. Over the past decade, many algorithms have\nbeen proposed to integrate cheaper, lower-fidelity approximations of the\nobjective function into the optimization process, with the goal of converging\ntowards the global optimum at a reduced cost. This task is generally referred\nto as multi-fidelity Bayesian optimization (MFBO). However, MFBO algorithms can\nlead to higher optimization costs than their vanilla BO counterparts,\nespecially when the low-fidelity sources are poor approximations of the\nobjective function, therefore defeating their purpose. To address this issue,\nwe propose rMFBO (robust MFBO), a methodology to make any GP-based MFBO scheme\nrobust to the addition of unreliable information sources. rMFBO comes with a\ntheoretical guarantee that its performance can be bound to its vanilla BO\nanalog, with high controllable probability. We demonstrate the effectiveness of\nthe proposed methodology on a number of numerical benchmarks, outperforming\nearlier MFBO methods on unreliable sources. We expect rMFBO to be particularly\nuseful to reliably include human experts with varying knowledge within BO\nprocesses.\n", "date": "2022-10-25", "categories": []}
{"id": "2211.06149", "title": "Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian\n  Optimization", "abstract": "  Bayesian Optimization is a useful tool for experiment design. Unfortunately,\nthe classical, sequential setting of Bayesian Optimization does not translate\nwell into laboratory experiments, for instance battery design, where\nmeasurements may come from different sources and their evaluations may require\nsignificant waiting times. Multi-fidelity Bayesian Optimization addresses the\nsetting with measurements from different sources. Asynchronous batch Bayesian\nOptimization provides a framework to select new experiments before the results\nof the prior experiments are revealed. This paper proposes an algorithm\ncombining multi-fidelity and asynchronous batch methods. We empirically study\nthe algorithm behavior, and show it can outperform single-fidelity batch\nmethods and multi-fidelity sequential methods. As an application, we consider\ndesigning electrode materials for optimal performance in pouch cells using\nexperiments with coin cells to approximate battery performance.\n", "date": "2022-11-11", "categories": []}
{"id": "2301.10123", "title": "Inducing Point Allocation for Sparse Gaussian Processes in\n  High-Throughput Bayesian Optimisation", "abstract": "  Sparse Gaussian Processes are a key component of high-throughput Bayesian\nOptimisation (BO) loops; however, we show that existing methods for allocating\ntheir inducing points severely hamper optimisation performance. By exploiting\nthe quality-diversity decomposition of Determinantal Point Processes, we\npropose the first inducing point allocation strategy designed specifically for\nuse in BO. Unlike existing methods which seek only to reduce global uncertainty\nin the objective function, our approach provides the local high-fidelity\nmodelling of promising regions required for precise optimisation. More\ngenerally, we demonstrate that our proposed framework provides a flexible way\nto allocate modelling capacity in sparse models and so is suitable broad range\nof downstream sequential decision making tasks.\n", "date": "2023-01-24", "categories": []}
{"id": "2302.08436", "title": "Trieste: Efficiently Exploring The Depths of Black-box Functions with\n  TensorFlow", "abstract": "  We present Trieste, an open-source Python package for Bayesian optimization\nand active learning benefiting from the scalability and efficiency of\nTensorFlow. Our library enables the plug-and-play of popular TensorFlow-based\nmodels within sequential decision-making loops, e.g. Gaussian processes from\nGPflow or GPflux, or neural networks from Keras. This modular mindset is\ncentral to the package and extends to our acquisition functions and the\ninternal dynamics of the decision-making loop, both of which can be tailored\nand extended by researchers or engineers when tackling custom use cases.\nTrieste is a research-friendly and production-ready toolkit backed by a\ncomprehensive test suite, extensive documentation, and available at\nhttps://github.com/secondmind-labs/trieste.\n", "date": "2023-02-16", "categories": []}
{"id": "2302.05927", "title": "Transfer Learning for Bayesian Optimization: A Survey", "abstract": "  A wide spectrum of design and decision problems, including parameter tuning,\nA/B testing and drug design, intrinsically are instances of black-box\noptimization. Bayesian optimization (BO) is a powerful tool that models and\noptimizes such expensive \"black-box\" functions. However, at the beginning of\noptimization, vanilla Bayesian optimization methods often suffer from slow\nconvergence issue due to inaccurate modeling based on few trials. To address\nthis issue, researchers in the BO community propose to incorporate the spirit\nof transfer learning to accelerate optimization process, which could borrow\nstrength from the past tasks (source tasks) to accelerate the current\noptimization problem (target task). This survey paper first summarizes transfer\nlearning methods for Bayesian optimization from four perspectives: initial\npoints design, search space design, surrogate model, and acquisition function.\nThen it highlights its methodological aspects and technical details for each\napproach. Finally, it showcases a wide range of applications and proposes\npromising future directions.\n", "date": "2023-02-12", "categories": []}
{"id": "2302.03255", "title": "DivBO: Diversity-aware CASH for Ensemble Learning", "abstract": "  The Combined Algorithm Selection and Hyperparameters optimization (CASH)\nproblem is one of the fundamental problems in Automated Machine Learning\n(AutoML). Motivated by the success of ensemble learning, recent AutoML systems\nbuild post-hoc ensembles to output the final predictions instead of using the\nbest single learner. However, while most CASH methods focus on searching for a\nsingle learner with the best performance, they neglect the diversity among base\nlearners (i.e., they may suggest similar configurations to previously evaluated\nones), which is also a crucial consideration when building an ensemble. To\ntackle this issue and further enhance the ensemble performance, we propose\nDivBO, a diversity-aware framework to inject explicit search of diversity into\nthe CASH problems. In the framework, we propose to use a diversity surrogate to\npredict the pair-wise diversity of two unseen configurations. Furthermore, we\nintroduce a temporary pool and a weighted acquisition function to guide the\nsearch of both performance and diversity based on Bayesian optimization.\nEmpirical results on 15 public datasets show that DivBO achieves the best\naverage ranks (1.82 and 1.73) on both validation and test errors among 10\ncompared methods, including post-hoc designs in recent AutoML systems and\nstate-of-the-art baselines for ensemble learning on CASH problems.\n", "date": "2023-02-07", "categories": []}
{"id": "2301.12099", "title": "Violation-Aware Contextual Bayesian Optimization for Controller\n  Performance Optimization with Unmodeled Constraints", "abstract": "  We study the problem of performance optimization of closed-loop control\nsystems with unmodeled dynamics. Bayesian optimization (BO) has been\ndemonstrated to be effective for improving closed-loop performance by\nautomatically tuning controller gains or reference setpoints in a model-free\nmanner. However, BO methods have rarely been tested on dynamical systems with\nunmodeled constraints and time-varying ambient conditions. In this paper, we\npropose a violation-aware contextual BO algorithm (VACBO) that optimizes\nclosed-loop performance while simultaneously learning constraint-feasible\nsolutions under time-varying ambient conditions. Unlike classical constrained\nBO methods which allow unlimited constraint violations, or 'safe' BO algorithms\nthat are conservative and try to operate with near-zero violations, we allow\nbudgeted constraint violations to improve constraint learning and accelerate\noptimization. We demonstrate the effectiveness of our proposed VACBO method for\nenergy minimization of industrial vapor compression systems under time-varying\nambient temperature and humidity.\n", "date": "2023-01-28", "categories": []}
{"id": "2301.12581", "title": "Intrinsic Bayesian Optimisation on Complex Constrained Domain", "abstract": "  Motivated by the success of Bayesian optimisation algorithms in the Euclidean\nspace, we propose a novel approach to construct Intrinsic Bayesian optimisation\n(In-BO) on manifolds with a primary focus on complex constrained domains or\nirregular-shaped spaces arising as submanifolds of R2, R3 and beyond. Data may\nbe collected in a spatial domain but restricted to a complex or intricately\nstructured region corresponding to a geographic feature, such as lakes.\nTraditional Bayesian Optimisation (Tra-BO) defined with a Radial basis function\n(RBF) kernel cannot accommodate these complex constrained conditions. The In-BO\nuses the Sparse Intrinsic Gaussian Processes (SIn-GP) surrogate model to take\ninto account the geometric structure of the manifold. SInGPs are constructed\nusing the heat kernel of the manifold which is estimated as the transition\ndensity of the Brownian Motion on manifolds. The efficiency of In-BO is\ndemonstrated through simulation studies on a U-shaped domain, a Bitten torus,\nand a real dataset from the Aral sea. Its performance is compared to that of\ntraditional BO, which is defined in Euclidean space.\n", "date": "2023-01-29", "categories": []}
{"id": "2301.11810", "title": "BOMP-NAS: Bayesian Optimization Mixed Precision NAS", "abstract": "  Bayesian Optimization Mixed-Precision Neural Architecture Search (BOMP-NAS)\nis an approach to quantization-aware neural architecture search (QA-NAS) that\nleverages both Bayesian optimization (BO) and mixed-precision quantization (MP)\nto efficiently search for compact, high performance deep neural networks. The\nresults show that integrating quantization-aware fine-tuning (QAFT) into the\nNAS loop is a necessary step to find networks that perform well under\nlow-precision quantization: integrating it allows a model size reduction of\nnearly 50\\% on the CIFAR-10 dataset. BOMP-NAS is able to find neural networks\nthat achieve state of the art performance at much lower design costs. This\nstudy shows that BOMP-NAS can find these neural networks at a 6x shorter search\ntime compared to the closest related work.\n", "date": "2023-01-27", "categories": []}
