Daily Papers

Diffusion Large Language Models (dLLMs) commonly decode responses by proceeding autoregressively across blocks while iteratively denoising multiple tokens within each block. This structure makes block-level policy optimization a natural adaptation of autoregressive policy optimization. However, the exact likelihood of a completed block is intractable because it marginalizes over the intermediate states and reveal orders of the denoising process. To realize the block-level formulation, we construct a prefix-block state and use a single model evaluation to define a factorized one-step surrogate for the block likelihood. The resulting block surrogate ratio is a product of its token surrogate ratios, allowing variation at individual positions to propagate across the entire block before clipping. We therefore introduce Prefix-Block Policy Optimization (PBPO), which preserves block-level conditioning but applies surrogate importance weighting and clipping separately to each token. PBPO further diversifies repeated updates by resampling corrupted views of the prompt and revealed prefix, a design motivated by masked-dLLM pre-training. Under our analysis assumptions, block-product weighting amplifies the variance of gradient contributions relative to token-local weighting. Across two LLaDA-family initializations, six benchmarks, and three generation lengths, PBPO achieves competitive performance against existing dLLM RL methods.

Autoregressive rollout generation is a major computational cost in reinforcement learning for large language models. Reusing each rollout batch for additional learner updates amortizes this cost, but later updates become increasingly off-policy as the learner departs from the behavior policy. At a token position, exact off-policy correction must account for both the current action and the probability of reaching its prefix. The cumulative importance ratio provides this correction, but its product form can produce an unwieldy dynamic range. We study Prefix-Normalized Policy Optimization (PNPO), which replaces the cumulative ratio with the geometric mean of likelihood ratios along each causal prefix, preserving causal-prefix dependence at each position while compressing the log-weight scale. In controlled long-context mathematical reasoning experiments, we induce two off-policy regimes by using one or four policy-update epochs per rollout batch. PNPO does not consistently outperform GSPO with one epoch. With four epochs, it attains the highest observed Avg@32 on each benchmark; the unweighted mean of the three independently selected benchmark peaks is 50.24, 3.00 percentage points above GSPO. Under a matched 2,400-update budget, four-epoch PNPO reaches a final macro Avg@32 of 49.66 after 150 rollout batches, comparable to the 49.56 reached after 600 batches with one epoch. These results provide preliminary evidence that PNPO can be advantageous as training moves further off-policy.

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO's approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

Group Relative Policy Optimization (GRPO) enhances policy learning by computing gradients from relative comparisons among candidate outputs that share a common input prefix. Despite its effectiveness, GRPO introduces substantial computational overhead when processing long shared prefixes, which must be redundantly encoded for each group member. This inefficiency becomes a major scalability bottleneck in long-context learning scenarios. We propose Prefix Grouper, an efficient GRPO training algorithm that eliminates redundant prefix computation via a Shared-Prefix Forward strategy. In particular, by restructuring self-attention into two parts, our method enables the shared prefix to be encoded only once, while preserving full differentiability and compatibility with end-to-end training. We provide both theoretical and empirical evidence that Prefix Grouper is training-equivalent to standard GRPO: it yields identical forward outputs and backward gradients, ensuring that the optimization dynamics and final policy performance remain unchanged. Empirically, our experiments confirm that Prefix Grouper achieves consistent results while significantly reducing the computational cost of training, particularly in long-prefix scenarios. The proposed method is fully plug-and-play: it is compatible with existing GRPO-based architectures and can be seamlessly integrated into current training pipelines as a drop-in replacement, requiring no structural modifications and only minimal changes to input construction and attention computation. Prefix Grouper enables the use of larger group sizes under the same computational budget, thereby improving the scalability of GRPO to more complex tasks and larger models. Code is now available at https://github.com/johncaged/PrefixGrouper

Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.

Group Relative Policy Optimization (GRPO) assigns a single scalar advantage to all tokens in a completion. For structured generations with explicit segments and objectives, this couples unrelated reward signals across segments, leading to objective interference and misattributed credit. We propose Blockwise Advantage Estimation, a family of GRPO-compatible methods that assigns each objective its own advantage and applies it only to the tokens in the corresponding text block, reducing reliance on hand-designed scalar rewards and scaling naturally to additional objectives. A key challenge is estimating advantages for later blocks whose rewards are conditioned on sampled prefixes; standard unbiased approaches require expensive nested rollouts from intermediate states. Concretely, we introduce an Outcome-Conditioned Baseline that approximates intermediate state values using only within-group statistics by stratifying samples according to a prefix-derived intermediate outcome. On math tasks with uncertainty estimation, our method mitigates reward interference, is competitive with a state-of-the-art reward-designed approach, and preserves test-time gains from confidence-weighted ensembling. More broadly, it provides a modular recipe for optimizing sequential objectives in structured generations without additional rollouts.

We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advantage signal as groups become uniformly correct. Process reward models (PRM) offer richer supervision, but directly using PRM scores causes reward hacking, where models exploit verbosity to inflate scores while accuracy collapses. PAPO resolves both by composing the advantage from an outcome component Aout, derived from ORM and normalized over all responses, and a process component Aproc, derived from a rubric-based PRM and normalized exclusively among correct responses. This decoupled design ensures that Aout anchors training on correctness while Aproc differentiates reasoning quality without distorting the outcome signal. Experiments across multiple model scales and six benchmarks demonstrate that PAPO consistently outperforms ORM, reaching 51.3% vs.\ 46.3% on OlympiadBench while continuing to improve as ORM plateaus and declines.

Reinforcement learning (RL) has emerged as a powerful framework for improving the reasoning capabilities of large language models (LLMs). However, most existing RL approaches rely on sparse outcome rewards, which fail to credit correct intermediate steps in partially successful solutions. Process reward models (PRMs) offer fine-grained step-level supervision, but their scores are often noisy and difficult to evaluate. As a result, recent PRM benchmarks focus on a more objective capability: detecting the first incorrect step in a reasoning path. However, this evaluation target is misaligned with how PRMs are typically used in RL, where their step-wise scores are treated as raw rewards to maximize. To bridge this gap, we propose Verifiable Prefix Policy Optimization (VPPO), which uses PRMs only to localize the first error during RL. Given an incorrect rollout, VPPO partitions the trajectory into a verified correct prefix and an erroneous suffix based on the first error, rewarding the former while applying targeted penalties only after the detected mistake. This design yields stable, interpretable learning signals and improves credit assignment. Across multiple reasoning benchmarks, VPPO consistently outperforms sparse-reward RL and prior PRM-guided baselines on both Pass@1 and Pass@K.

Large language models are increasingly trained as heterogeneous systems spanning multiple domains, expert partitions, and agentic pipelines, yet prevalent proximal objectives operate at a single scale and lack a principled mechanism for coupling token-level, trajectory-level, and higher-level hierarchical stability control. To bridge this gap, we derive the Aggregational Policy Censoring Objective (APC-Obj), the first exact unconstrained reformulation of sample-based TV-TRPO, establishing that clipping-based surrogate design and trust-region optimization are dual formulations of the same problem. Building on this foundation, we develop Fiber Bundle Gating (FBG), an algebraic framework that organizes sampled RL data as a fiber bundle and decomposes ratio gating into a base-level gate on trajectory aggregates and a fiber-level gate on per-token residuals, with provable first-order agreement with the true RL objective near on-policy. From APC-Obj and FBG we derive Fibration Policy Optimization (or simply, FiberPO), a concrete objective whose Jacobian is block-diagonal over trajectories, reduces to identity at on-policy, and provides better update direction thus improving token efficiency. The compositional nature of the framework extends beyond the trajectory-token case: fibrations compose algebraically into a Fibration Gating Hierarchy (FGH) that scales the same gating mechanism to arbitrary hierarchical depth without new primitives, as demonstrated by FiberPO-Domain, a four-level instantiation with independent trust-region budgets at the domain, prompt group, trajectory, and token levels. Together, these results connect the trust-region theory, a compositional algebraic structure, and practical multi-scale stability control into a unified framework for LLM policy optimization.

Latent diffusion models are the state-of-the-art for synthetic image generation. To align these models with human preferences, training the models using reinforcement learning on human feedback is crucial. Black et. al 2024 introduced denoising diffusion policy optimisation (DDPO), which accounts for the iterative denoising nature of the generation by modelling it as a Markov chain with a final reward. As the reward is a single value that determines the model's performance on the entire image, the model has to navigate a very sparse reward landscape and so requires a large sample count. In this work, we extend the DDPO by presenting the Pixel-wise Policy Optimisation (PXPO) algorithm, which can take feedback for each pixel, providing a more nuanced reward to the model.

A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation in each training step. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, the forward computational graphs of all MC samples need to be retained for the gradient computation of non-linear terms in the RL objective, resulting in significant memory overhead. This constraint restricts feasible sample sizes, leading to imprecise likelihood approximations and ultimately distorting the RL objective. To overcome this limitation, we propose Boundary-Guided Policy Optimization (BGPO), a memory-efficient RL algorithm that maximizes a specially constructed lower bound of the ELBO-based objective. This lower bound is carefully designed to satisfy two key properties: (1) Linearity: it is formulated in a linear sum where each term depends only on a single MC sample, thereby enabling gradient accumulation across samples and ensuring constant memory usage; (2) Equivalence: Both the value and gradient of this lower bound are equal to those of the ELBO-based objective in on-policy training, making it also an effective approximation for the original RL objective. These properties allow BGPO to adopt a large MC sample size, resulting in more accurate likelihood approximations and improved RL objective estimation, which in turn leads to enhanced performance. Experiments show that BGPO significantly outperforms previous RL algorithms for dLLMs in math problem solving, code generation, and planning tasks.

This paper presents Post-Decision Proximal Policy Optimization (PDPPO), a novel variation of the leading deep reinforcement learning method, Proximal Policy Optimization (PPO). The PDPPO state transition process is divided into two steps: a deterministic step resulting in the post-decision state and a stochastic step leading to the next state. Our approach incorporates post-decision states and dual critics to reduce the problem's dimensionality and enhance the accuracy of value function estimation. Lot-sizing is a mixed integer programming problem for which we exemplify such dynamics. The objective of lot-sizing is to optimize production, delivery fulfillment, and inventory levels in uncertain demand and cost parameters. This paper evaluates the performance of PDPPO across various environments and configurations. Notably, PDPPO with a dual critic architecture achieves nearly double the maximum reward of vanilla PPO in specific scenarios, requiring fewer episode iterations and demonstrating faster and more consistent learning across different initializations. On average, PDPPO outperforms PPO in environments with a stochastic component in the state transition. These results support the benefits of using a post-decision state. Integrating this post-decision state in the value function approximation leads to more informed and efficient learning in high-dimensional and stochastic environments.

We introduce Diffusion Policy Policy Optimization, DPPO, an algorithmic framework including best practices for fine-tuning diffusion-based policies (e.g. Diffusion Policy) in continuous control and robot learning tasks using the policy gradient (PG) method from reinforcement learning (RL). PG methods are ubiquitous in training RL policies with other policy parameterizations; nevertheless, they had been conjectured to be less efficient for diffusion-based policies. Surprisingly, we show that DPPO achieves the strongest overall performance and efficiency for fine-tuning in common benchmarks compared to other RL methods for diffusion-based policies and also compared to PG fine-tuning of other policy parameterizations. Through experimental investigation, we find that DPPO takes advantage of unique synergies between RL fine-tuning and the diffusion parameterization, leading to structured and on-manifold exploration, stable training, and strong policy robustness. We further demonstrate the strengths of DPPO in a range of realistic settings, including simulated robotic tasks with pixel observations, and via zero-shot deployment of simulation-trained policies on robot hardware in a long-horizon, multi-stage manipulation task. Website with code: diffusion-ppo.github.io

Reinforcement learning with verifiable rewards (RLVR) has become standard for improving LLM reasoning. However, existing PPO-style trust-region mechanisms remain position-agnostic by enforcing uniform thresholds across all tokens independently. This pointwise treatment conflicts with autoregressive generation in two critical ways. First, uniform thresholds ignore autoregressive asymmetry. Early-stage deviations produce compounding sequence-level drift, causing static thresholds to under-regulate early divergence and excessively constrain late-stage exploration. Second, evaluating token-level divergence in isolation overlooks cumulative prefix drift, granting the same divergence allowance regardless of how far the conditioning history has already deviated from the rollout policy. To address this limitation, we propose CPPO (Cumulative Prefix-divergence Policy Optimization), a token-level masking rule that aligns updates with a finite-horizon policy-improvement bound via two coupled mechanisms. First, a position-weighted threshold imposes stricter limits at early positions whose effects persist longer, relaxing constraints for late-stage tokens. Second, a cumulative prefix budget tracks historical deviations, dynamically restricting further token-level deviation to prevent compounding errors along the prefix. Empirically, CPPO enhances training stability and significantly improves reasoning accuracy across various model scales.

The exploration-exploitation (EE) trade-off is a central challenge in reinforcement learning (RL) for large language models (LLMs). With Group Relative Policy Optimization (GRPO), training tends to be exploitation driven: entropy decreases monotonically, samples convergence, and exploration fades. Most existing fixes are sample-centric: they seek or bonus rare samples, assuming exploration comes from novel trajectories and tokens. These heuristics depend on the "luck" of informative samples, lack principled control of the policy, and often yield limited or inconsistent gains. In this work, we are the first to introduce a distribution-centric perspective for RL, in which exploration is always guided by a "better" target distribution, and reveal that a policy's ability to resist entropy collapse is governed by the distribution itself rather than individual samples. Building on this insight, we propose Distribution-Centric Policy Optimization (DCPO), which reformulates entropy regulation as distribution-level regularization. DCPO achieves controllable entropy fully on-policy without sampling from external distributions, enabling efficient exploration while maintaining training stability. Across multiple models and seven benchmarks, DCPO improves over GRPO by about 20\% on average. Overall, DCPO replaces sample-level heuristics with distribution-level principles, offering a theoretically grounded and flexible framework for controllable exploration and a stronger EE trade-off. The code is available in https://github.com/597358816/DCPO.

Proximal constraints are fundamental to the stability of the Large Language Model reinforcement learning. While the canonical clipping mechanism in PPO serves as an efficient surrogate for trust regions, we identify a critical bottleneck: fixed bounds strictly constrain the upward update margin of low-probability actions, disproportionately suppressing high-advantage tail strategies and inducing rapid entropy collapse. To address this, we introduce Band-constrained Policy Optimization (BandPO). BandPO replaces canonical clipping with Band, a unified theoretical operator that projects trust regions defined by f-divergences into dynamic, probability-aware clipping intervals. Theoretical analysis confirms that Band effectively resolves this exploration bottleneck. We formulate this mapping as a convex optimization problem, guaranteeing a globally optimal numerical solution while deriving closed-form solutions for specific divergences. Extensive experiments across diverse models and datasets demonstrate that BandPO consistently outperforms canonical clipping and Clip-Higher, while robustly mitigating entropy collapse.

Trust Region Policy Optimization (TRPO) is a popular and empirically successful policy search algorithm in reinforcement learning (RL). It iteratively solved the surrogate problem which restricts consecutive policies to be close to each other. TRPO is an on-policy algorithm. On-policy methods bring many benefits, like the ability to gauge each resulting policy. However, they typically discard all the knowledge about the policies which existed before. In this work, we use a replay buffer to borrow from the off-policy learning setting to TRPO. Entropy regularization is usually used to improve policy optimization in reinforcement learning. It is thought to aid exploration and generalization by encouraging more random policy choices. We add an Entropy regularization term to advantage over π, accumulated over time steps, in TRPO. We call this update EnTRPO. Our experiments demonstrate EnTRPO achieves better performance for controlling a Cart-Pole system compared with the original TRPO

Reinforcement learning (RL) has recently become the core paradigm for aligning and strengthening large language models (LLMs). Yet, applying RL in off-policy settings--where stale data from past policies are used for training--improves sample efficiency, but remains challenging: policy entropy declines sharply, optimization often becomes unstable and may even collapse. Through theoretical and empirical analysis, we identify two key insights: (i) an imbalance in optimization, where negative-advantage samples dominate the policy gradient, suppressing useful behaviors and risking gradient explosions; and (ii) the derived Entropy-Clip Rule, which reveals that the fixed clipping mechanism in PPO-like objectives systematically blocks entropy-increasing updates, thereby driving the policy toward over-exploitation at the expense of exploration. Building on these insights, we propose BAlanced Policy Optimization with Adaptive Clipping (BAPO), a simple yet effective method that dynamically adjusts clipping bounds to adaptively re-balance positive and negative contributions, preserve entropy, and stabilize RL optimization. Across diverse off-policy scenarios--including sample replay and partial rollout--BAPO achieves fast, stable, and data-efficient training. On AIME 2024 and AIME 2025 benchmarks, our 7B BAPO model surpasses open-source counterparts such as SkyWork-OR1-7B, while our 32B BAPO model not only achieves state-of-the-art results among models of the same scale but also outperforms leading proprietary systems like o3-mini and Gemini-2.5-Flash-Thinking.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for enhancing the reasoning capabilities of Large Language Models (LLMs). However, dominant approaches like Group Relative Policy Optimization (GRPO) face critical stability challenges: they suffer from high estimator variance under computational constraints (small group sizes) and vanishing gradient signals in saturated failure regimes where all responses yield identical zero rewards. To address this, we propose Empirical Bayes Policy Optimization (EBPO), a novel framework that regularizes local group-based baselines by borrowing strength from the policy's accumulated global statistics. Instead of estimating baselines in isolation, EBPO employs a shrinkage estimator that dynamically balances local group statistics with a global prior updated via Welford's online algorithm. Theoretically, we demonstrate that EBPO guarantees strictly lower Mean Squared Error (MSE), bounded entropy decay, and non-vanishing penalty signals in failure scenarios compared to GRPO. Empirically, EBPO consistently outperforms GRPO and other established baselines across diverse benchmarks, including AIME and OlympiadBench. Notably, EBPO exhibits superior training stability, achieving high-performance gains even with small group sizes, and benefits significantly from difficulty-stratified curriculum learning.

Offline reinforcement learning (RL) is a challenging setting where existing off-policy actor-critic methods perform poorly due to the overestimation of out-of-distribution state-action pairs. Thus, various additional augmentations are proposed to keep the learned policy close to the offline dataset (or the behavior policy). In this work, starting from the analysis of offline monotonic policy improvement, we get a surprising finding that some online on-policy algorithms are naturally able to solve offline RL. Specifically, the inherent conservatism of these on-policy algorithms is exactly what the offline RL method needs to overcome the overestimation. Based on this, we propose Behavior Proximal Policy Optimization (BPPO), which solves offline RL without any extra constraint or regularization introduced compared to PPO. Extensive experiments on the D4RL benchmark indicate this extremely succinct method outperforms state-of-the-art offline RL algorithms. Our implementation is available at https://github.com/Dragon-Zhuang/BPPO.

Hybrid training methods for large language models combine supervised fine tuning (SFT) on expert demonstrations with reinforcement learning (RL) on model rollouts, typically at the sample level. We propose Entropy Gated Selective Policy Optimization (EGSPO), a three stage framework that extends sample level mixing with token level gradient modulation. Stage 1, SFT expert learning, establishes a reliable warm up policy using expert demonstrations with a pure SFT loss. Stage 2, RL rollout generation, samples trajectories from the current policy and computes per token predictive entropy. Stage 3, the EGSPO mechanism, applies entropy gated gradient allocation: a predictive entropy module routes high entropy tokens to full PPO updates to encourage exploration, and low entropy tokens to attenuated PPO updates to reduce variance and preserve knowledge. Critically, both branches incorporate the advantage function A_t, ensuring that incorrect trajectories receive consistent negative learning signals and preventing reinforcement of confident errors. EGSPO achieves consistent improvements on mathematical reasoning benchmarks, with gains of 3.8 percent on AIME and 2.9 percent on MATH over the CHORD phi baseline, while incurring only 3.4 percent additional computational overhead.

Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old sampling FLOPs (from prior inference or RL training) in the form of off-policy traces. Standard off-policy methods supervise against off-policy data, causing instabilities during RL optimization. We introduce PrefixRL, where we condition on the prefix of successful off-policy traces and run on-policy RL to complete them, side-stepping off-policy instabilities. PrefixRL boosts the learning signal on hard problems by modulating the difficulty of the problem through the off-policy prefix length. We prove that the PrefixRL objective is not only consistent with the standard RL objective but also more sample efficient. Empirically, we discover back-generalization: training only on prefixed problems generalizes to out-of-distribution unprefixed performance, with learned strategies often differing from those in the prefix. In our experiments, we source the off-policy traces by rejection sampling with the base model, creating a self-improvement loop. On hard reasoning problems, PrefixRL reaches the same training reward 2x faster than the strongest baseline (SFT on off-policy data then RL), even after accounting for the compute spent on the initial rejection sampling, and increases the final reward by 3x. The gains transfer to held-out benchmarks, and PrefixRL is still effective when off-policy traces are derived from a different model family, validating its flexibility in practical settings.

Group Relative Policy Optimization (GRPO) stalls on a model's hardest problems: when no rollout in a group succeeds, the group-relative advantages vanish and the problem contributes no gradient, wasting the frontier examples we most want to learn from. Prepending a correct prefix of a reference solution raises the success rate, making prefix length a continuous knob on difficulty. Concurrent methods set the knob once; AdaPrefix-GRPO turns it into a feedback controller: throughout training it adjusts how much of the solution each problem gets, holding its success rate near 50%, where GRPO's gradient signal is largest, then withdraws the assistance entirely, so the deployed model solves problems unaided. On hard math, at matched training FLOPs, it more than doubles GRPO's accuracy on held-out problems from the training distribution for a 0.6B model (2.1x), with 1.6x on Qwen3-1.7B and 1.7x on AIME, while roughly halving trace length. The method is implemented in data preparation plus a loss mask on prefix tokens; the trainer is otherwise stock. The smaller the model, the larger the gain.

Block Diffusion Models (BDMs) support parallel generation, flexible-length output, and KV caching, making them promising for efficient document parsing. However, existing BDMs bind denoising and cache commitment to fixed block boundaries: parallelism shrinks during intra-block denoising, while generated tokens cannot be cached until the whole block is completed. Moreover, intra-block bidirectional denoising conflicts with inter-block autoregression, creating inconsistent information flow that can challenge structure-sensitive recognition. We propose the Prefix-Adaptive Block Diffusion Model (PA-BDM), which replaces intra-block bidirectional denoising with causal denoising from prefix to suffix and treats the block size as a maximum candidate range rather than a fixed commitment unit. PA-BDM uses Confidence-gated Structural Loss (CSL) to build low-entropy prefixes before extending training to longer continuations. During inference, Progressive Prefix Commitment (PPC) then dynamically commits the longest reliable prefix into the KV cache and resets the next candidate range from the updated prefix, restoring a large parallel decoding space at each step. Experiments show that the 3B PA-BDM achieves higher recognition scores on several benchmarks and improves inference throughput by 71.6\% over the 2.5B MinerU-Diffusion.