{"id": "2206.04771", "title": "Joint Entropy Search for Maximally-Informed Bayesian Optimization", "abstract": "  Information-theoretic Bayesian optimization techniques have become popular\nfor optimizing expensive-to-evaluate black-box functions due to their\nnon-myopic qualities. Entropy Search and Predictive Entropy Search both\nconsider the entropy over the optimum in the input space, while the recent\nMax-value Entropy Search considers the entropy over the optimal value in the\noutput space. We propose Joint Entropy Search (JES), a novel\ninformation-theoretic acquisition function that considers an entirely new\nquantity, namely the entropy over the joint optimal probability density over\nboth input and output space. To incorporate this information, we consider the\nreduction in entropy from conditioning on fantasized optimal input/output\npairs. The resulting approach primarily relies on standard GP machinery and\nremoves complex approximations typically associated with information-theoretic\nmethods. With minimal computational overhead, JES shows superior\ndecision-making, and yields state-of-the-art performance for\ninformation-theoretic approaches across a wide suite of tasks. As a\nlight-weight approach with superior results, JES provides a new go-to\nacquisition function for Bayesian optimization.\n", "date": "2022-06-09", "categories": []}
{"id": "2210.11662", "title": "Local Bayesian optimization via maximizing probability of descent", "abstract": "  Local optimization presents a promising approach to expensive,\nhigh-dimensional black-box optimization by sidestepping the need to globally\nexplore the search space. For objective functions whose gradient cannot be\nevaluated directly, Bayesian optimization offers one solution -- we construct a\nprobabilistic model of the objective, design a policy to learn about the\ngradient at the current location, and use the resulting information to navigate\nthe objective landscape. Previous work has realized this scheme by minimizing\nthe variance in the estimate of the gradient, then moving in the direction of\nthe expected gradient. In this paper, we re-examine and refine this approach.\nWe demonstrate that, surprisingly, the expected value of the gradient is not\nalways the direction maximizing the probability of descent, and in fact, these\ndirections may be nearly orthogonal. This observation then inspires an elegant\noptimization scheme seeking to maximize the probability of descent while moving\nin the direction of most-probable descent. Experiments on both synthetic and\nreal-world objectives show that our method outperforms previous realizations of\nthis optimization scheme and is competitive against other, significantly more\ncomplicated baselines.\n", "date": "2022-10-21", "categories": []}
{"id": "2212.10299", "title": "Cell-Free Data Power Control Via Scalable Multi-Objective Bayesian\n  Optimisation", "abstract": "  Cell-free multi-user multiple input multiple output networks are a promising\nalternative to classical cellular architectures, since they have the potential\nto provide uniform service quality and high resource utilisation over the\nentire coverage area of the network. To realise this potential, previous works\nhave developed radio resource management mechanisms using various optimisation\nengines. In this work, we consider the problem of overall ergodic spectral\nefficiency maximisation in the context of uplink-downlink data power control in\ncell-free networks. To solve this problem in large networks, and to address\nconvergence-time limitations, we apply scalable multi-objective Bayesian\noptimisation. Furthermore, we discuss how an intersection of multi-fidelity\nemulation and Bayesian optimisation can improve radio resource management in\ncell-free networks.\n", "date": "2022-12-20", "categories": []}
{"id": "2301.05983", "title": "On the role of Model Uncertainties in Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is a popular method for black-box optimization,\nwhich relies on uncertainty as part of its decision-making process when\ndeciding which experiment to perform next. However, not much work has addressed\nthe effect of uncertainty on the performance of the BO algorithm and to what\nextent calibrated uncertainties improve the ability to find the global optimum.\nIn this work, we provide an extensive study of the relationship between the BO\nperformance (regret) and uncertainty calibration for popular surrogate models\nand compare them across both synthetic and real-world experiments. Our results\nconfirm that Gaussian Processes are strong surrogate models and that they tend\nto outperform other popular models. Our results further show a positive\nassociation between calibration error and regret, but interestingly, this\nassociation disappears when we control for the type of model in the analysis.\nWe also studied the effect of re-calibration and demonstrate that it generally\ndoes not lead to improved regret. Finally, we provide theoretical justification\nfor why uncertainty calibration might be difficult to combine with BO due to\nthe small sample sizes commonly used.\n", "date": "2023-01-14", "categories": []}
{"id": "2209.04722", "title": "Batch Bayesian Optimization via Particle Gradient Flows", "abstract": "  Bayesian Optimisation (BO) methods seek to find global optima of objective\nfunctions which are only available as a black-box or are expensive to evaluate.\nSuch methods construct a surrogate model for the objective function,\nquantifying the uncertainty in that surrogate through Bayesian inference.\nObjective evaluations are sequentially determined by maximising an acquisition\nfunction at each step. However, this ancilliary optimisation problem can be\nhighly non-trivial to solve, due to the non-convexity of the acquisition\nfunction, particularly in the case of batch Bayesian optimisation, where\nmultiple points are selected in every step. In this work we reformulate batch\nBO as an optimisation problem over the space of probability measures. We\nconstruct a new acquisition function based on multipoint expected improvement\nwhich is convex over the space of probability measures. Practical schemes for\nsolving this `inner' optimisation problem arise naturally as gradient flows of\nthis objective function. We demonstrate the efficacy of this new method on\ndifferent benchmark functions and compare with state-of-the-art batch BO\nmethods.\n", "date": "2022-09-10", "categories": []}
{"id": "2301.01594", "title": "Finding Needles in Haystack: Formal Generative Models for Efficient\n  Massive Parallel Simulations", "abstract": "  The increase in complexity of autonomous systems is accompanied by a need of\ndata-driven development and validation strategies. Advances in computer\ngraphics and cloud clusters have opened the way to massive parallel high\nfidelity simulations to qualitatively address the large number of operational\nscenarios. However, exploration of all possible scenarios is still\nprohibitively expensive and outcomes of scenarios are generally unknown\napriori. To this end, the authors propose a method based on bayesian\noptimization to efficiently learn generative models on scenarios that would\ndeliver desired outcomes (e.g. collisions) with high probability. The\nmethodology is integrated in an end-to-end framework, which uses the\nOpenSCENARIO standard to describe scenarios, and deploys highly configurable\ndigital twins of the scenario participants on a Virtual Test Bed cluster.\n", "date": "2023-01-03", "categories": []}
{"id": "2207.00879", "title": "Tree ensemble kernels for Bayesian optimization with known constraints\n  over mixed-feature spaces", "abstract": "  Tree ensembles can be well-suited for black-box optimization tasks such as\nalgorithm tuning and neural architecture search, as they achieve good\npredictive performance with little or no manual tuning, naturally handle\ndiscrete feature spaces, and are relatively insensitive to outliers in the\ntraining data. Two well-known challenges in using tree ensembles for black-box\noptimization are (i) effectively quantifying model uncertainty for exploration\nand (ii) optimizing over the piece-wise constant acquisition function. To\naddress both points simultaneously, we propose using the kernel interpretation\nof tree ensembles as a Gaussian Process prior to obtain model variance\nestimates, and we develop a compatible optimization formulation for the\nacquisition function. The latter further allows us to seamlessly integrate\nknown constraints to improve sampling efficiency by considering\ndomain-knowledge in engineering settings and modeling search space symmetries,\ne.g., hierarchical relationships in neural architecture search. Our framework\nperforms as well as state-of-the-art methods for unconstrained black-box\noptimization over continuous/discrete features and outperforms competing\nmethods for problems combining mixed-variable feature spaces and known input\nconstraints.\n", "date": "2022-07-02", "categories": []}
{"id": "2212.13886", "title": "Extrinsic Bayesian Optimizations on Manifolds", "abstract": "  We propose an extrinsic Bayesian optimization (eBO) framework for general\noptimization problems on manifolds. Bayesian optimization algorithms build a\nsurrogate of the objective function by employing Gaussian processes and\nquantify the uncertainty in that surrogate by deriving an acquisition function.\nThis acquisition function represents the probability of improvement based on\nthe kernel of the Gaussian process, which guides the search in the optimization\nprocess. The critical challenge for designing Bayesian optimization algorithms\non manifolds lies in the difficulty of constructing valid covariance kernels\nfor Gaussian processes on general manifolds. Our approach is to employ\nextrinsic Gaussian processes by first embedding the manifold onto some higher\ndimensional Euclidean space via equivariant embeddings and then constructing a\nvalid covariance kernel on the image manifold after the embedding. This leads\nto efficient and scalable algorithms for optimization over complex manifolds.\nSimulation study and real data analysis are carried out to demonstrate the\nutilities of our eBO framework by applying the eBO to various optimization\nproblems over manifolds such as the sphere, the Grassmannian, and the manifold\nof positive definite matrices.\n", "date": "2022-12-21", "categories": []}
{"id": "2210.03484", "title": "Multi-objective and multi-fidelity Bayesian optimization of laser-plasma\n  acceleration", "abstract": "  Beam parameter optimization in accelerators involves multiple, sometimes\ncompeting objectives. Condensing these individual objectives into a single\nfigure of merit unavoidably results in a bias towards particular outcomes, in\nabsence of prior knowledge often in a non-desired way. Finding an optimal\nobjective definition then requires operators to iterate over many possible\nobjective weights and definitions, a process that can take many times longer\nthan the optimization itself. A more versatile approach is multi-objective\noptimization, which establishes the trade-off curve or Pareto front between\nobjectives. Here we present the first results on multi-objective Bayesian\noptimization of a simulated laser-plasma accelerator. We find that\nmulti-objective optimization reaches comparable performance to its\nsingle-objective counterparts while allowing for instant evaluation of entirely\nnew objectives. This dramatically reduces the time required to find appropriate\nobjective definitions for new problems. Additionally, our multi-objective,\nmulti-fidelity method reduces the time required for an optimization run by an\norder of magnitude. It does so by dynamically choosing simulation resolution\nand box size, requiring fewer slow and expensive simulations as it learns about\nthe Pareto-optimal solutions from fast low-resolution runs. The techniques\ndemonstrated in this paper can easily be translated into many different\ncomputational and experimental use cases beyond accelerator optimization.\n", "date": "2022-10-07", "categories": []}
{"id": "2209.00055", "title": "Computational design of antimicrobial active surfaces via automated\n  Bayesian optimization", "abstract": "  Biofilms pose significant problems for engineers in diverse fields, such as\nmarine science, bioenergy, and biomedicine, where effective biofilm control is\na long-term goal. The adhesion and surface mechanics of biofilms play crucial\nroles in generating and removing biofilm. Designing customized nano-surfaces\nwith different surface topologies can alter the adhesive properties to remove\nbiofilms more easily and greatly improve long-term biofilm control. To rapidly\ndesign such topologies, we employ individual-based modeling and Bayesian\noptimization to automate the design process and generate different active\nsurfaces for effective biofilm removal. Our framework successfully generated\nideal nano-surfaces for biofilm removal through applied shear and vibration.\nDensely distributed short pillar topography is the optimal geometry to prevent\nbiofilm formation. Under fluidic shearing, the optimal topography is to\nsparsely distribute tall, slim, pillar-like structures. When subjected to\neither vertical or lateral vibrations, thick trapezoidal cones are found to be\noptimal. Optimizing the vibrational loading indicates a small vibration\nmagnitude with relatively low frequencies is more efficient in removing\nbiofilm. Our results provide insights into various engineering fields that\nrequire surface-mediated biofilm control. Our framework can also be applied to\nmore general materials design and optimization.\n", "date": "2022-08-31", "categories": []}
{"id": "2211.15860", "title": "Bayesian Experimental Design for Symbolic Discovery", "abstract": "  This study concerns the formulation and application of Bayesian optimal\nexperimental design to symbolic discovery, which is the inference from\nobservational data of predictive models taking general functional forms. We\napply constrained first-order methods to optimize an appropriate selection\ncriterion, using Hamiltonian Monte Carlo to sample from the prior. A step for\ncomputing the predictive distribution, involving convolution, is computed via\neither numerical integration, or via fast transform methods.\n", "date": "2022-11-29", "categories": []}
{"id": "2211.09888", "title": "Bayesian Optimization of 2D Echocardiography Segmentation", "abstract": "  Bayesian Optimization (BO) is a well-studied hyperparameter tuning technique\nthat is more efficient than grid search for high-cost, high-parameter machine\nlearning problems. Echocardiography is a ubiquitous modality for evaluating\nheart structure and function in cardiology. In this work, we use BO to optimize\nthe architectural and training-related hyperparameters of a previously\npublished deep fully convolutional neural network model for multi-structure\nsegmentation in echocardiography. In a fair comparison, the resulting model\noutperforms this recent state-of-the-art on the annotated CAMUS dataset in both\napical two- and four-chamber echo views. We report mean Dice overlaps of 0.95,\n0.96, and 0.93 on left ventricular (LV) endocardium, LV epicardium, and left\natrium respectively. We also observe significant improvement in derived\nclinical indices, including smaller median absolute errors for LV end-diastolic\nvolume (4.9mL vs. 6.7), end-systolic volume (3.1mL vs. 5.2), and ejection\nfraction (2.6% vs. 3.7); and much tighter limits of agreement, which were\nalready within inter-rater variability for non-contrast echo. These results\ndemonstrate the benefits of BO for echocardiography segmentation over a recent\nstate-of-the-art framework, although validation using large-scale independent\nclinical data is required.\n", "date": "2022-11-17", "categories": []}
{"id": "2211.09678", "title": "Towards Automated Design of Bayesian Optimization via Exploratory\n  Landscape Analysis", "abstract": "  Bayesian optimization (BO) algorithms form a class of surrogate-based\nheuristics, aimed at efficiently computing high-quality solutions for numerical\nblack-box optimization problems. The BO pipeline is highly modular, with\ndifferent design choices for the initial sampling strategy, the surrogate\nmodel, the acquisition function (AF), the solver used to optimize the AF, etc.\nWe demonstrate in this work that a dynamic selection of the AF can benefit the\nBO design. More precisely, we show that already a na\\\"ive random forest\nregression model, built on top of exploratory landscape analysis features that\nare computed from the initial design points, suffices to recommend AFs that\noutperform any static choice, when considering performance over the classic\nBBOB benchmark suite for derivative-free numerical optimization methods on the\nCOCO platform. Our work hence paves a way towards AutoML-assisted, on-the-fly\nBO designs that adjust their behavior on a run-by-run basis.\n", "date": "2022-11-17", "categories": []}
{"id": "2210.01628", "title": "Monte Carlo Tree Search based Variable Selection for High Dimensional\n  Bayesian Optimization", "abstract": "  Bayesian optimization (BO) is a class of popular methods for expensive\nblack-box optimization, and has been widely applied to many scenarios. However,\nBO suffers from the curse of dimensionality, and scaling it to high-dimensional\nproblems is still a challenge. In this paper, we propose a variable selection\nmethod MCTS-VS based on Monte Carlo tree search (MCTS), to iteratively select\nand optimize a subset of variables. That is, MCTS-VS constructs a\nlow-dimensional subspace via MCTS and optimizes in the subspace with any BO\nalgorithm. We give a theoretical analysis of the general variable selection\nmethod to reveal how it can work. Experiments on high-dimensional synthetic\nfunctions and real-world problems (i.e., NAS-bench problems and MuJoCo\nlocomotion tasks) show that MCTS-VS equipped with a proper BO optimizer can\nachieve state-of-the-art performance.\n", "date": "2022-10-04", "categories": []}
{"id": "2207.11451", "title": "Optimization of the Shape of a Hydrokinetic Turbine's Draft Tube and Hub\n  Assembly Using Design-by-Morphing with Bayesian Optimization", "abstract": "  Finding the optimal design of a hydrodynamic or aerodynamic surface is often\nimpossible due to the expense of evaluating the cost functions (say, with\ncomputational fluid dynamics) needed to determine the performances of the flows\nthat the surface controls. In addition, inherent limitations of the design\nspace itself due to imposed geometric constraints, conventional\nparameterization methods, and user bias can restrict {\\it all} of the designs\nwithin a chosen design space regardless of whether traditional optimization\nmethods or newer, data-driven design algorithms with machine learning are used\nto search the design space. We present a 2-pronged attack to address these\ndifficulties: we propose (1) a methodology to create the design space using\nmorphing that we call {\\it Design-by-Morphing} (DbM); and (2) an optimization\nalgorithm to search that space that uses a novel Bayesian Optimization (BO)\nstrategy that we call {\\it Mixed variable, Multi-Objective Bayesian\nOptimization} (MixMOBO). We apply this shape optimization strategy to maximize\nthe power output of a hydrokinetic turbine. Applying these two strategies in\ntandem, we demonstrate that we can create a novel, geometrically-unconstrained,\ndesign space of a draft tube and hub shape and then optimize them\nsimultaneously with a {\\it minimum} number of cost function calls. Our\nframework is versatile and can be applied to the shape optimization of a\nvariety of fluid problems.\n", "date": "2022-07-23", "categories": []}
{"id": "2206.03301", "title": "Recent Advances in Bayesian Optimization", "abstract": "  Bayesian optimization has emerged at the forefront of expensive black-box\noptimization due to its data efficiency. Recent years have witnessed a\nproliferation of studies on the development of new Bayesian optimization\nalgorithms and their applications. Hence, this paper attempts to provide a\ncomprehensive and updated survey of recent advances in Bayesian optimization\nand identify interesting open problems. We categorize the existing work on\nBayesian optimization into nine main groups according to the motivations and\nfocus of the proposed algorithms. For each category, we present the main\nadvances with respect to the construction of surrogate models and adaptation of\nthe acquisition functions. Finally, we discuss the open questions and suggest\npromising future research directions, in particular with regard to\nheterogeneity, privacy preservation, and fairness in distributed and federated\noptimization systems.\n", "date": "2022-06-07", "categories": []}
{"id": "2211.01455", "title": "PI is back! Switching Acquisition Functions in Bayesian Optimization", "abstract": "  Bayesian Optimization (BO) is a powerful, sample-efficient technique to\noptimize expensive-to-evaluate functions. Each of the BO components, such as\nthe surrogate model, the acquisition function (AF), or the initial design, is\nsubject to a wide range of design choices. Selecting the right components for a\ngiven optimization task is a challenging task, which can have significant\nimpact on the quality of the obtained results. In this work, we initiate the\nanalysis of which AF to favor for which optimization scenarios. To this end, we\nbenchmark SMAC3 using Expected Improvement (EI) and Probability of Improvement\n(PI) as acquisition functions on the 24 BBOB functions of the COCO environment.\nWe compare their results with those of schedules switching between AFs. One\nschedule aims to use EI's explorative behavior in the early optimization steps,\nand then switches to PI for a better exploitation in the final steps. We also\ncompare this to a random schedule and round-robin selection of EI and PI. We\nobserve that dynamic schedules oftentimes outperform any single static one. Our\nresults suggest that a schedule that allocates the first 25 % of the\noptimization budget to EI and the last 75 % to PI is a reliable default.\nHowever, we also observe considerable performance differences for the 24\nfunctions, suggesting that a per-instance allocation, possibly learned on the\nfly, could offer significant improvement over the state-of-the-art BO designs.\n", "date": "2022-11-02", "categories": []}