The study of decentralized learning or independent learning in cooperative multi-agent reinforcement learning has a history of decades. Recently empirical studies show that independent PPO (IPPO) can obtain good performance, close to or even better than the methods of centralized training with decentralized execution, in several benchmarks. However, decentralized actor-critic with convergence guarantee is still open. In this paper, we propose decentralized policy optimization (DPO), a decentralized actor-critic algorithm with monotonic improvement and convergence guarantee. We derive a novel decentralized surrogate for policy optimization such that the monotonic improvement of joint policy can be guaranteed by each agent independently optimizing the surrogate. In practice, this decentralized surrogate can be realized by two adaptive coefficients for policy optimization at each agent. Empirically, we compare DPO with IPPO in a variety of cooperative multi-agent tasks, covering discrete and continuous action spaces, and fully and partially observable environments. The results show DPO outperforms IPPO in most tasks, which can be the evidence for our theoretical results.

We investigate a narrow but common failure mode of GRPO-style reinforcement learning in the context of sparse verifiable rewards: early updates contain more responses with negative advantages than those with positive advantages, while response-level length normalization ties the magnitude of the update to the length of the output. We propose Hysteretic Policy Optimization (HPO), a minimal modification of GRPO that reduces the weight of negative-advantage updates and replaces per-response length normalization with mean-length normalization. We further introduce Adaptive HPO (A-HPO), which sets the hysteretic weight based on batch-level advantage-sign statistics, thereby removing the need for tuning a fixed hysteretic weight. In our TeleLogs and Countdown experiments, A-HPO improves the reward per update compared to GRPO, with the largest gains in early sparse reward regimes. On TeleLogs, A-HPO achieves a final reward of 0.84, outperforming SAPO by 5%, GSPO by 11%, and GRPO by 15%, while maintaining a comparable response-length. On Countdown, A-HPO achieves the largest gains in initial and most difficult configurations across 1.5B-7B models. Ablation studies on the hysteretic weight show that the gains of A-HPO come from better balancing the contributions of positive and negative advantages compared to positive-only or fully symmetric updates.

Large reasoning models achieve remarkable performance through extensive chain-of-thought generation, yet exhibit significant computational inefficiency by applying uniform reasoning strategies regardless of problem complexity. We present Hierarchical Budget Policy Optimization (HBPO), a reinforcement learning framework that enables models to learn problem-specific reasoning depths without sacrificing capability. HBPO addresses the fundamental challenge of exploration space collapse in efficiency-oriented training, where penalties on long output length systematically bias models away from necessary long reasoning paths. Through hierarchical budget exploration, our approach partitions rollout samples into multiple subgroups with distinct token budgets, aiming to enable efficient resource allocation while preventing degradation of capability. We introduce differentiated reward mechanisms that create budget-aware incentives aligned with the complexity of the problem, allowing models to discover natural correspondences between task requirements and computational effort. Extensive experiments demonstrate that HBPO reduces average token usage by up to 60.6% while improving accuracy by 3.14% across four reasoning benchmarks. Unlike existing methods that impose external constraints or rely on discrete mode selection, HBPO exhibits emergent adaptive behavior where models automatically adjust reasoning depth based on problem complexity. Our results suggest that reasoning efficiency and capability are not inherently conflicting, and can be simultaneously optimized through appropriately structured hierarchical training that preserves exploration diversity.

Reinforcement learning has emerged as an effective paradigm for enhancing the mathematical reasoning capabilities of large language models. Among existing policy optimization methods, Proximal Policy Optimization (PPO) remains particularly appealing because its learned critic can, in principle, provide token-level credit assignment. However, in mathematical reasoning tasks characterized by long reasoning horizons and sparse outcome rewards, reliable token-level credit assignment remains challenging. The standard critic often fails to accurately evaluate intermediate reasoning states, resulting in noisy advantage estimates and suboptimal policy updates. In this paper, we propose ReDiPPO, a Reference-guided and Discrepancy-aware PPO framework for mathematical reasoning. ReDiPPO introduces a reference-guided critic that uses reference answers as training-time privileged signals to provide more accurate value estimation. Meanwhile, it retains a standard critic and quantifies the token-level reference-standard discrepancy between the standard value estimate and the reference-guided value estimate. This discrepancy serves as an indicator of difficult reasoning states and is used to reweight the corresponding token-level advantages during PPO optimization. Extensive experiments on diverse mathematical reasoning benchmarks demonstrate that ReDiPPO improves value-estimation accuracy and consistently outperforms strong policy optimization baselines, including PPO, DAPO, and GSPO, in final reasoning performance. Our code is available on https://github.com/cii030/ReDiPPO.

Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.

Multi-objective reinforcement learning (MORL) seeks to learn policies that balance multiple, often conflicting objectives. Although a single preference-conditioned policy is the most flexible and scalable solution, existing approaches remain brittle in practice, frequently failing to recover complete Pareto fronts. We show that this failure stems from two structural issues in current methods: destructive gradient interference caused by premature scalarization and representational collapse across the preference space. We introduce D^3PO, a PPO-based framework that reorganizes multi-objective policy optimization to address these issues directly. D^3PO preserves per-objective learning signals through a decomposed optimization pipeline and integrates preferences only after stabilization, enabling reliable credit assignment. In addition, a scaled diversity regularizer enforces sensitivity of policy behavior to preference changes, preventing collapse. Across standard MORL benchmarks, including high-dimensional and many-objective control tasks, D^3PO consistently discovers broader and higher-quality Pareto fronts than prior single- and multi-policy methods, matching or exceeding state-of-the-art hypervolume and expected utility while using a single deployable policy.

Group relative policy optimization for reinforcement learning with verifiable rewards (RLVR) typically uses a fixed importance-sampling (IS) ratio clipping boundary across all rollouts. We identify a key limitation: rare correct rollouts on harder problems and abundant correct rollouts on easier problems are clipped at comparable rates, despite contributing very different learning signals. Rollouts with low group success exhibit larger IS ratios and carry stronger gradient signal for exploration and solving new problems, yet are disproportionately suppressed by fixed clipping. To address this, we propose Group Adaptive Clipping Policy Optimization (GAPO), a plug-in modification to GRPO methods that adapts the clipping boundary to the rollout advantage. GAPO is motivated by a reverse-KL trust-region perspective, which suggests that rollouts with larger learning signal should receive proportionally greater update headroom. GAPO requires no reward shaping and preserves the standard PPO/GSPO surrogate while adapting only the clipping threshold. Across Qwen and Llama models, GAPO consistently improves both Pass@1 and Pass@k over fixed clipping and advantage-shaping baselines on math reasoning and coding benchmarks where the pass rates by the base model are relatively low.

Recent approaches to reinforcement learning (RL) post-training for large language models increasingly remove the critic to reduce training instability and memory overhead. Even where a critic is trained, it is discarded once training ends, although it has learned to predict outcomes. We revisit this trend and show that a pretrained critic's ability to predict future outcomes can make it a valuable asset for efficient long-horizon reasoning. First, we find that instability in critic-based RL for long chain-of-thought reasoning is largely an optimization artifact: keeping policy updates small and low in variance restores stable convergence. Second, a well-pretrained critic estimates the posterior probability of eventual success from later trajectory states and unfinished prefixes. Its predictions provide outcome-derived, dense, per-prefix learning signals that, during policy optimization, require neither completed rollouts, step-level annotations, nor external reward labels. Building on this insight, we introduce Reward-Free Policy Optimization (RFPO), which repurposes a single calibrated, frozen critic as a rollout-level reward, a value baseline for generalized advantage estimation, and a success forecaster for unfinished prefixes. We further show that binarizing the debiased score stops the policy from exploiting the critic's length bias. Binarized, RFPO matches supervised PPO without a single label in the training loop, while cutting compute and memory overhead. This makes RFPO well suited to long-horizon reasoning tasks, where outcomes arrive late and generation dominates cost: because rollouts can be rewarded before they finish, training no longer has to pay for waiting on every trajectory to complete. Our findings challenge the prevailing critic-free paradigm and establish critic-based, reward-free optimization as a scalable and computationally efficient path for LLM post-training.

Recent advancements in reinforcement learning from human feedback have shown that utilizing fine-grained token-level reward models can substantially enhance the performance of Proximal Policy Optimization (PPO) in aligning large language models. However, it is challenging to leverage such token-level reward as guidance for Direct Preference Optimization (DPO), since DPO is formulated as a sequence-level bandit problem. To address this challenge, this work decomposes the sequence-level PPO into a sequence of token-level proximal policy optimization problems and then frames the problem of token-level PPO with token-level reward guidance, from which closed-form optimal token-level policy and the corresponding token-level reward can be derived. Using the obtained reward and Bradley-Terry model, this work establishes a framework of computable loss functions with token-level reward guidance for DPO, and proposes a practical reward guidance based on the induced DPO reward. This formulation enables different tokens to exhibit varying degrees of deviation from reference policy based on their respective rewards. Experiment results demonstrate that our method achieves substantial performance improvements over DPO, with win rate gains of up to 7.5 points on MT-Bench, 6.2 points on AlpacaEval 2, and 4.3 points on Arena-Hard. Code is available at https://github.com/dvlab-research/TGDPO.

Reinforcement learning (RL) has become a powerful paradigm for optimizing large language models (LLMs) to handle complex reasoning tasks. A core challenge in this process lies in managing policy entropy, which reflects the balance between exploration and exploitation during training. Existing methods, such as proximal policy optimization (PPO) and its variants, discard valuable gradient signals from low-probability tokens due to the clipping mechanism. We systematically analyze the entropy dynamics and reveal that these clipped tokens play a critical yet overlooked role in regulating entropy evolution. We propose Controlling Entropy via Gradient-Preserving Policy Optimization (CE-GPPO), a novel algorithm that reintroduces gradients from clipped tokens in native PPO in a gentle and bounded manner. By controlling the magnitude of gradients from tokens outside the clipping interval, CE-GPPO is able to achieve an exploration-exploitation trade-off. We provide theoretical justification and empirical evidence showing that CE-GPPO effectively mitigates entropy instability. Extensive experiments on mathematical reasoning benchmarks show that CE-GPPO consistently outperforms strong baselines across different model scales.

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

As LLMs advance, post-training reinforcement learning (RL) increasingly relies on multi-dimensional rewards to cultivate comprehensive capabilities. This shift demands new algorithms capable of optimizing diverse and potentially competing objectives simultaneously. To address this, existing methods such as Group reward-Decoupled Policy Optimization (GDPO) decompose the overall score into independent reward groups, then compute the RL loss separately within each group. However, this strategy still encounters multi-reward conflicts: a single rollout can yield positive advantages on certain reward dimensions but negative ones on others, causing opposing signals to cancel each other out during aggregation, further hindering RL training efficiency. Inspired by Dynamic sAmpling Policy Optimization (DAPO), which improves RL training efficiency by filtering out ineffective rollouts with near-zero advantages, we propose Group-Dynamic reward-Decoupled Policy Optimization (GD^2PO). Specifically, GD^2PO employs a conflict-aware filtering mechanism to mask out rollouts suffering from severe reward-wise disagreement. By preventing conflicting signals from canceling each other out, this masking strategy preserves and enhances the magnitude of effective RL advantages, thereby significantly accelerating learning efficiency. Furthermore, we introduce query-level reweighting to dynamically adjust the update intensity of each query based on its overall reward consensus. Experiments on various multi-reward scenarios, including tool calling and human preference alignment, demonstrate that GD^2PO consistently and significantly outperforms existing baselines. The code is available at https://github.com/Qwen-Applications/GD2PO.

We revisit policy-gradient optimization for Large Language Models (LLMs) from a single-stream perspective. Prevailing group-based methods like GRPO reduce variance with on-the-fly baselines but suffer from critical flaws: frequent degenerate groups erase learning signals, and synchronization barriers hinder scalability. We introduce Single-stream Policy Optimization (SPO), which eliminates these issues by design. SPO replaces per-group baselines with a persistent, KL-adaptive value tracker and normalizes advantages globally across the batch, providing a stable, low-variance learning signal for every sample. Being group-free, SPO enables higher throughput and scales effectively in long-horizon or tool-integrated settings where generation times vary. Furthermore, the persistent value tracker naturally enables an adaptive curriculum via prioritized sampling. Experiments using Qwen3-8B show that SPO converges more smoothly and attains higher accuracy than GRPO, while eliminating computation wasted on degenerate groups. Ablation studies confirm that SPO's gains stem from its principled approach to baseline estimation and advantage normalization, offering a more robust and efficient path for LLM reasoning. Across five hard math benchmarks with Qwen3 8B, SPO improves the average maj@32 by +3.4 percentage points (pp) over GRPO, driven by substantial absolute point gains on challenging datasets, including +7.3 pp on BRUMO 25, +4.4 pp on AIME 25, +3.3 pp on HMMT 25, and achieves consistent relative gain in pass@k across the evaluated k values. SPO's success challenges the prevailing trend of adding incidental complexity to RL algorithms, highlighting a path where fundamental principles, not architectural workarounds, drive the next wave of progress in LLM reasoning.

Recent advancements in aligning large language models via reinforcement learning have achieved remarkable gains in solving complex reasoning problems, but at the cost of expensive on-policy rollouts and limited exploration of diverse reasoning paths. In this work, we introduce TreePO, involving a self-guided rollout algorithm that views sequence generation as a tree-structured searching process. Composed of dynamic tree sampling policy and fixed-length segment decoding, TreePO leverages local uncertainty to warrant additional branches. By amortizing computation across common prefixes and pruning low-value paths early, TreePO essentially reduces the per-update compute burden while preserving or enhancing exploration diversity. Key contributions include: (1) a segment-wise sampling algorithm that alleviates the KV cache burden through contiguous segments and spawns new branches along with an early-stop mechanism; (2) a tree-based segment-level advantage estimation that considers both global and local proximal policy optimization. and (3) analysis on the effectiveness of probability and quality-driven dynamic divergence and fallback strategy. We empirically validate the performance gain of TreePO on a set reasoning benchmarks and the efficiency saving of GPU hours from 22\% up to 43\% of the sampling design for the trained models, meanwhile showing up to 40\% reduction at trajectory-level and 35\% at token-level sampling compute for the existing models. While offering a free lunch of inference efficiency, TreePO reveals a practical path toward scaling RL-based post-training with fewer samples and less compute. Home page locates at https://m-a-p.ai/TreePO.

Reinforcement learning (RL) has become central to enhancing reasoning in large language models (LLMs). Yet on-policy algorithms such as Group Relative Policy Optimization (GRPO) often suffer in early training: noisy gradients from low-quality rollouts lead to unstable updates and inefficient exploration. We introduce Slow-Fast Policy Optimization (SFPO), a simple yet efficient framework to address these limitations via decomposing each step into three stages: a short fast trajectory of inner steps on the same batch, a reposition mechanism to control off-policy drift, and a final slow correction. This reposition-before-update design preserves the objective and rollout process unchanged, making SFPO plug-compatible with existing policy-gradient pipelines. Extensive experiments demonstrate that SFPO consistently improves stability, reduces rollouts, and accelerates convergence of reasoning RL training. Specifically, it outperforms GRPO by up to 2.80 points in average on math reasoning benchmarks. It also achieves up to 4.93 fewer rollouts and a 4.19 reduction in wall-clock time to match GRPO's best accuracy.

We propose a new family of policy gradient methods for reinforcement learning, which alternate between sampling data through interaction with the environment, and optimizing a "surrogate" objective function using stochastic gradient ascent. Whereas standard policy gradient methods perform one gradient update per data sample, we propose a novel objective function that enables multiple epochs of minibatch updates. The new methods, which we call proximal policy optimization (PPO), have some of the benefits of trust region policy optimization (TRPO), but they are much simpler to implement, more general, and have better sample complexity (empirically). Our experiments test PPO on a collection of benchmark tasks, including simulated robotic locomotion and Atari game playing, and we show that PPO outperforms other online policy gradient methods, and overall strikes a favorable balance between sample complexity, simplicity, and wall-time.

Reinforcement Learning with Verifiable Rewards (RLVR) significantly enhances the reasoning capability of Large Language Models (LLMs). Current RLVR approaches typically conduct training across all generated tokens, but neglect to explore which tokens (e.g., prefix tokens) actually contribute to reasoning. This uniform training strategy spends substantial effort on optimizing low-return tokens, which in turn impedes the potential improvement from high-return tokens and reduces overall training effectiveness. To address this issue, we propose a novel RLVR approach called Progressive Prefix-token Policy Optimization (PPPO), which highlights the significance of the prefix segment of generated outputs. Specifically, inspired by the well-established human thinking theory of Path Dependence, where early-stage thoughts substantially constrain subsequent thinking trajectory, we identify an analogous phenomenon in LLM reasoning termed Beginning Lock-in Effect (BLE). PPPO leverages this finding by focusing its optimization objective on the prefix reasoning process of LLMs. This targeted optimization strategy can positively influence subsequent reasoning processes, and ultimately improve final results. To improve the learning effectiveness of LLMs on how to start reasoning with high quality, PPPO introduces two training strategies: (a) Progressive Prefix Retention, which shapes a progressive learning process by increasing the proportion of retained prefix tokens during training; (b) Continuation Accumulated Reward, which mitigates reward bias by sampling multiple continuations for one prefix token sequence, and accumulating their scores as the reward signal. Extensive experimental results on various reasoning tasks demonstrate that our proposed PPPO outperforms representative RLVR methods, with the accuracy improvements of 18.02% on only 26.17% training tokens.

Proximal Policy Optimization (PPO) is widely used in reinforcement learning with verifiable rewards for language-model reasoning. While value evolution along trajectory characterizes relative token-level credit, yet standard critics often fail to track it under sparse terminal rewards. To model this evolution, we analyze the relation between successive prefix values and show that they admit a Bayesian decomposition with additive updates in log-odds space. We use this additive structure to construct Tracking-Value PPO (\method), a cumulative value parameterization that sums position-wise scalar outputs into value logits. These outputs are learned through terminal-outcome supervision on the reconstructed values. \method improves aggregate mathematical reasoning scores over PPO by 7.0 and 8.4 points on Qwen3-4B-Base and Qwen3-8B-Base, respectively, while improving out-of-distribution generalization. Gains extend to Qwen3-4B, Qwen2.5-Math-1.5B, Qwen3.5-9B and to countdown, and scientific coding tasks. Further analysis shows more accurate tracking of value evolution and more reliable advantage estimates. Our code is publicly available in https://github.com/LINs-lab/TPPO.

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models. While Group Relative Policy Optimization (GRPO) is widely adopted, its coarse credit assignment uniformly penalizes failed rollouts, lacking the token-level focus needed to efficiently address specific deviations. Self-Distillation Policy Optimization (SDPO) addresses this by providing denser, more targeted logit-level supervision that facilitates rapid early improvement, yet it frequently collapses during prolonged training. We trace this late-stage instability to two intrinsic flaws: self-distillation on already-correct samples introduces optimization ambiguity, and the self-teacher's signal reliability progressively degrades. To resolve these issues, we propose Sample-Routed Policy Optimization (SRPO), a unified on-policy framework that routes correct samples to GRPO's reward-aligned reinforcement and failed samples to SDPO's targeted logit-level correction. SRPO further incorporates an entropy-aware dynamic weighting mechanism to suppress high-entropy, unreliable distillation targets while emphasizing confident ones. Evaluated across five benchmarks and two model scales, SRPO achieves both the rapid early improvement of SDPO and the long-horizon stability of GRPO. It consistently surpasses the peak performance of both baselines, raising the five-benchmark average on Qwen3-8B by 3.4% over GRPO and 6.3% over SDPO, while simultaneously yielding moderate response lengths and lowering per-step compute cost by up to 17.2%.

Decoupled loss has been a successful reinforcement learning (RL) algorithm to deal with the high data staleness under the asynchronous RL setting. Decoupled loss improves coupled-loss style of algorithms' (e.g., PPO, GRPO) learning stability by introducing a proximal policy to decouple the off-policy corrections (importance weight) from the controlling policy updates (trust region). However, the proximal policy requires an extra forward pass through the network at each training step, creating a computational bottleneck for large language models. We observe that since the proximal policy only serves as a trust region anchor between the behavior and target policies, we can approximate it through simple interpolation without explicit computation. We call this approach A-3PO (APproximated Proximal Policy Optimization). A-3PO eliminates this overhead, reducing training time by 18% while maintaining comparable performance. Code & off-the-shelf example are available at: https://github.com/inclusionAI/AReaL/blob/main/docs/algorithms/prox_approx.md

We explore reinforcement learning (RL) techniques to enhance reasoning within targeted problem spaces in large language models (LLMs) under memory and compute constraints. Our focus is on critic-free methods compatible with LoRA fine-tuning on a single 40GB GPU, a common limitation in academic settings. We introduce S-GRPO, a memory-efficient variant of Group Relative Policy Optimization, and T-SPMO, a token-level prefix matching strategy for fine-grained credit assignment. Despite limited resources, when used to fine-tune Qwen2-1.5B both methods significantly improve SVAMP benchmark accuracy from 46% to above 70% using LoRA training. T-SPMO also excels in multi-digit multiplication tasks, underscoring the potential of RL fine-tuning under hardware constraints. Additionally, we find that our full-token GRPO baseline under LoRA fine-tuning did not improve model performance (compared to base model) on either task, suggesting that our memory-efficient methods may act as a form of regularization that stabilizes training when only a small subset of parameters are updated.

We present Ruyi2.5, a multimodal familial model built on the AI Flow framework. Extending Ruyi2's "Train Once, Deploy Many" paradigm to the multimodal domain, Ruyi2.5 constructs a shared-backbone architecture that co-trains models of varying scales within a single unified pipeline, ensuring semantic consistency across all deployment tiers. Built upon Ruyi2.5, Ruyi2.5-Camera model is developed as a privacy-preserving camera service system, which instantiates Ruyi2.5-Camera into a two-stage recognition pipeline: an edge model applies information-bottleneck-guided irreversible feature mapping to de-identify raw frames at the source, while a cloud model performs deep behavior reasoning. To accelerate reinforcement learning fine-tuning, we further propose Binary Prefix Policy Optimization (BPPO), which reduces sample redundancy via binary response selection and focuses gradient updates on response prefixes, achieving a 2 to 3 times training speedup over GRPO. Experiments show Ruyi2.5 matches Qwen3-VL on the general multimodal benchmarks, while Ruyi2.5-Camera substantially outperforms Qwen3-VL on privacy-constrained surveillance tasks.

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning LLMs.

Offline paired preference optimization algorithms have become a popular approach for fine-tuning on preference data, outperforming traditional supervised fine-tuning in various tasks. However, traditional implementations often involve redundant computations, especially for tasks with long shared prompts. We introduce prefix sharing for preference tuning, a novel technique that processes chosen and rejected responses as one sequence with a shared prefix. To prevent cross-response contamination, we use a custom block-sparse attention mask. Our method achieves 1.1-1.5times improvement in training throughput on popular DPO datasets, without any effect on convergence. When combined with sequence packing, we observe consistent 1.3-1.6times speedups, benefiting even datasets with smaller sequence lengths. While we focus on Direct Preference Optimization (DPO), our approach is applicable to other paired preference tuning methods. By enhancing computational efficiency, our work contributes to making preference-based fine-tuning more accessible for a wider range of applications and model sizes. We open-source our code at https://github.com/frankxwang/dpo-prefix-sharing.