{"id": "2211.00947", "title": "Linear Embedding-based High-dimensional Batch Bayesian Optimization\n  without Reconstruction Mappings", "abstract": "  The optimization of high-dimensional black-box functions is a challenging\nproblem. When a low-dimensional linear embedding structure can be assumed,\nexisting Bayesian optimization (BO) methods often transform the original\nproblem into optimization in a low-dimensional space. They exploit the\nlow-dimensional structure and reduce the computational burden. However, we\nreveal that this approach could be limited or inefficient in exploring the\nhigh-dimensional space mainly due to the biased reconstruction of the\nhigh-dimensional queries from the low-dimensional queries. In this paper, we\ninvestigate a simple alternative approach: tackling the problem in the original\nhigh-dimensional space using the information from the learned low-dimensional\nstructure. We provide a theoretical analysis of the exploration ability.\nFurthermore, we show that our method is applicable to batch optimization\nproblems with thousands of dimensions without any computational difficulty. We\ndemonstrate the effectiveness of our method on high-dimensional benchmarks and\na real-world function.\n", "date": "2022-11-02", "categories": []}
{"id": "2211.01053", "title": "Fantasizing with Dual GPs in Bayesian Optimization and Active Learning", "abstract": "  Gaussian processes (GPs) are the main surrogate functions used for sequential\nmodelling such as Bayesian Optimization and Active Learning. Their drawbacks\nare poor scaling with data and the need to run an optimization loop when using\na non-Gaussian likelihood. In this paper, we focus on `fantasizing' batch\nacquisition functions that need the ability to condition on new fantasized data\ncomputationally efficiently. By using a sparse Dual GP parameterization, we\ngain linear scaling with batch size as well as one-step updates for\nnon-Gaussian likelihoods, thus extending sparse models to greedy batch\nfantasizing acquisition functions.\n", "date": "2022-11-02", "categories": []}
{"id": "2211.00077", "title": "Optimizing Closed-Loop Performance with Data from Similar Systems: A\n  Bayesian Meta-Learning Approach", "abstract": "  Bayesian optimization (BO) has demonstrated potential for optimizing control\nperformance in data-limited settings, especially for systems with unknown\ndynamics or unmodeled performance objectives. The BO algorithm efficiently\ntrades-off exploration and exploitation by leveraging uncertainty estimates\nusing surrogate models. These surrogates are usually learned using data\ncollected from the target dynamical system to be optimized. Intuitively, the\nconvergence rate of BO is better for surrogate models that can accurately\npredict the target system performance. In classical BO, initial surrogate\nmodels are constructed using very limited data points, and therefore rarely\nyield accurate predictions of system performance. In this paper, we propose the\nuse of meta-learning to generate an initial surrogate model based on data\ncollected from performance optimization tasks performed on a variety of systems\nthat are different to the target system. To this end, we employ deep kernel\nnetworks (DKNs) which are simple to train and which comprise encoded Gaussian\nprocess models that integrate seamlessly with classical BO. The effectiveness\nof our proposed DKN-BO approach for speeding up control system performance\noptimization is demonstrated using a well-studied nonlinear system with unknown\ndynamics and an unmodeled performance function.\n", "date": "2022-10-31", "categories": []}
{"id": "2210.17213", "title": "Deep Gaussian Process-based Multi-fidelity Bayesian Optimization for\n  Simulated Chemical Reactors", "abstract": "  New manufacturing techniques such as 3D printing have recently enabled the\ncreation of previously infeasible chemical reactor designs. Optimizing the\ngeometry of the next generation of chemical reactors is important to understand\nthe underlying physics and to ensure reactor feasibility in the real world.\nThis optimization problem is computationally expensive, nonlinear, and\nderivative-free making it challenging to solve. In this work, we apply deep\nGaussian processes (DGPs) to model multi-fidelity coiled-tube reactor\nsimulations in a Bayesian optimization setting. By applying a multi-fidelity\nBayesian optimization method, the search space of reactor geometries is\nexplored through an amalgam of different fidelity simulations which are chosen\nbased on prediction uncertainty and simulation cost, maximizing the use of\ncomputational budget. The use of DGPs provides an end-to-end model for five\ndiscrete mesh fidelities, enabling less computational effort to gain good\nsolutions during optimization. The accuracy of simulations for these five\nfidelities is determined against experimental data obtained from a 3D printed\nreactor configuration, providing insights into appropriate hyper-parameters. We\nhope this work provides interesting insight into the practical use of DGP-based\nmulti-fidelity Bayesian optimization for engineering discovery.\n", "date": "2022-10-31", "categories": []}
{"id": "2209.10715", "title": "Batch Bayesian optimisation via density-ratio estimation with guarantees", "abstract": "  Bayesian optimisation (BO) algorithms have shown remarkable success in\napplications involving expensive black-box functions. Traditionally BO has been\nset as a sequential decision-making process which estimates the utility of\nquery points via an acquisition function and a prior over functions, such as a\nGaussian process. Recently, however, a reformulation of BO via density-ratio\nestimation (BORE) allowed reinterpreting the acquisition function as a\nprobabilistic binary classifier, removing the need for an explicit prior over\nfunctions and increasing scalability. In this paper, we present a theoretical\nanalysis of BORE's regret and an extension of the algorithm with improved\nuncertainty estimates. We also show that BORE can be naturally extended to a\nbatch optimisation setting by recasting the problem as approximate Bayesian\ninference. The resulting algorithms come equipped with theoretical performance\nguarantees and are assessed against other batch and sequential BO baselines in\na series of experiments.\n", "date": "2022-09-22", "categories": []}
{"id": "2210.03283", "title": "Design Amortization for Bayesian Optimal Experimental Design", "abstract": "  Bayesian optimal experimental design is a sub-field of statistics focused on\ndeveloping methods to make efficient use of experimental resources. Any\npotential design is evaluated in terms of a utility function, such as the\n(theoretically well-justified) expected information gain (EIG); unfortunately\nhowever, under most circumstances the EIG is intractable to evaluate. In this\nwork we build off of successful variational approaches, which optimize a\nparameterized variational model with respect to bounds on the EIG. Past work\nfocused on learning a new variational model from scratch for each new design\nconsidered. Here we present a novel neural architecture that allows\nexperimenters to optimize a single variational model that can estimate the EIG\nfor potentially infinitely many designs. To further improve computational\nefficiency, we also propose to train the variational model on a significantly\ncheaper-to-evaluate lower bound, and show empirically that the resulting model\nprovides an excellent guide for more accurate, but expensive to evaluate bounds\non the EIG. We demonstrate the effectiveness of our technique on generalized\nlinear models, a class of statistical models that is widely used in the\nanalysis of controlled experiments. Experiments show that our method is able to\ngreatly improve accuracy over existing approximation strategies, and achieve\nthese results with far better sample efficiency.\n", "date": "2022-10-07", "categories": []}
{"id": "2210.10199", "title": "Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic\n  Reparameterization", "abstract": "  Optimizing expensive-to-evaluate black-box functions of discrete (and\npotentially continuous) design parameters is a ubiquitous problem in scientific\nand engineering applications. Bayesian optimization (BO) is a popular,\nsample-efficient method that leverages a probabilistic surrogate model and an\nacquisition function (AF) to select promising designs to evaluate. However,\nmaximizing the AF over mixed or high-cardinality discrete search spaces is\nchallenging standard gradient-based methods cannot be used directly or\nevaluating the AF at every point in the search space would be computationally\nprohibitive. To address this issue, we propose using probabilistic\nreparameterization (PR). Instead of directly optimizing the AF over the search\nspace containing discrete parameters, we instead maximize the expectation of\nthe AF over a probability distribution defined by continuous parameters. We\nprove that under suitable reparameterizations, the BO policy that maximizes the\nprobabilistic objective is the same as that which maximizes the AF, and\ntherefore, PR enjoys the same regret bounds as the original BO policy using the\nunderlying AF. Moreover, our approach provably converges to a stationary point\nof the probabilistic objective under gradient ascent using scalable, unbiased\nestimators of both the probabilistic objective and its gradient. Therefore, as\nthe number of starting points and gradient steps increase, our approach will\nrecover of a maximizer of the AF (an often-neglected requisite for commonly\nused BO regret bounds). We validate our approach empirically and demonstrate\nstate-of-the-art optimization performance on a wide range of real-world\napplications. PR is complementary to (and benefits) recent work and naturally\ngeneralizes to settings with multiple objectives and black-box constraints.\n", "date": "2022-10-18", "categories": []}
{"id": "2210.08087", "title": "Movement Penalized Bayesian Optimization with Application to Wind Energy\n  Systems", "abstract": "  Contextual Bayesian optimization (CBO) is a powerful framework for sequential\ndecision-making given side information, with important applications, e.g., in\nwind energy systems. In this setting, the learner receives context (e.g.,\nweather conditions) at each round, and has to choose an action (e.g., turbine\nparameters). Standard algorithms assume no cost for switching their decisions\nat every round. However, in many practical applications, there is a cost\nassociated with such changes, which should be minimized. We introduce the\nepisodic CBO with movement costs problem and, based on the online learning\napproach for metrical task systems of Coester and Lee (2019), propose a novel\nrandomized mirror descent algorithm that makes use of Gaussian Process\nconfidence bounds. We compare its performance with the offline optimal sequence\nfor each episode and provide rigorous regret guarantees. We further demonstrate\nour approach on the important real-world application of altitude optimization\nfor Airborne Wind Energy Systems. In the presence of substantial movement\ncosts, our algorithm consistently outperforms standard CBO algorithms.\n", "date": "2022-10-14", "categories": []}