Direct Preference Optimization (DPO) is a simple and efficient framework that has attracted substantial attention. However, it often struggles to meet its primary objectives -- increasing the generation probability of chosen responses while reducing that of rejected responses -- due to the dominant influence of rejected responses on the loss function. This imbalance leads to suboptimal performance in promoting preferred responses. In this work, we systematically analyze the limitations of DPO and existing algorithms designed to achieve the objectives stated above. To address these limitations, we propose Bounded-DPO (BDPO), a novel method that bounds the influence of rejected responses while maintaining the original optimization structure of DPO. Through theoretical analysis and empirical evaluations, we demonstrate that BDPO achieves a balanced optimization of the chosen and rejected responses, outperforming existing algorithms.

On-policy distillation (OPD) provides teacher supervision on student-generated trajectories, but a single trajectory realizes only one continuation at each decision, limiting supervision coverage under a finite sampling budget. We propose BranchOPD (Branching On-Policy Distillation), which selects informative decision points using student uncertainty and teacher-student disagreement, resamples student-policy continuations from shared prefixes, and applies token-level teacher supervision to both main trajectories and branches. BranchOPD operates at token-level decisions in mathematics and within-turn decisions in agent tasks. Shared-prefix reuse reduces student-generated token costs by approximately 19% on ALFWorld and 31% on WebShop relative to seven independent trajectories. We also introduce protocol-boundary repair (PBR), which uses targeted supervision under protocol constraints to mitigate repetition and wasted generation. BranchOPD outperforms Vanilla OPD and Multi-Rollout OPD (n=7) across all evaluated benchmarks, with gains over Vanilla OPD of 18.55 percentage points in mean mathematics accuracy over 16 sampled answers (avg@16) and 13.8 points in mean ALFWorld ID/OOD success. Mechanistic analyses and selection ablations show that branching at uncertain decisions expands subsequent behavior coverage and outperforms random selection and turn-initial branching.

Training large language models (LLMs) with reinforcement learning (RL) methods such as PPO and GRPO commonly relies on ratio clipping to stabilise updates. While effective at preventing instability, clipping discards information and introduces gradient discontinuities. We propose Probability Smoothing Policy Optimisation (PSPO), which smooths the current policy's probabilities toward the old (behaviour) policy before computing the importance ratio, analogous to label smoothing. Unlike clipping, PSPO preserves gradient signal, while interpolation toward the old policy creates a soft trust region that discourages large, destabilising updates, with formal guarantees. We instantiate PSPO within GRPO (GR-PSPO) and fine-tune Qwen2.5-0.5B and Qwen2.5-1.5B on GSM8K, evaluating on GSM8K test and the cross-dataset generalisation on SVAMP, ASDiv, and MATH-500. Relative to unclipped GRPO (single iteration; no data reuse, ratio always = 1), GR-PSPO achieves similar performance but improves the reasoning leading to clearer and more concise responses which are more logical. Compared to clipped GRPO, GR-PSPO substantially improves performance both the 0.5B and 1.5B models, with a boost of over 20% on GSM8K (39.7% vs. 17.6% for 0.5B, 59.4% vs. 37.8% for 1.5B).

This paper introduces Completion Pruning Policy Optimization (CPPO) to accelerate the training of reasoning models based on Group Relative Policy Optimization (GRPO). GRPO, while effective, incurs high training costs due to the need for sampling multiple completions for each question. Our experiment and theoretical analysis reveals that the number of completions impacts model accuracy yet increases training time multiplicatively, and not all completions contribute equally to policy training -- their contribution depends on their relative advantage. To address these issues, we propose CPPO, which prunes completions with low absolute advantages, significantly reducing the number needed for gradient calculation and updates. Additionally, we introduce a dynamic completion allocation strategy to maximize GPU utilization by incorporating additional questions, further enhancing training efficiency. Experimental results demonstrate that CPPO achieves up to 8.32times speedup on GSM8K and 3.51times on Math while preserving or even enhancing the accuracy compared to the original GRPO. We release our code at https://github.com/lzhxmu/CPPO.

Reinforcement learning (RL) has emerged as a powerful tool for fine-tuning large language models (LLMs) to improve complex reasoning abilities. However, state-of-the-art policy optimization methods often suffer from high computational overhead and memory consumption, primarily due to the need for multiple generations per prompt and the reliance on critic networks or advantage estimates of the current policy. In this paper, we propose A*-PO, a novel two-stage policy optimization framework that directly approximates the optimal advantage function and enables efficient training of LLMs for reasoning tasks. In the first stage, we leverage offline sampling from a reference policy to estimate the optimal value function V*, eliminating the need for costly online value estimation. In the second stage, we perform on-policy updates using a simple least-squares regression loss with only a single generation per prompt. Theoretically, we establish performance guarantees and prove that the KL-regularized RL objective can be optimized without requiring complex exploration strategies. Empirically, A*-PO achieves competitive performance across a wide range of mathematical reasoning benchmarks, while reducing training time by up to 2times and peak memory usage by over 30% compared to PPO, GRPO, and REBEL. Implementation of A*-PO can be found at https://github.com/ZhaolinGao/A-PO.

Recent advancements in Large Reasoning Models (LRMs), exemplified by DeepSeek-R1, have underscored the potential of scaling inference-time compute through Group Relative Policy Optimization (GRPO). However, GRPO frequently suffers from gradient signal attenuation when encountering problems that are either too trivial or overly complex. In these scenarios, the disappearance of inter-group advantages makes the gradient signal susceptible to noise, thereby jeopardizing convergence stability. While variants like DAPO attempt to rectify gradient vanishing, they do not alleviate the substantial computational overhead incurred by exhaustive rollouts on low-utility samples. In this paper, we propose Difficulty-Estimated Policy Optimization (DEPO), a novel framework designed to optimize the efficiency and robustness of reasoning alignment. DEPO integrates an online Difficulty Estimator that dynamically assesses and filters training data before the rollout phase. This mechanism ensures that computational resources are prioritized for samples with high learning potential. Empirical results demonstrate that DEPO achieves up to a 2x reduction in rollout costs without compromising model performance. Our approach significantly lowers the computational barrier for training high-performance reasoning models, offering a more sustainable path for reasoning scaling. Code and data will be released upon acceptance.

Policy optimization (PO) for Large Language Models faces a stability--exploration trade-off, currently mediated by an action-side Policy-KL regularizer. This puts practitioners in a double bind: keeping Policy-KL constrains response behavior and consumes the action-side exploration budget, while dropping it leaves the optimization without an explicit drift control. We argue for an alternative that breaks the dilemma by moving regularization to the input side. As training progresses, the distribution over training queries induced by the current policy drifts unchecked from its pre-RL reference distribution. Concretely, Environment-Regularized Policy Optimization (ERPO) introduces a Query-KL (QKL) term that bounds this query distribution shift, together with a dataset-static reference-derived per-query weight that biases each per-query update toward queries typical under the reference. The QKL gradient flows strictly through the query likelihood; the response score function used by policy-gradient estimators does not appear in the QKL term, so QKL exerts no direct gradient pressure on the response distribution---exploration is preserved. ERPO plugs into GRPO/PPO/REINFORCE-style pipelines without additional forward passes. On six mathematical reasoning benchmarks, ERPO replaces the standard Policy-KL regularizer while achieving effective control over query distribution drift, delivering stronger accuracy and substantially more stable behavior under high-temperature decoding and long-horizon training.Our source code are available at https://github.com/alibaba/ERPO

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff'' phenomenon: when faced with problems far beyond their current capabilities, models consistently fail, yielding a persistent zero-reward signal. In policy optimization algorithms like GRPO, this collapses the advantage calculation to zero, rendering these difficult problems invisible to the learning gradient and stalling progress. To overcome this, we introduce Scaf-GRPO (Scaffolded Group Relative Policy Optimization), a progressive training framework that strategically provides minimal guidance only when a model's independent learning has plateaued. The framework first diagnoses learning stagnation and then intervenes by injecting tiered in-prompt hints, ranging from abstract concepts to concrete steps, enabling the model to construct a valid solution by itself. Extensive experiments on challenging mathematics benchmarks demonstrate Scaf-GRPO's effectiveness, boosting the pass@1 score of the Qwen2.5-Math-7B model on the AIME24 benchmark by a relative 44.3% over a vanilla GRPO baseline. This result demonstrates our framework provides a robust and effective methodology for unlocking a model's ability to solve problems previously beyond its reach, a critical step towards extending the frontier of autonomous reasoning in LLM.

Multi-attribute user records are inherently heterogeneous, often combining continuous, categorical, and binary attributes, and they frequently exhibit strong cross-attribute dependencies. Designing high-utility metric differential privacy (mDP) mechanisms for such records is challenging. Simple predefined mechanisms, such as distance-based noise, may be poorly aligned with task-specific utility loss, whereas fully optimization-based mechanisms can be computationally prohibitive for multi-attribute records. We propose Dependency-aware Heterogeneous Data Perturbation (DepHDP)}, a framework for multi-attribute mDP that combines dependency-aware attribute grouping with heterogeneous perturbation design. Rather than applying a one-size-fits-all mechanism, DepHDP selects an appropriate perturbation strategy for each attribute or attribute group, choosing between efficient predefined mechanisms, such as Laplace or Exponential mechanisms, and optimization-based designs. This selection is guided by both domain size and a predefined-noise adequacy criterion, which quantifies whether task-induced utility loss can be well explained by perturbation magnitude. To support scalable end-to-end optimization, DepHDP estimates group-level utility loss through sampling and lightweight surrogate modeling, and jointly optimizes privacy-budget allocation and group-wise mechanism design under a global ell_p-metric mDP constraint. Across three case studies, DepHDP improves privacy--utility trade-offs over uniform baselines at lower computational cost than full-record OPT on evaluated domains.

In reinforcement learning (RL), rewards of states are typically considered additive, and following the Markov assumption, they are independent of states visited previously. In many important applications, such as coverage control, experiment design and informative path planning, rewards naturally have diminishing returns, i.e., their value decreases in light of similar states visited previously. To tackle this, we propose submodular RL (SubRL), a paradigm which seeks to optimize more general, non-additive (and history-dependent) rewards modelled via submodular set functions which capture diminishing returns. Unfortunately, in general, even in tabular settings, we show that the resulting optimization problem is hard to approximate. On the other hand, motivated by the success of greedy algorithms in classical submodular optimization, we propose SubPO, a simple policy gradient-based algorithm for SubRL that handles non-additive rewards by greedily maximizing marginal gains. Indeed, under some assumptions on the underlying Markov Decision Process (MDP), SubPO recovers optimal constant factor approximations of submodular bandits. Moreover, we derive a natural policy gradient approach for locally optimizing SubRL instances even in large state- and action- spaces. We showcase the versatility of our approach by applying SubPO to several applications, such as biodiversity monitoring, Bayesian experiment design, informative path planning, and coverage maximization. Our results demonstrate sample efficiency, as well as scalability to high-dimensional state-action spaces.

Reinforcement learning algorithms such as GRPO have driven recent advances in large language model (LLM) reasoning. While scaling the number of rollouts stabilizes training, existing approaches suffer from limited exploration on challenging prompts and leave informative feedback signals underexploited, due to context-independent rollout allocation across prompts (e.g., generating 16 rollouts per prompt) and relying heavily on sparse rewards. This paper presents XRPO(eXplore - eXploit GRPO), a unified framework that recasts policy optimization through the principled lens of rollout exploration-exploitation. To enhance exploration, XRPO introduces a mathematically grounded rollout allocator that adaptively prioritizes prompts with higher potential for uncertainty reduction. It further addresses stagnation on zero-reward prompts through an in-context seeding strategy that injects curated exemplars, steering the model into more difficult reasoning trajectories. To strengthen exploitation, XRPO develops a group-relative, novelty-aware advantage sharpening mechanism that leverages sequence likelihoods to amplify low-probability yet correct responses, thereby extending the policy's reach beyond sparse rewards. Experiments across diverse math and coding benchmarks on both reasoning and non-reasoning models demonstrate that XRPO outperforms existing advances (e.g., GRPO and GSPO) up to 4% pass@1 and 6% cons@32, while accelerating training convergence by up to 2.7X.