{"id": "2210.06850", "title": "Sample-Then-Optimize Batch Neural Thompson Sampling", "abstract": "  Bayesian optimization (BO), which uses a Gaussian process (GP) as a surrogate\nto model its objective function, is popular for black-box optimization.\nHowever, due to the limitations of GPs, BO underperforms in some problems such\nas those with categorical, high-dimensional or image inputs. To this end,\nrecent works have used the highly expressive neural networks (NNs) as the\nsurrogate model and derived theoretical guarantees using the theory of neural\ntangent kernel (NTK). However, these works suffer from the limitations of the\nrequirement to invert an extremely large parameter matrix and the restriction\nto the sequential (rather than batch) setting. To overcome these limitations,\nwe introduce two algorithms based on the Thompson sampling (TS) policy named\nSample-Then-Optimize Batch Neural TS (STO-BNTS) and STO-BNTS-Linear. To choose\nan input query, we only need to train an NN (resp. a linear model) and then\nchoose the query by maximizing the trained NN (resp. linear model), which is\nequivalently sampled from the GP posterior with the NTK as the kernel function.\nAs a result, our algorithms sidestep the need to invert the large parameter\nmatrix yet still preserve the validity of the TS policy. Next, we derive regret\nupper bounds for our algorithms with batch evaluations, and use insights from\nbatch BO and NTK to show that they are asymptotically no-regret under certain\nconditions. Finally, we verify their empirical effectiveness using practical\nAutoML and reinforcement learning experiments.\n", "date": "2022-10-13", "categories": []}
{"id": "2210.04096", "title": "PropertyDAG: Multi-objective Bayesian optimization of partially ordered,\n  mixed-variable properties for biological sequence design", "abstract": "  Bayesian optimization offers a sample-efficient framework for navigating the\nexploration-exploitation trade-off in the vast design space of biological\nsequences. Whereas it is possible to optimize the various properties of\ninterest jointly using a multi-objective acquisition function, such as the\nexpected hypervolume improvement (EHVI), this approach does not account for\nobjectives with a hierarchical dependency structure. We consider a common use\ncase where some regions of the Pareto frontier are prioritized over others\naccording to a specified $\\textit{partial ordering}$ in the objectives. For\ninstance, when designing antibodies, we would like to maximize the binding\naffinity to a target antigen only if it can be expressed in live cell culture\n-- modeling the experimental dependency in which affinity can only be measured\nfor antibodies that can be expressed and thus produced in viable quantities. In\ngeneral, we may want to confer a partial ordering to the properties such that\neach property is optimized conditioned on its parent properties satisfying some\nfeasibility condition. To this end, we present PropertyDAG, a framework that\noperates on top of the traditional multi-objective BO to impose this desired\nordering on the objectives, e.g. expression $\\rightarrow$ affinity. We\ndemonstrate its performance over multiple simulated active learning iterations\non a penicillin production task, toy numerical problem, and a real-world\nantibody design task.\n", "date": "2022-10-08", "categories": []}
{"id": "2206.13035", "title": "A General Recipe for Likelihood-free Bayesian Optimization", "abstract": "  The acquisition function, a critical component in Bayesian optimization (BO),\ncan often be written as the expectation of a utility function under a surrogate\nmodel. However, to ensure that acquisition functions are tractable to optimize,\nrestrictions must be placed on the surrogate model and utility function. To\nextend BO to a broader class of models and utilities, we propose\nlikelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO\ndirectly models the acquisition function without having to separately perform\ninference with a probabilistic surrogate model. We show that computing the\nacquisition function in LFBO can be reduced to optimizing a weighted\nclassification problem, where the weights correspond to the utility being\nchosen. By choosing the utility function for expected improvement (EI), LFBO\noutperforms various state-of-the-art black-box optimization methods on several\nreal-world optimization problems. LFBO can also effectively leverage composite\nstructures of the objective function, which further improves its regret by\nseveral orders of magnitude.\n", "date": "2022-06-27", "categories": []}
{"id": "2210.03481", "title": "Neighbor Regularized Bayesian Optimization for Hyperparameter\n  Optimization", "abstract": "  Bayesian Optimization (BO) is a common solution to search optimal\nhyperparameters based on sample observations of a machine learning model.\nExisting BO algorithms could converge slowly even collapse when the potential\nobservation noise misdirects the optimization. In this paper, we propose a\nnovel BO algorithm called Neighbor Regularized Bayesian Optimization (NRBO) to\nsolve the problem. We first propose a neighbor-based regularization to smooth\neach sample observation, which could reduce the observation noise efficiently\nwithout any extra training cost. Since the neighbor regularization highly\ndepends on the sample density of a neighbor area, we further design a\ndensity-based acquisition function to adjust the acquisition reward and obtain\nmore stable statistics. In addition, we design a adjustment mechanism to ensure\nthe framework maintains a reasonable regularization strength and density reward\nconditioned on remaining computation resources. We conduct experiments on the\nbayesmark benchmark and important computer vision benchmarks such as ImageNet\nand COCO. Extensive experiments demonstrate the effectiveness of NRBO and it\nconsistently outperforms other state-of-the-art methods.\n", "date": "2022-10-07", "categories": []}
{"id": "2210.02905", "title": "Joint Entropy Search for Multi-objective Bayesian Optimization", "abstract": "  Many real-world problems can be phrased as a multi-objective optimization\nproblem, where the goal is to identify the best set of compromises between the\ncompeting objectives. Multi-objective Bayesian optimization (BO) is a sample\nefficient strategy that can be deployed to solve these vector-valued\noptimization problems where access is limited to a number of noisy objective\nfunction evaluations. In this paper, we propose a novel information-theoretic\nacquisition function for BO called Joint Entropy Search (JES), which considers\nthe joint information gain for the optimal set of inputs and outputs. We\npresent several analytical approximations to the JES acquisition function and\nalso introduce an extension to the batch setting. We showcase the effectiveness\nof this new approach on a range of synthetic and real-world problems in terms\nof the hypervolume and its weighted variants.\n", "date": "2022-10-06", "categories": []}
{"id": "2210.01383", "title": "Generalizing Bayesian Optimization with Decision-theoretic Entropies", "abstract": "  Bayesian optimization (BO) is a popular method for efficiently inferring\noptima of an expensive black-box function via a sequence of queries. Existing\ninformation-theoretic BO procedures aim to make queries that most reduce the\nuncertainty about optima, where the uncertainty is captured by Shannon entropy.\nHowever, an optimal measure of uncertainty would, ideally, factor in how we\nintend to use the inferred quantity in some downstream procedure. In this\npaper, we instead consider a generalization of Shannon entropy from work in\nstatistical decision theory (DeGroot 1962, Rao 1984), which contains a broad\nclass of uncertainty measures parameterized by a problem-specific loss function\ncorresponding to a downstream task. We first show that special cases of this\nentropy lead to popular acquisition functions used in BO procedures such as\nknowledge gradient, expected improvement, and entropy search. We then show how\nalternative choices for the loss yield a flexible family of acquisition\nfunctions that can be customized for use in novel optimization settings.\nAdditionally, we develop gradient-based methods to efficiently optimize our\nproposed family of acquisition functions, and demonstrate strong empirical\nperformance on a diverse set of sequential decision making tasks, including\nvariants of top-$k$ optimization, multi-level set estimation, and sequence\nsearch.\n", "date": "2022-10-04", "categories": []}
{"id": "2210.00476", "title": "Robust Bayesian optimization with reinforcement learned acquisition\n  functions", "abstract": "  In Bayesian optimization (BO) for expensive black-box optimization tasks,\nacquisition function (AF) guides sequential sampling and plays a pivotal role\nfor efficient convergence to better optima. Prevailing AFs usually rely on\nartificial experiences in terms of preferences for exploration or exploitation,\nwhich runs a risk of a computational waste or traps in local optima and\nresultant re-optimization. To address the crux, the idea of data-driven AF\nselection is proposed, and the sequential AF selection task is further\nformalized as a Markov decision process (MDP) and resort to powerful\nreinforcement learning (RL) technologies. Appropriate selection policy for AFs\nis learned from superior BO trajectories to balance between exploration and\nexploitation in real time, which is called reinforcement-learning-assisted\nBayesian optimization (RLABO). Competitive and robust BO evaluations on five\nbenchmark problems demonstrate RL's recognition of the implicit AF selection\npattern and imply the proposal's potential practicality for intelligent AF\nselection as well as efficient optimization in expensive black-box problems.\n", "date": "2022-10-02", "categories": []}
{"id": "2210.00798", "title": "HPC Storage Service Autotuning Using Variational-Autoencoder-Guided\n  Asynchronous Bayesian Optimization", "abstract": "  Distributed data storage services tailored to specific applications have\ngrown popular in the high-performance computing (HPC) community as a way to\naddress I/O and storage challenges. These services offer a variety of specific\ninterfaces, semantics, and data representations. They also expose many tuning\nparameters, making it difficult for their users to find the best configuration\nfor a given workload and platform.\n  To address this issue, we develop a novel variational-autoencoder-guided\nasynchronous Bayesian optimization method to tune HPC storage service\nparameters. Our approach uses transfer learning to leverage prior tuning\nresults and use a dynamically updated surrogate model to explore the large\nparameter search space in a systematic way.\n  We implement our approach within the DeepHyper open-source framework, and\napply it to the autotuning of a high-energy physics workflow on Argonne's Theta\nsupercomputer. We show that our transfer-learning approach enables a more than\n$40\\times$ search speedup over random search, compared with a $2.5\\times$ to\n$10\\times$ speedup when not using transfer learning. Additionally, we show that\nour approach is on par with state-of-the-art autotuning frameworks in speed and\noutperforms them in resource utilization and parallelization capabilities.\n", "date": "2022-10-03", "categories": []}
{"id": "2209.15367", "title": "Efficient computation of the Knowledge Gradient for Bayesian\n  Optimization", "abstract": "  Bayesian optimization is a powerful collection of methods for optimizing\nstochastic expensive black box functions. One key component of a Bayesian\noptimization algorithm is the acquisition function that determines which\nsolution should be evaluated in every iteration. A popular and very effective\nchoice is the Knowledge Gradient acquisition function, however there is no\nanalytical way to compute it. Several different implementations make different\napproximations. In this paper, we review and compare the spectrum of Knowledge\nGradient implementations and propose One-shot Hybrid KG, a new approach that\ncombines several of the previously proposed ideas and is cheap to compute as\nwell as powerful and efficient. We prove the new method preserves theoretical\nproperties of previous methods and empirically show the drastically reduced\ncomputational overhead with equal or improved performance. All experiments are\nimplemented in BOTorch and code is available on github.\n", "date": "2022-09-30", "categories": []}
{"id": "2207.05041", "title": "Parallel Bayesian Optimization of Agent-based Transportation Simulation", "abstract": "  MATSim (Multi-Agent Transport Simulation Toolkit) is an open source\nlarge-scale agent-based transportation planning project applied to various\nareas like road transport, public transport, freight transport, regional\nevacuation, etc. BEAM (Behavior, Energy, Autonomy, and Mobility) framework\nextends MATSim to enable powerful and scalable analysis of urban transportation\nsystems. The agents from the BEAM simulation exhibit 'mode choice' behavior\nbased on multinomial logit model. In our study, we consider eight mode choices\nviz. bike, car, walk, ride hail, driving to transit, walking to transit, ride\nhail to transit, and ride hail pooling. The 'alternative specific constants'\nfor each mode choice are critical hyperparameters in a configuration file\nrelated to a particular scenario under experimentation. We use the\n'Urbansim-10k' BEAM scenario (with 10,000 population size) for all our\nexperiments. Since these hyperparameters affect the simulation in complex ways,\nmanual calibration methods are time consuming. We present a parallel Bayesian\noptimization method with early stopping rule to achieve fast convergence for\nthe given multi-in-multi-out problem to its optimal configurations. Our model\nis based on an open source HpBandSter package. This approach combines hierarchy\nof several 1D Kernel Density Estimators (KDE) with a cheap evaluator\n(Hyperband, a single multidimensional KDE). Our model has also incorporated\nextrapolation based early stopping rule. With our model, we could achieve a 25%\nL1 norm for a large-scale BEAM simulation in fully autonomous manner. To the\nbest of our knowledge, our work is the first of its kind applied to large-scale\nmulti-agent transportation simulations. This work can be useful for surrogate\nmodeling of scenarios with very large populations.\n", "date": "2022-07-11", "categories": []}
{"id": "2209.04340", "title": "Multi-objective hyperparameter optimization with performance uncertainty", "abstract": "  The performance of any Machine Learning (ML) algorithm is impacted by the\nchoice of its hyperparameters. As training and evaluating a ML algorithm is\nusually expensive, the hyperparameter optimization (HPO) method needs to be\ncomputationally efficient to be useful in practice. Most of the existing\napproaches on multi-objective HPO use evolutionary strategies and\nmetamodel-based optimization. However, few methods have been developed to\naccount for uncertainty in the performance measurements. This paper presents\nresults on multi-objective hyperparameter optimization with uncertainty on the\nevaluation of ML algorithms. We combine the sampling strategy of\nTree-structured Parzen Estimators (TPE) with the metamodel obtained after\ntraining a Gaussian Process Regression (GPR) with heterogeneous noise.\nExperimental results on three analytical test functions and three ML problems\nshow the improvement over multi-objective TPE and GPR, achieved with respect to\nthe hypervolume indicator.\n", "date": "2022-09-09", "categories": []}
{"id": "2209.00895", "title": "Optimistic Optimization of Gaussian Process Samples", "abstract": "  Bayesian optimization is a popular formalism for global optimization, but its\ncomputational costs limit it to expensive-to-evaluate functions. A competing,\ncomputationally more efficient, global optimization framework is optimistic\noptimization, which exploits prior knowledge about the geometry of the search\nspace in form of a dissimilarity function. We investigate to which degree the\nconceptual advantages of Bayesian Optimization can be combined with the\ncomputational efficiency of optimistic optimization. By mapping the kernel to a\ndissimilarity, we obtain an optimistic optimization algorithm for the Bayesian\nOptimization setting with a run-time of up to $\\mathcal{O}(N \\log N)$. As a\nhigh-level take-away we find that, when using stationary kernels on objectives\nof relatively low evaluation cost, optimistic optimization can be strongly\npreferable over Bayesian optimization, while for strongly coupled and\nparametric models, good implementations of Bayesian optimization can perform\nmuch better, even at low evaluation cost. We argue that there is a new research\ndomain between geometric and probabilistic search, i.e. methods that run\ndrastically faster than traditional Bayesian optimization, while retaining some\nof the crucial functionality of Bayesian optimization.\n", "date": "2022-09-02", "categories": []}
{"id": "2208.13960", "title": "The case for fully Bayesian optimisation in small-sample trials", "abstract": "  While sample efficiency is the main motive for use of Bayesian optimisation\nwhen black-box functions are expensive to evaluate, the standard approach based\non type II maximum likelihood (ML-II) may fail and result in disappointing\nperformance in small-sample trials. The paper provides three compelling reasons\nto adopt fully Bayesian optimisation (FBO) as an alternative. First, failures\nof ML-II are more commonplace than implied by the existing studies using the\ncontrived settings. Second, FBO is more robust than ML-II, and the price of\nrobustness is almost trivial. Third, FBO has become simple to implement and\nfast enough to be practical. The paper supports the argument using relevant\nexperiments, which reflect the current practice regarding models, algorithms,\nand software platforms. Since the benefits seem to outweigh the costs,\nresearchers should consider adopting FBO for their applications so that they\ncan guard against potential failures that end up wasting precious research\nresources.\n", "date": "2022-08-30", "categories": []}
{"id": "2208.08742", "title": "Bayesian Optimization Augmented with Actively Elicited Expert Knowledge", "abstract": "  Bayesian optimization (BO) is a well-established method to optimize black-box\nfunctions whose direct evaluations are costly. In this paper, we tackle the\nproblem of incorporating expert knowledge into BO, with the goal of further\naccelerating the optimization, which has received very little attention so far.\nWe design a multi-task learning architecture for this task, with the goal of\njointly eliciting the expert knowledge and minimizing the objective function.\nIn particular, this allows for the expert knowledge to be transferred into the\nBO task. We introduce a specific architecture based on Siamese neural networks\nto handle the knowledge elicitation from pairwise queries. Experiments on\nvarious benchmark functions with both simulated and actual human experts show\nthat the proposed method significantly speeds up BO even when the expert\nknowledge is biased compared to the objective function.\n", "date": "2022-08-18", "categories": []}
{"id": "2207.12355", "title": "Developing Optimal Causal Cyber-Defence Agents via Cyber Security\n  Simulation", "abstract": "  In this paper we explore cyber security defence, through the unification of a\nnovel cyber security simulator with models for (causal) decision-making through\noptimisation. Particular attention is paid to a recently published approach:\ndynamic causal Bayesian optimisation (DCBO). We propose that DCBO can act as a\nblue agent when provided with a view of a simulated network and a causal model\nof how a red agent spreads within that network. To investigate how DCBO can\nperform optimal interventions on host nodes, in order to reduce the cost of\nintrusions caused by the red agent. Through this we demonstrate a complete\ncyber-simulation system, which we use to generate observational data for DCBO\nand provide numerical quantitative results which lay the foundations for future\nwork in this space.\n", "date": "2022-07-25", "categories": []}
{"id": "2207.14174", "title": "Bayesian Optimization-Based Beam Alignment for MmWave MIMO Communication\n  Systems", "abstract": "  Due to the very narrow beam used in millimeter wave communication (mmWave),\nbeam alignment (BA) is a critical issue. In this work, we investigate the issue\nof mmWave BA and present a novel beam alignment scheme on the basis of a\nmachine learning strategy, Bayesian optimization (BO). In this context, we\nconsider the beam alignment issue to be a black box function and then use BO to\nfind the possible optimal beam pair. During the BA procedure, this strategy\nexploits information from the measured beam pairs to predict the best beam\npair. In addition, we suggest a novel BO algorithm based on the gradient\nboosting regression tree model. The simulation results demonstrate the spectral\nefficiency performance of our proposed schemes for BA using three different\nsurrogate models. They also demonstrate that the proposed schemes can achieve\nspectral efficiency with a small overhead when compared to the orthogonal match\npursuit (OMP) algorithm and the Thompson sampling-based multi-armed bandit\n(TS-MAB) method.\n", "date": "2022-07-28", "categories": []}