Recent advances in online reinforcement learning (RL) for large language models (LLMs) have demonstrated promising performance in complex reasoning tasks. However, they often exhibit an imbalanced exploration-exploitation trade-off, resulting in unstable optimization and sub-optimal performance. We introduce IB-Score, a novel metric grounded in Information Bottleneck theory that evaluates policy's exploration-exploitation balance by quantifying the trade-off between step-level reasoning diversity and mutual information shared with the correct answer. Analysis based on IB-Score shows that popular online RL approaches (e.g., GRPO) with common regularizers fail to consistently maintain balance during training with suboptimal results. To address this, we propose Information Bottleneck-driven Tree-based Policy Optimization (IB-TPO), a principled framework that formulates IB-Score as a fine-grained optimization objective and utilizes a novel IB-guided tree sampling strategy that not only improves the efficiency of online sampling with 50% more trajectories under the same token budget, but also reuses the tree structure for effective IB-Score Monte Carlo estimation. Extensive experiments across standard benchmarks show that our method significantly outperforms GRPO baseline by 2.9% to 3.6% and also outperforms other state-of-the-art online RL approaches. Our code is available at https://github.com/alibaba/EfficientRL.

Recent studies, including DeepSeek-R1 and Kimi-k1.5, have demonstrated that reinforcement learning with rule-based, binary-valued reward functions can significantly enhance the reasoning capabilities of large language models. These models primarily utilize REINFORCE-based policy optimization techniques, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation remains: current policy optimization methods either neglect reward normalization or employ static normalization strategies, which fail to adapt to the dynamic nature of policy updates during training. This may result in unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel policy optimization method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. BNPO aligns the normalization with the changing policy distribution, enabling more precise and lower-variance gradient estimation, which in turn promotes stable training dynamics. We provide theoretical analysis demonstrating BNPO's variance-reducing properties and show that it generalizes both REINFORCE and GRPO under binary-valued reward settings. Furthermore, we introduce an advantage decomposition mechanism to extend BNPO's applicability to more complex reward systems. Experimental results confirm that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks. The code is available at https://github.com/changyi7231/BNPO.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: Token-level methods (e.g., PPO) aim to provide the fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving 6-12 percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving 7-11 percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

Reinforcement learning from human feedback (RLHF) is one of the key techniques that helps large language models (LLMs) to follow instructions and provide helpful and harmless responses. While direct policy optimization methods exist, state-of-the-art LLMs adopt RL-based methods (usually PPO) in RLHF to train the policy to generate good responses guided by a reward model learned from preference data. The main challenge of these methods is the inaccuracy of the intermediate reward model, especially in code generation tasks that require long and complex reasoning to score a response. We find that the reliability of the reward model varies across responses assigned with different rewards. This motivates us to filter the samples whose rewards may be unreliable to improve signal-to-noise ratio during policy learning, resulting in Policy Filtration for Proximal Policy Optimization (PF-PPO). To choose a proper policy filtration strategy for a given reward model, the coefficient of determination (R^2) between rewards and actual scores on filtered samples serves as a good metrics and helps us find several promising strategies. We provide extensive experiments to validate the effectiveness of PF-PPO in code generation tasks, and find that some variants of PF-PPO are highly effective and achieve new state-of-the-art performance across 7-billion-parameter models on HumanEval, MBPP, and a new and more challenging LeetCode Contest benchmark.

Policy Optimization (PO) is one of the most popular methods in Reinforcement Learning (RL). Thus, theoretical guarantees for PO algorithms have become especially important to the RL community. In this paper, we study PO in adversarial MDPs with a challenge that arises in almost every real-world application -- delayed bandit feedback. We give the first near-optimal regret bounds for PO in tabular MDPs, and may even surpass state-of-the-art (which uses less efficient methods). Our novel Delay-Adapted PO (DAPO) is easy to implement and to generalize, allowing us to extend our algorithm to: (i) infinite state space under the assumption of linear Q-function, proving the first regret bounds for delayed feedback with function approximation. (ii) deep RL, demonstrating its effectiveness in experiments on MuJoCo domains.

Large language models trained with reinforcement learning with verifiable rewards tend to trade accuracy for length--inflating response lengths to achieve gains in accuracy. While longer answers may be warranted for harder problems, many tokens are merely "filler": repetitive, verbose text that makes no real progress. We introduce GFPO (Group Filtered Policy Optimization), which curbs this length explosion by sampling larger groups per problem during training and filtering responses to train on based on two key metrics: (1) response length and (2) token efficiency: reward per token ratio. By sampling more at training time, we teach models to think less at inference time. On the Phi-4-reasoning model, GFPO cuts GRPO's length inflation by 46-71% across challenging STEM and coding benchmarks (AIME 24/25, GPQA, Omni-MATH, LiveCodeBench) while maintaining accuracy. Optimizing for reward per token further increases reductions in length inflation to 71-85%. We also propose Adaptive Difficulty GFPO, which dynamically allocates more training resources to harder problems based on real-time difficulty estimates, improving the balance between computational efficiency and accuracy especially on difficult questions. GFPO demonstrates that increased training-time compute directly translates to reduced test-time compute--a simple yet effective trade-off for efficient reasoning.

Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but GRPO-style optimization remains prone to collapse. We analyse this instability through token-level gradient dynamics, deriving a taxonomy that predicts how updates affect next-token probabilities and entropy. The taxonomy shows that stability depends jointly on the advantage sign and token distribution under the current policy. Motivated by this finding, we propose Winner Advantage Policy Optimization (WAPO), a simple online clipped policy-gradient objective that updates only on positive-advantage completions. Across mathematical reasoning and multi-hop QA benchmarks, WAPO improves training stability and matches or outperforms baselines across multiple model families. Full code can be found at https://github.com/layer6ai-labs/wapo.

Tool-integrated reasoning (TIR) augments large language models (LLMs) with the ability to invoke external tools, such as search engines and code interpreters, to solve tasks beyond the capabilities of language-only reasoning. While reinforcement learning (RL) has shown promise in improving TIR by optimizing final answer correctness, existing approaches often overlook the efficiency and cost associated with tool usage. This can lead to suboptimal behavior, including excessive tool calls that increase computational and financial overhead, or insufficient tool use that compromises answer quality. In this work, we propose Optimal Tool Call-controlled Policy Optimization (OTC-PO), a simple yet effective RL-based framework that encourages models to produce accurate answers with minimal tool calls. Our method introduces a tool-integrated reward that jointly considers correctness and tool efficiency, promoting high tool productivity. We instantiate this framework within both Proximal Policy Optimization (PPO) and Group Relative Preference Optimization (GRPO), resulting in OTC-PPO and OTC-GRPO. Experiments with Qwen-2.5 and Qwen-Math across multiple QA benchmarks show that our approach reduces tool calls by up to 73.1\% and improves tool productivity by up to 229.4\%, while maintaining comparable answer accuracy. To the best of our knowledge, this is the first RL-based framework that explicitly optimizes tool-use efficiency in TIR.

Plateaus, where an agent's performance stagnates at a suboptimal level, are a common problem in deep on-policy RL. Focusing on PPO due to its widespread adoption, we show that plateaus in certain regimes arise not because of known exploration, capacity, or optimization challenges, but because sample-based estimates of the loss eventually become poor proxies for the true objective over the course of training. As a recap, PPO switches between sampling rollouts from several parallel environments online using the current policy (which we call the outer loop) and performing repeated minibatch SGD steps against this offline dataset (the inner loop). In our work we consider only the outer loop, and conceptually model it as stochastic optimization. The step size is then controlled by the regularization strength towards the previous policy and the gradient noise by the number of samples collected between policy update steps. This model predicts that performance will plateau at a suboptimal level if the outer step size is too large relative to the noise. Recasting PPO in this light makes it clear that there are two ways to address this particular type of learning stagnation: either reduce the step size or increase the number of samples collected between updates. We first validate the predictions of our model and investigate how hyperparameter choices influence the step size and update noise, concluding that increasing the number of parallel environments is a simple and robust way to reduce both factors. Next, we propose a recipe for how to co-scale the other hyperparameters when increasing parallelization, and show that incorrectly doing so can lead to severe performance degradation. Finally, we vastly outperform prior baselines in a complex open-ended domain by scaling PPO to more than 1M parallel environments, thereby enabling monotonic performance improvement up to one trillion transitions.

Reinforcement learning (RL) post-training has increasingly demonstrated strong ability to elicit reasoning behaviors in large language models (LLMs). For training efficiency, rollouts are typically generated in an off-policy manner using an older sampling policy and then used to update the current target policy. To correct the resulting discrepancy between the sampling and target policies, most existing RL objectives rely on a token-level importance sampling ratio, primarily due to its computational simplicity and numerical stability. However, we observe that token-level correction often leads to unstable training dynamics when the degree of off-policyness is large. In this paper, we revisit LLM policy optimization under off-policy conditions and show that the theoretically rigorous correction term is the prefix importance ratio, and that relaxing it to a token-level approximation can induce instability in RL post-training. To stabilize LLM optimization under large off-policy drift, we propose a simple yet effective objective, Minimum Prefix Ratio (MinPRO). MinPRO replaces the unstable cumulative prefix ratio with a non-cumulative surrogate based on the minimum token-level ratio observed in the preceding prefix. Extensive experiments on both dense and mixture-of-experts LLMs, across multiple mathematical reasoning benchmarks, demonstrate that MinPRO substantially improves training stability and peak performance in off-policy regimes.

Reinforcement learning has become central to post-training large language models, yet dominant algorithms rely on clipping mechanisms that introduce optimization issues at scale, including zero-gradient regions, reward hacking, and training instability. We propose Clipping-Free Policy Optimization (CFPO), which replaces heuristic clipping with a convex quadratic penalty derived from Total Variation divergence constraints, yielding an everywhere-differentiable objective that enforces stable policy updates without hard boundaries. We evaluate CFPO across both reasoning and alignment settings. In reasoning, CFPO matches clipping-based methods on downstream benchmarks while extending the stable training regime. In alignment, CFPO mitigates verbosity exploitation and reduces capability degradation, while achieving competitive instruction-following performance. CFPO requires only a one-line code change and no additional hyperparameters. Our results suggest that CFPO is a promising drop-in alternative to clipping-based methods for LLM post-training.

Group Relative Policy Optimization (GRPO) has been a key driver of recent progress in reinforcement learning with verifiable rewards (RLVR) for large language models, but it is typically trained in a low-staleness, near-on-policy regime that incurs substantial system overhead. We ask a simple question: How off-policy can GRPO be? We show that GRPO-style algorithms can tolerate substantially larger rollout staleness than previously assumed, and propose Mu-GRPO, an RL training framework that organizes training into a small number (e.g., four) of large sequential generation-optimization stages. This design induces high rollout staleness while greatly reducing rollout-optimization switching overhead. To stabilize learning under stale data, Mu-GRPO combines relaxed clipping, which preserves useful stale-rollout gradients, with negative-advantage veto, which removes destabilizing post-trigger suffix updates in negative-advantage responses. Across five language models and multiple math reasoning benchmarks, Mu-GRPO matches or exceeds the performance of standard GRPO while achieving around 2x speedup in wall-clock training time, establishing a substantially improved performance-efficiency trade-off for LLM reinforcement learning.