{"id": "2207.08398", "title": "Bayesian Optimization for Macro Placement", "abstract": "  Macro placement is the problem of placing memory blocks on a chip canvas. It\ncan be formulated as a combinatorial optimization problem over sequence pairs,\na representation which describes the relative positions of macros. Solving this\nproblem is particularly challenging since the objective function is expensive\nto evaluate. In this paper, we develop a novel approach to macro placement\nusing Bayesian optimization (BO) over sequence pairs. BO is a machine learning\ntechnique that uses a probabilistic surrogate model and an acquisition function\nthat balances exploration and exploitation to efficiently optimize a black-box\nobjective function. BO is more sample-efficient than reinforcement learning and\ntherefore can be used with more realistic objectives. Additionally, the ability\nto learn from data and adapt the algorithm to the objective function makes BO\nan appealing alternative to other black-box optimization methods such as\nsimulated annealing, which relies on problem-dependent heuristics and\nparameter-tuning. We benchmark our algorithm on the fixed-outline macro\nplacement problem with the half-perimeter wire length objective and demonstrate\ncompetitive performance.\n", "date": "2022-07-18", "categories": []}
{"id": "2206.02437", "title": "Information-theoretic Inducing Point Placement for High-throughput\n  Bayesian Optimisation", "abstract": "  Sparse Gaussian Processes are a key component of high-throughput Bayesian\noptimisation (BO) loops -- an increasingly common setting where evaluation\nbudgets are large and highly parallelised. By using representative subsets of\nthe available data to build approximate posteriors, sparse models dramatically\nreduce the computational costs of surrogate modelling by relying on a small set\nof pseudo-observations, the so-called inducing points, in lieu of the full data\nset. However, current approaches to design inducing points are not appropriate\nwithin BO loops as they seek to reduce global uncertainty in the objective\nfunction. Thus, the high-fidelity modelling of promising and data-dense regions\nrequired for precise optimisation is sacrificed and computational resources are\ninstead wasted on modelling areas of the space already known to be sub-optimal.\nInspired by entropy-based BO methods, we propose a novel inducing point design\nthat uses a principled information-theoretic criterion to select inducing\npoints. By choosing inducing points to maximally reduce both global uncertainty\nand uncertainty in the maximum value of the objective function, we build\nsurrogate models able to support high-precision high-throughput BO.\n", "date": "2022-06-06", "categories": []}
{"id": "2207.03084", "title": "Pre-training helps Bayesian optimization too", "abstract": "  Bayesian optimization (BO) has become a popular strategy for global\noptimization of many expensive real-world functions. Contrary to a common\nbelief that BO is suited to optimizing black-box functions, it actually\nrequires domain knowledge on characteristics of those functions to deploy BO\nsuccessfully. Such domain knowledge often manifests in Gaussian process priors\nthat specify initial beliefs on functions. However, even with expert knowledge,\nit is not an easy task to select a prior. This is especially true for\nhyperparameter tuning problems on complex machine learning models, where\nlandscapes of tuning objectives are often difficult to comprehend. We seek an\nalternative practice for setting these functional priors. In particular, we\nconsider the scenario where we have data from similar functions that allow us\nto pre-train a tighter distribution a priori. To verify our approach in\nrealistic model training setups, we collected a large multi-task hyperparameter\ntuning dataset by training tens of thousands of configurations of\nnear-state-of-the-art models on popular image and text datasets, as well as a\nprotein sequence dataset. Our results show that on average, our method is able\nto locate good hyperparameters at least 3 times more efficiently than the best\ncompeting methods.\n", "date": "2022-07-07", "categories": []}
{"id": "2206.13326", "title": "A penalisation method for batch multi-objective Bayesian optimisation\n  with application in heat exchanger design", "abstract": "  We present HIghly Parallelisable Pareto Optimisation (HIPPO) -- a batch\nacquisition function that enables multi-objective Bayesian optimisation methods\nto efficiently exploit parallel processing resources. Multi-Objective Bayesian\nOptimisation (MOBO) is a very efficient tool for tackling expensive black-box\nproblems. However, most MOBO algorithms are designed as purely sequential\nstrategies, and existing batch approaches are prohibitively expensive for all\nbut the smallest of batch sizes. We show that by encouraging batch diversity\nthrough penalising evaluations with similar predicted objective values, HIPPO\nis able to cheaply build large batches of informative points. Our extensive\nexperimental validation demonstrates that HIPPO is at least as efficient as\nexisting alternatives whilst incurring an order of magnitude lower\ncomputational overhead and scaling easily to batch sizes considerably higher\nthan currently supported in the literature. Additionally, we demonstrate the\napplication of HIPPO to a challenging heat exchanger design problem, stressing\nthe real-world utility of our highly parallelisable approach to MOBO.\n", "date": "2022-06-27", "categories": []}
{"id": "2206.09341", "title": "Bayesian Optimization under Stochastic Delayed Feedback", "abstract": "  Bayesian optimization (BO) is a widely-used sequential method for\nzeroth-order optimization of complex and expensive-to-compute black-box\nfunctions. The existing BO methods assume that the function evaluation\n(feedback) is available to the learner immediately or after a fixed delay. Such\nassumptions may not be practical in many real-life problems like online\nrecommendations, clinical trials, and hyperparameter tuning where feedback is\navailable after a random delay. To benefit from the experimental\nparallelization in these problems, the learner needs to start new function\nevaluations without waiting for delayed feedback. In this paper, we consider\nthe BO under stochastic delayed feedback problem. We propose algorithms with\nsub-linear regret guarantees that efficiently address the dilemma of selecting\nnew function queries while waiting for randomly delayed feedback. Building on\nour results, we also make novel contributions to batch BO and contextual\nGaussian process bandits. Experiments on synthetic and real-life datasets\nverify the performance of our algorithms.\n", "date": "2022-06-19", "categories": []}
{"id": "2206.06872", "title": "On Provably Robust Meta-Bayesian Optimization", "abstract": "  Bayesian optimization (BO) has become popular for sequential optimization of\nblack-box functions. When BO is used to optimize a target function, we often\nhave access to previous evaluations of potentially related functions. This begs\nthe question as to whether we can leverage these previous experiences to\naccelerate the current BO task through meta-learning (meta-BO), while ensuring\nrobustness against potentially harmful dissimilar tasks that could sabotage the\nconvergence of BO. This paper introduces two scalable and provably robust\nmeta-BO algorithms: robust meta-Gaussian process-upper confidence bound\n(RM-GP-UCB) and RM-GP-Thompson sampling (RM-GP-TS). We prove that both\nalgorithms are asymptotically no-regret even when some or all previous tasks\nare dissimilar to the current task, and show that RM-GP-UCB enjoys a better\ntheoretical robustness than RM-GP-TS. We also exploit the theoretical\nguarantees to optimize the weights assigned to individual previous tasks\nthrough regret minimization via online learning, which diminishes the impact of\ndissimilar tasks and hence further enhances the robustness. Empirical\nevaluations show that (a) RM-GP-UCB performs effectively and consistently\nacross various applications, and (b) RM-GP-TS, despite being less robust than\nRM-GP-UCB both in theory and in practice, performs competitively in some\nscenarios with less dissimilar tasks and is more computationally efficient.\n", "date": "2022-06-14", "categories": []}
{"id": "2206.07834", "title": "Efficient Approximation of Expected Hypervolume Improvement using\n  Gauss-Hermite Quadrature", "abstract": "  Many methods for performing multi-objective optimisation of computationally\nexpensive problems have been proposed recently. Typically, a probabilistic\nsurrogate for each objective is constructed from an initial dataset. The\nsurrogates can then be used to produce predictive densities in the objective\nspace for any solution. Using the predictive densities, we can compute the\nexpected hypervolume improvement (EHVI) due to a solution. Maximising the EHVI,\nwe can locate the most promising solution that may be expensively evaluated\nnext. There are closed-form expressions for computing the EHVI, integrating\nover the multivariate predictive densities. However, they require partitioning\nthe objective space, which can be prohibitively expensive for more than three\nobjectives. Furthermore, there are no closed-form expressions for a problem\nwhere the predictive densities are dependent, capturing the correlations\nbetween objectives. Monte Carlo approximation is used instead in such cases,\nwhich is not cheap. Hence, the need to develop new accurate but cheaper\napproximation methods remains. Here we investigate an alternative approach\ntoward approximating the EHVI using Gauss-Hermite quadrature. We show that it\ncan be an accurate alternative to Monte Carlo for both independent and\ncorrelated predictive densities with statistically significant rank\ncorrelations for a range of popular test problems.\n", "date": "2022-06-15", "categories": []}
{"id": "2206.08366", "title": "Scalable First-Order Bayesian Optimization via Structured Automatic\n  Differentiation", "abstract": "  Bayesian Optimization (BO) has shown great promise for the global\noptimization of functions that are expensive to evaluate, but despite many\nsuccesses, standard approaches can struggle in high dimensions. To improve the\nperformance of BO, prior work suggested incorporating gradient information into\na Gaussian process surrogate of the objective, giving rise to kernel matrices\nof size $nd \\times nd$ for $n$ observations in $d$ dimensions. Na\\\"ively\nmultiplying with (resp. inverting) these matrices requires\n$\\mathcal{O}(n^2d^2)$ (resp. $\\mathcal{O}(n^3d^3$)) operations, which becomes\ninfeasible for moderate dimensions and sample sizes. Here, we observe that a\nwide range of kernels gives rise to structured matrices, enabling an exact\n$\\mathcal{O}(n^2d)$ matrix-vector multiply for gradient observations and\n$\\mathcal{O}(n^2d^2)$ for Hessian observations. Beyond canonical kernel\nclasses, we derive a programmatic approach to leveraging this type of structure\nfor transformations and combinations of the discussed kernel classes, which\nconstitutes a structure-aware automatic differentiation algorithm. Our methods\napply to virtually all canonical kernels and automatically extend to complex\nkernels, like the neural network, radial basis function network, and spectral\nmixture kernels without any additional derivations, enabling flexible,\nproblem-dependent modeling while scaling first-order BO to high $d$.\n", "date": "2022-06-16", "categories": []}
{"id": "2206.05988", "title": "High-Dimensional Bayesian Optimization with Constraints: Application to\n  Powder Weighing", "abstract": "  Bayesian optimization works effectively optimizing parameters in black-box\nproblems. However, this method did not work for high-dimensional parameters in\nlimited trials. Parameters can be efficiently explored by nonlinearly embedding\nthem into a low-dimensional space; however, the constraints cannot be\nconsidered. We proposed combining parameter decomposition by introducing\ndisentangled representation learning into nonlinear embedding to consider both\nknown equality and unknown inequality constraints in high-dimensional Bayesian\noptimization. We applied the proposed method to a powder weighing task as a\nusage scenario. Based on the experimental results, the proposed method\nconsiders the constraints and contributes to reducing the number of trials by\napproximately 66% compared to manual parameter tuning.\n", "date": "2022-06-13", "categories": []}
{"id": "2206.02511", "title": "Transfer Learning based Search Space Design for Hyperparameter Tuning", "abstract": "  The tuning of hyperparameters becomes increasingly important as machine\nlearning (ML) models have been extensively applied in data mining applications.\nAmong various approaches, Bayesian optimization (BO) is a successful\nmethodology to tune hyper-parameters automatically. While traditional methods\noptimize each tuning task in isolation, there has been recent interest in\nspeeding up BO by transferring knowledge across previous tasks. In this work,\nwe introduce an automatic method to design the BO search space with the aid of\ntuning history from past tasks. This simple yet effective approach can be used\nto endow many existing BO methods with transfer learning capabilities. In\naddition, it enjoys the three advantages: universality, generality, and\nsafeness. The extensive experiments show that our approach considerably boosts\nBO by designing a promising and compact search space instead of using the\nentire space, and outperforms the state-of-the-arts on a wide range of\nbenchmarks, including machine learning and deep learning tuning tasks, and\nneural architecture search.\n", "date": "2022-06-06", "categories": []}
{"id": "2606.21092", "title": "BASIL: Bayesian Application for Scientific Iteration and Learning", "abstract": "We introduce BASIL, a user-friendly desktop application for process optimization. BASIL employs a Bayesian approach, incorporating special acquisition functions that can be used to solve both single and multi-objective optimization problems. It provides a graphical interface that enables users to input their experimental parameters, optimization objectives, and legacy data. This is then used to build surrogate models, which are coupled with acquisition functions to guide and optimize a process towards a desired objective. To facilitate model building, BASIL provides a variety of predefined surrogate model templates. BASIL can be used to optimize any arbitrary experiment or process with known, user-defined input variables, optimization objectives, and defined output.", "date": "2026-06-19", "categories": []}
{"id": "2606.23662", "title": "Action-BED: Task-Driven Bayesian Experimental Design with Singly Intractable Objectives", "abstract": "Bayesian experimental design (BED) has traditionally been based on maximising expected uncertainty reductions from prior to posterior. A major shortfall of this approach is that it leads to doubly intractable objectives that are difficult to optimise, while customising them to particular downstream tasks of interest can also be difficult. Following first principles decision theory, we demonstrate that BED can alternatively be formulated in terms of an expected future loss (EFL) on downstream actions, providing a simple and naturally task-driven framework. Critically, we then show that all such EFLs can be rearranged into singly intractable objectives that can be jointly optimised with respect to both the design policy and a downstream action policy using stochastic gradients, an approach we refer to as ACTION-BED. This formulation further sidesteps the need for any explicit posterior or marginal likelihood estimation and is naturally implicit, requiring only the ability to sample from the joint model over model parameters and data, and evaluate the downstream loss function. It thus allows design policies to be learned more effectively, efficiently, and simply than existing methods, while providing easy customisation to different downstream tasks and losses.", "date": "2026-06-22", "categories": []}
{"id": "2606.25197", "title": "Efficient Adaptive Data Acquisition via Pretrained Belief Representations", "abstract": "Learning effective policies for adaptive data acquisition remains challenging: posterior-based methods rely on surrogate models and posterior approximations that can be misspecified or biased, while direct policy-learning methods map from historical observations and fail to exploit available model representations, making learning harder. We introduce policy learning with belief representations (POLAR), based on the insight that optimal data acquisition depends on the observation history only through a sufficient belief state. Specifically, POLAR decouples representation learning from policy learning by leveraging pretrained predictive foundation models as belief-state encoders, training a policy head on top of their representations. This yields a simple, unified amortised policy learning framework for Bayesian experimental design, Bayesian optimisation, and active learning, differing only in the task-specific utility used to train the policy. Empirically, we find that POLAR outperforms state-of-the-art amortised methods across diverse tasks while requiring far fewer training samples, demonstrating a significant step in the scalability and efficiency of amortised data acquisition.", "date": "2026-06-23", "categories": []}
{"id": "2606.26657", "title": "Target-Aware Bandit Allocation for Scalable Surrogate Optimization in Chemical Space", "abstract": "Identifying high-utility candidates from massive discrete spaces under expensive evaluations is a recurring challenge across the sciences, with structure-based drug discovery as a prominent example. While surrogate-based optimization can increase sample efficiency by reducing the number of expensive evaluations, modern molecular libraries have reached billions to trillions of compounds, making full-library surrogate inference itself a major computational bottleneck. We introduce BOBa, a bandit-guided surrogate optimization framework that eliminates full-library inference by adaptively allocating computation across partitions of the action space. By treating partitions as arms in a multi-armed bandit, BOBa concentrates inference and evaluations on empirically promising partitions while maintaining principled exploration. Experiments on real-world synthesis-on-demand libraries demonstrate that optimism-under-uncertainty bandits, combined with meaningful action space partitioning, are essential for effective allocation of inference and evaluations. Our findings reveal a tunable tradeoff between screening performance and surrogate inference cost, which supports practical optimization over current libraries, and establishes a viable route to ultra-large library virtual screening.", "date": "2026-06-25", "categories": []}
{"id": "2606.28578", "title": "Surrogate-Gated Generation and Foundation-Model Embeddings for Bayesian Materials Design", "abstract": "Closed-loop materials discovery iterates between proposing candidate structures and evaluating their properties, and property evaluation dominates the cost. In the generative variant, a learned prior proposes candidate crystals and a property oracle scores them; we ask whether a cheap probabilistic surrogate can triage the generator's output, and what such a surrogate must do well. Across three architecturally distinct pretrained diffusion priors (MatterGen, CrystalFlow, ADiT) and two targets (room-temperature heat capacity and bulk modulus), we insert a Gaussian process acquisition gate between structure generation and the oracle in an RL-steered generative workflow. The gate matches or exceeds ungated fine-tuning of the generative model while capping oracle calls at a fixed per-cycle budget. Budget-matched ablations isolate the mechanism. At an identical four-call budget, ranking-based selection outperforms arbitrary selection, confirming that the gain comes from the surrogate's choice; the gate comes within $\\sim$9\\% of exhaustive oracle spending at roughly one-fifth of the calls. A density-functional-theory check of the bulk-modulus discoveries confirms the learned oracle to within 2.5\\% on average and the surrogate's ranking of the generated structures at Spearman $\\rho = 0.94$. A cross-factorial benchmark of surrogate performance spanning mechanical, electronic, and vibrational properties identifies pretrained ORB embeddings with a Gaussian process as the most reliable combination, which we adopt as the building blocks of the proposed workflow. The complete pipeline is released as open-source software.", "date": "2026-06-26", "categories": []}
{"id": "2606.30228", "title": "B3O: Scalable Boltzmann Batch Bayesian Optimization", "abstract": "Modern engineering workflows increasingly rely on massive parallel simulation, driving the need for scalable, large-batch Bayesian Optimization (BO). Existing batch BO methods, however, incur large computational cost or rely on approximations that erode batch diversity. We propose B3O (Boltzmann Batch Bayesian Optimization), a framework that reframes batch generation as a pure sampling problem: drawing samples directly from the Boltzmann distribution defined by the acquisition function avoids the bottlenecks of existing large-batch methods. Theoretically, we prove that queries sampled from this distribution incur only negligible additional regret. Empirically, B3O outperforms existing batch BO methods on standard synthetic benchmarks and adapts robustly across complex applied tasks, including multi-objective electrode design and mixed-variable race car configuration.", "date": "2026-06-29", "categories": []}