Asynchronous reinforcement learning improves throughput by decoupling rollout generation from optimization, but staleness is an inevitable byproduct compounded by policy lag, engine delays, and mixture-of-experts routing. From a trust-region perspective, this mismatch is critical: training-inference divergence governs approximation error in finite-horizon bounds, whereas PPO clipping only gates sampled outward updates, acting as a sampled surrogate rather than a full-policy constraint. As a result, high-staleness updates remain weakly controlled in the asynchronous regime where stale rollouts matter most. We introduce the Staleness-Adaptive Trust Region (SAT), which uses the detached sampled log-ratio as a practical staleness proxy, identifies high-mismatch tails within each batch via staleness-based kernel scaling, and contracts only the sign-selected endpoint of the nominal PPO interval. This preserves baseline behavior on ordinary tokens while enforcing more conservative updates on newly intercepted outward bands. We prove local interval containment and pointwise pessimism relative to PPO, showing how the adaptive rule reshapes update geometry under heterogeneous staleness. We evaluate SAT in a decoupled asynchronous RL setup built on Qwen3-30B-A3B-Base, using SGLang as the inference engine and Megatron for training. In this setting, SAT-GSPO w/ R3 achieves the best observed AIME24 avg@8, reaching 35.83 at lag 1 and 34.79 at lag 8, while SAT-GSPO reaches 34.17 at lag 1. Adaptive clipping and routing replay act as complementary stabilizers targeting mismatch tails and routing inconsistency, respectively. Overall, aligning clip intervals with staleness heterogeneity effectively stabilizes asynchronous RL.

As the era of large language models (LLMs) on behalf of users unfolds, Preference Optimization (PO) methods have become a central approach to aligning LLMs with human preferences and improving performance. We propose Maximum a Posteriori Preference Optimization (MaPPO), a framework for learning from preferences that explicitly incorporates prior reward knowledge into the optimization objective. While existing methods such as Direct Preference Optimization (DPO) and its variants treat preference learning as a Maximum Likelihood Estimation (MLE) problem, MaPPO extends this paradigm by integrating prior reward estimates into a principled Maximum a Posteriori (MaP) objective. This not only generalizes DPO and its variants, but also enhances alignment by mitigating the oversimplified binary classification of responses. More importantly, MaPPO introduces no additional hyperparameter, and supports preference optimization in both offline and online settings. In addition, MaPPO can be used as a plugin with consistent improvement on DPO variants, including widely used SimPO, IPO, and CPO. Extensive empirical evaluations of different model sizes and model series on three standard benchmarks, including MT-Bench, AlpacaEval 2.0, and Arena-Hard, demonstrate consistent improvements in alignment performance without sacrificing computational efficiency.

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level rewards introduces a key limitation as uniform credit assignment across all tokens fails to capture fine-grained, token-level contributions. To address this issue, we propose Guidance Contrastive Policy Optimization (GCPO), a novel algorithm that enables per-token credit assignment by contrasting model predictions under positive and negative prompts. Rather than uniformly broadcasting sample-level advantages, GCPO assigns token-level advantages proportional to the difference between these contrastive predictions, allowing more precise and informative learning signals. Empirically, we find that GCPO emphasizes semantically relevant regions such as visual areas aligned with textual prompts in text-to-image generation, and critical keywords within reasoning traces for chain-of-thought tasks. Through extensive experiments, GCPO consistently outperforms GRPO and DAPO baselines on both text-to-image generation and chain-of-thought reasoning benchmarks, demonstrating its effectiveness as a general and scalable optimization strategy for discrete policy learning.

Model-based reinforcement learning (RL) can be effectively supported at scale through the use of world models. However, in practice, scaling such approaches remains fundamentally limited. A commonly recognized challenge is model bias and error compounding, which degrade long-horizon predictions. Beyond these issues, we identify a more critical yet underexplored bottleneck: a structural misalignment between search and value learning in existing world model approaches. In particular, policy improvement often relies on value functions induced by a separate, non-search policy, resulting in training inconsistency and ultimately suboptimal learning. To address this limitation, we propose Model-Based Diffusion Policy Optimization (MBDPO) in world models, a framework that unifies search and policy optimization through diffusion policy representations, thereby unlocking the potential of world models for scalable policy learning. Instead of constructing an explicit planner over a learned world model, we reformulate policy optimization as a diffusion process over searched trajectories in latent world models. In this view, we extract an implicit energy function from the collected dataset that anchors the policy, enabling MBDPO to refine the score field for policy optimization while mitigating misalignment. We evaluate MBDPO across a wide range of settings, including multi-task offline pretraining, online learning, and offline-to-online fine-tuning. In the offline regime, we further investigate its scaling behavior by pretraining on large-scale datasets, observing consistent and monotonic performance gains with increasing model capacity.

Group-based reinforcement learning methods such as GRPO for large language models avoid training a critic by sampling multiple responses for each prompt. A reliable critic could instead estimate token-level advantages from one response, but standard critic-based training recipes are often unstable. We study this instability and develop **Best Practice Critic Optimization (BPCO)**, a recipe that combines DPPO, value predictions bounded to the reward range, Monte Carlo value targets, unnormalized policy advantages, and length-adaptive generalized advantage estimation. Because the critic is used only during training, BPCO can also condition it on reward-defining information, such as a reference answer or grading rubric, that is hidden from the policy. Controlled experiments isolate the effect of each design choice. Across mathematical reasoning tasks with models ranging from 1.5B parameters to 30B-A3B mixtures of experts, BPCO improves a strong critic-based baseline consistently, and matches or exceeds a group-based baseline while sampling one response per prompt. The same recipe also improves learning with rubric-based rewards. These results show that a carefully designed critic provides a reliable alternative to group-relative advantage estimation. Code is available at https://github.com/QPHutu/golden_critic.

Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where pre-training and RL post-training share the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the same score/flow-matching loss as pretraining to obtain a lower-variance objective and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This unifies pretraining and RL conceptually and practically, is consistent with policy-gradient theory, reduces variance, and yields faster convergence. This simple yet effective design yields substantial benefits: on GenEval, OCR, and PickScore benchmarks, AWM delivers up to a 24times speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching.

Reinforcement learning (RL)-based fine-tuning has emerged as a powerful approach for aligning diffusion models with black-box objectives. Proximal policy optimization (PPO) is the most popular choice of method for policy optimization. While effective in terms of performance, PPO is highly sensitive to hyper-parameters and involves substantial computational overhead. REINFORCE, on the other hand, mitigates some computational complexities such as high memory overhead and sensitive hyper-parameter tuning, but has suboptimal performance due to high-variance and sample inefficiency. While the variance of the REINFORCE can be reduced by sampling multiple actions per input prompt and using a baseline correction term, it still suffers from sample inefficiency. To address these challenges, we systematically analyze the efficiency-effectiveness trade-off between REINFORCE and PPO, and propose leave-one-out PPO (LOOP), a novel RL for diffusion fine-tuning method. LOOP combines variance reduction techniques from REINFORCE, such as sampling multiple actions per input prompt and a baseline correction term, with the robustness and sample efficiency of PPO via clipping and importance sampling. Our results demonstrate that LOOP effectively improves diffusion models on various black-box objectives, and achieves a better balance between computational efficiency and performance.

Reinforcement Learning with Verifiable Rewards (RLVR) offers a promising framework for optimizing large language models in reasoning tasks. However, existing RLVR algorithms focus on different granularities, and each has complementary strengths and limitations. Group Relative Policy Optimization (GRPO) updates the policy with token-level importance ratios, which preserves fine-grained credit assignment but often suffers from high variance and instability. In contrast, Group Sequence Policy Optimization (GSPO) applies single sequence-level importance ratios across all tokens in a response that better matches sequence-level rewards, but sacrifices token-wise credit assignment. In this paper, we propose Dynamic Hybrid Policy Optimization (DHPO) to bridge GRPO and GSPO within a single clipped surrogate objective. DHPO combines token-level and sequence-level importance ratios using weighting mechanisms. We explore two variants of the mixing mechanism, including an averaged mixing and an entropy-guided mixing. To further stabilize training, we employ a branch-specific clipping strategy that constrains token-level and sequence-level ratios within separate trust regions before mixing, preventing outliers in either branch from dominating the update. Across seven challenging mathematical reasoning benchmarks, experiments on both dense and MoE models from the Qwen3 series show that DHPO consistently outperforms GRPO and GSPO. We will release our code upon acceptance of this paper.

Value-model-free RLVR methods such as GRPO assign uniform advantages to all tokens in a rollout, ignoring that tokens contribute unequally. Recent methods use token entropy as an importance proxy but compute it globally across the batch, conflating importance with prompt difficulty and positional trends. We argue that importance should instead be measured relative to the local context of each token. We introduce proximal entropy, a local measure of token importance relative to neighboring tokens, and prove it is invariant to both confounders. Proximal Entropy Policy Optimization (PEPO) uses it to weight per-token advantages and outperforms GRPO and entropy-based baselines on mathematical reasoning across Qwen3-1.7B, Qwen3-4B, and Llama-3.2-3B-Instruct. We also show the formulation generalizes to other algorithms where substituting proximal entropy into existing methods improves, and applying it to single-stream RL succeeds where global entropy fails.

Reinforcement learning from human feedback (RLHF) is a promising solution to align large language models (LLMs) more closely with human values. Off-policy preference optimization, where the preference data is obtained from other models, is widely adopted due to its cost efficiency and scalability. However, off-policy preference optimization often suffers from a distributional gap between the policy used for data collection and the target policy, leading to suboptimal optimization. In this paper, we propose a novel strategy to mitigate this problem by simulating on-policy learning with off-policy preference data. Our Weighted Preference Optimization (WPO) method adapts off-policy data to resemble on-policy data more closely by reweighting preference pairs according to their probability under the current policy. This method not only addresses the distributional gap problem but also enhances the optimization process without incurring additional costs. We validate our method on instruction following benchmarks including Alpaca Eval 2 and MT-bench. WPO not only outperforms Direct Preference Optimization (DPO) by up to 5.6% on Alpaca Eval 2 but also establishes a remarkable length-controlled winning rate against GPT-4-turbo of 48.6% based on Llama-3-8B-Instruct, making it the strongest 8B model on the leaderboard. We will release the code and models at https://github.com/wzhouad/WPO.

We argue that inventory management presents unique opportunities for the reliable application of deep reinforcement learning (DRL). To enable this, we emphasize and test two complementary techniques. The first is Hindsight Differentiable Policy Optimization (HDPO), which uses pathwise gradients from offline counterfactual simulations to directly and efficiently optimize policy performance. Unlike standard policy gradient methods that rely on high-variance score-function estimators, HDPO computes gradients by differentiating through the known system dynamics. Via extensive benchmarking, we show that HDPO recovers near-optimal policies in settings with known or bounded optima, is more robust than variants of the REINFORCE algorithm, and significantly outperforms generalized newsvendor heuristics on problems using real time series data. Our second technique aligns neural policy architectures with the topology of the inventory network. We exploit Graph Neural Networks (GNNs) as a natural inductive bias for encoding supply chain structure, demonstrate that they can represent optimal and near-optimal policies in two theoretical settings, and empirically show that they reduce data requirements across six diverse inventory problems. A key obstacle to progress in this area is the lack of standardized benchmark problems. To address this gap, we open-source a suite of benchmark environments, along with our full codebase, to promote transparency and reproducibility. All resources are available at github.com/MatiasAlvo/Neural_inventory_control.

Reinforcement learning, including reinforcement learning with verifiable rewards (RLVR), has emerged as a powerful approach for LLM post-training. Central to these approaches is the design of the importance sampling (IS) ratio used in off-policy policy-gradient estimation. Existing methods face a fundamental bias-variance dilemma: token-level IS ratios, as adopted by PPO (Schulman et al., 2017) and GRPO (Shao et al., 2024), introduce bias by ignoring prefix state distribution mismatch; full sequence ratios provide exact trajectory-level correction but suffer from high variance due to the multiplicative accumulation of per-token ratios, while GSPO (Zheng et al., 2025) improves numerical stability via length normalization at the cost of deviating from the exact full-sequence IS correction. In this work, we identify the cumulative token IS ratio, the product of per-token ratios up to position t, as a theoretically principled solution to this dilemma. We prove that, under the token-level policy-gradient formulation, this ratio provides an unbiased prefix correction for each token-level gradient term and has strictly lower variance than the full sequence ratio. Building on this insight, we propose CTPO (Cumulative Token Policy Optimization), which combines the cumulative token IS ratio with position-adaptive clipping that scales log-space clip bounds according to the natural t growth of the cumulative log-ratio. This yields more consistent regularization across token positions. We implement and evaluate CTPO in the tool-integrated reasoning setting on several challenging mathematical reasoning benchmarks, achieving the best average performance across both model scales compared with strong GRPO and GSPO baselines. Code will be available at https://github.com/horizon-llm/CTPO.

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.

On-policy distillation (OPD) transfers teacher knowledge on student-generated trajectories, but efficient sampled objectives reduce the teacher distribution to scalar credit on individual tokens. Such credit indicates whether a token should gain or lose probability, yet leaves the corresponding redistribution unspecified. We recast OPD as teacher-guided probability transport and propose RouteOPD (Routed On-Policy Distillation), which decomposes local teacher--student disagreement into student-excess sources and teacher-deficit destinations and couples them into explicit transport pairs. RouteOPD optimizes pairwise log-odds toward jointly realizable targets obtained from a bounded teacher potential, while adapting the transport budget to the concentration of teacher demand. This formulation directs updates toward teacher-preferred destinations and controls their magnitude within a single transport operator. Experiments across four teacher--student settings and four mathematical-reasoning benchmarks demonstrate that RouteOPD consistently outperforms sampled reverse-KL OPD, with improvements accompanied by higher routing fidelity and lower background leakage. These results demonstrate the effectiveness of explicitly modeling probability transport in on-policy distillation.

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Explanations of these algorithms often assume prior knowledge, lack critical details, and/or are overly generalized and complex. Here, each method is discussed and developed step by step using simplified and explicit notation focused on LLMs, aiming to eliminate ambiguity and provide a clear and intuitive understanding of the concepts. By minimizing detours into the broader RL literature and connecting concepts to LLMs, we eliminate superfluous abstractions and reduce cognitive overhead. Following this exposition, we provide a literature review of new techniques and approaches beyond those detailed. Finally, new ideas for research and exploration in the form of GRAPE (Generalized Relative Advantage Policy Evolution) are presented.

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models (LLMs). We introduce Bellman Policy Optimization (BPO), a critic-free method derived from Policy Mirror Descent (PMD). For autoregressive generation with terminal rewards, BPO uses the Bellman equations to reformulate PMD as a trajectory-level objective. The reformulation avoids estimating state values at intermediate states. We prove that it has the same unique optimal solution as the original PMD objective. We derive the practical BPO loss by approximating this objective. Its mismatch-correction weight is a smoothed ratio of complementary token probabilities. Experiments on mathematical reasoning benchmarks demonstrate the effectiveness of BPO.

Reinforcement learning (RL) has become a key component of post-training large language models (LLMs). In practice, LLM RL is often off-policy because of training-inference mismatch and policy staleness, making trust-region control essential for stable optimization. Mainstream methods such as PPO and GRPO approximate this control with a ratio-clipping mechanism, but the importance ratio can be a poor proxy for distributional shift in long-tailed vocabularies. Recent work such as DPPO addresses this mismatch by replacing ratio-based clipping with a divergence-based mask, yielding a trust region defined by the sampled token's absolute probability shift. However, DPPO still relies on a hard mask: once a token crosses the trust-region boundary in a harmful direction, its gradient is discarded rather than corrected. To address this, we propose Divergence Regularized Policy Optimization (DRPO), which replaces the hard mask with a smooth advantage-weighted quadratic regularizer on policy shift. DRPO preserves the same trust-region geometry as DPPO while inducing bounded, continuous gradient weights that attenuate diverging updates and provide corrective signals beyond the boundary. Experiments across model scales, architectures, and precision settings show that DRPO improves the stability and efficiency of LLM RL training.

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

Group Relative Policy Optimisation (GRPO) enhances large language models by estimating advantages across a group of sampled trajectories. However, mapping these trajectory-level advantages to policy updates requires aggregating token-level probabilities within each sequence. Relying on a fixed aggregation mechanism for this step fundamentally limits the algorithm's adaptability. Empirically, we observe a critical trade-off: certain fixed aggregations frequently suffer from training collapse, while others fail to yield satisfactory performance. To resolve this, we propose HölderPO, a generalised policy optimisation framework unifying token-level probability aggregation via the Hölder mean. By explicitly modulating the parameter p, our framework provides continuous control over the trade-off between gradient concentration and variance bounds. Theoretically, we prove that a larger p concentrates the gradient to amplify sparse learning signals, whereas a smaller p strictly bounds gradient variance. Because no static configuration can universally resolve this concentration-stability trade-off, we instantiate the framework with a dynamic annealing algorithm that progressively schedules p across the training lifecycle. Extensive evaluations demonstrate superior stability and convergence over existing baselines. Specifically, our approach achieves a state-of-the-art average accuracy of 54.9% across multiple mathematical benchmarks, yielding a substantial 7.2% relative gain over standard GRPO and secures an exceptional 93.8% success rate on ALFWorld.

Group-relative reinforcement learning waits for sibling rollouts of the same prompt, which is costly for long and variable tool-use trajectories. Single-stream Policy Optimization (SPO) removes this dependency with a persistent prompt-level value estimate, but its recipe whitens one advantage per trajectory before optimizing a token-mean actor loss. We show that trajectory centering generally does not center the token-weighted quantity consumed by the actor, and fix the mismatch by standardizing terminal-outcome advantages under the action-token measure. We additionally organize prompt evidence by the policy event that generated it rather than learner receipt order. Across matched runs on ALFWorld at two model scales and on Math-TIR, SPO++ improves online learning efficiency over SPO. A paired ablation identifies action-token-measure normalization as the strongest tested component.

On-policy reinforcement learning (RL) has become a popular framework for solving sequential decision problems due to its computational efficiency and theoretical simplicity. Some on-policy methods guarantee every policy update is constrained to a trust region relative to the prior policy to ensure training stability. These methods often require computationally intensive non-linear optimization or require a particular form of action distribution. In this work, we show that applying KL penalization alone is nearly sufficient to enforce such trust regions. Then, we show that introducing a "fixup" phase is sufficient to guarantee a trust region is enforced on every policy update while adding fewer than 5% additional gradient steps in practice. The resulting algorithm, which we call FixPO, is able to train a variety of policy architectures and action spaces, is easy to implement, and produces results competitive with other trust region methods.

We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time (0,ε)-additive bicriteria approximation algorithm for finding optimal constrained policies across a broad class of recursively computable constraints, including almost-sure, chance, expectation, and their anytime variants. Matching lower bounds imply our approximation guarantees are optimal so long as P neq NP. The generality of our approach results in answers to several long-standing open complexity questions in the constrained reinforcement learning literature. Specifically, we are the first to prove polynomial-time approximability for the following settings: policies under chance constraints, deterministic policies under multiple expectation constraints, policies under non-homogeneous constraints (i.e., constraints of different types), and policies under constraints for continuous-state processes.

Reinforcement learning (RL) approaches for Large Language Models (LLMs) frequently use on-policy algorithms, such as PPO or GRPO. However, policy lag from distributed training architectures and differences between the training and inference policies break this assumption, making the data off-policy by design. To rectify this, prior work has focused on making this off-policy data appear more on-policy, either via importance sampling (IS), or by more closely aligning the training and inference policies by explicitly modifying the inference engine. In this work, we embrace off-policyness and propose a novel off-policy RL algorithm that does not require these modifications: Optimal Advantage-based Policy Optimization with Lagged Inference policy (OAPL). We show that OAPL outperforms GRPO with importance sampling on competition math benchmarks, and can match the performance of a publicly available coding model, DeepCoder, on LiveCodeBench, while using 3x fewer generations during training. We further empirically demonstrate that models trained via OAPL have improved test time scaling under the Pass@k metric. OAPL allows for efficient, effective post-training even with lags of more than 400 gradient steps between the training and inference policies, 100x more off-policy than prior approaches.

RL-based agentic search enables LLMs to solve complex questions via dynamic planning and external search. While this approach significantly enhances accuracy with agent policies optimized via large-scale reinforcement learning, we identify a critical gap in reliability: these agents fail to recognize their reasoning boundaries and rarely admit ``I DON'T KNOW'' (IDK) even when evidence is insufficient or reasoning reaches its limit. The lack of reliability often leads to plausible but unreliable answers, introducing significant risks in many real-world scenarios. To this end, we propose Boundary-Aware Policy Optimization (BAPO), a novel RL framework designed to cultivate reliable boundary awareness without compromising accuracy. BAPO introduces two key components: (i) a group-based boundary-aware reward that encourages an IDK response only when the reasoning reaches its limit, and (ii) an adaptive reward modulator that strategically suspends this reward during early exploration, preventing the model from exploiting IDK as a shortcut. Extensive experiments on four benchmarks demonstrate that BAPO substantially enhances the overall reliability of agentic search.

Agentic reinforcement learning can induce tool abuse, where models overuse external tools even for queries solvable by internal reasoning. Existing approaches mitigate this issue with uniform tool-use penalties or hard limits, which reduce tool frequency but may also suppress useful tool-assisted exploration. We propose EAPO, an Efficient Agentic Policy Optimization framework that learns selective tool use. EAPO introduces tool-free trajectories into each rollout group, applies difficulty-aware reward shaping to penalize redundant tool calls mainly on easier queries, and uses confidence-aware token reweighting to improve policy learning. Across nine mathematical and knowledge-intensive reasoning benchmarks, EAPO consistently improves the accuracy efficiency trade-off on Qwen2.5-3B, Qwen2.5-7B, and Llama3.1-8B. Compared with GRPO, EAPO improves average performance by 10.45%, 7.27%, and 9.69%, while reducing average tool calls by 18.33%, 18.33%, and 24.59%, respectively. These results show that agents can learn when not to use tools without compromising tool-integrated reasoning.

While reinforcement learning (RL) shows promise in training tool-use large language models (LLMs) using verifiable outcome rewards, existing methods largely overlook the potential of explicit reasoning rewards to bolster reasoning and tool utilization. Furthermore, natively combining reasoning and outcome rewards may yield suboptimal performance or conflict with the primary optimization objective. To address this, we propose advantage-weighted policy optimization (AWPO) -- a principled RL framework that effectively integrates explicit reasoning rewards to enhance tool-use capability. AWPO incorporates variance-aware gating and difficulty-aware weighting to adaptively modulate advantages from reasoning signals based on group-relative statistics, alongside a tailored clipping mechanism for stable optimization. Extensive experiments demonstrate that AWPO achieves state-of-the-art performance across standard tool-use benchmarks, significantly outperforming strong baselines and leading closed-source models in challenging multi-turn scenarios. Notably, with exceptional parameter efficiency, our 4B model surpasses Grok-4 by 16.0 percent in multi-turn accuracy while preserving generalization capability on the out-of-distribution MMLU-Pro benchmark.

Reinforcement learning with verifiable rewards improves reasoning, while the allocation of learning signal shapes which solutions remain accessible under repeated sampling. Group-relative objectives assign equal advantages to equally rewarded responses, making aggregate credit proportional to sampled mode frequency. We introduce Exploration-Preserving Policy Optimization (ExPPO), a lightweight advantage-shaping rule that redistributes credit using prompt-relative, length-normalized response surprisal and prompt pass rate. ExPPO combines bounded shaping with shared normalization to preserve verifier polarity and approximately maintain each prompt group's total absolute sequence-advantage mass. Our analysis characterizes response-level credit allocation alongside sampled mode updates, deriving local conditions for gains in entropy and correct-mode discovery. Experiments show improved in-domain and out-of-domain reasoning coverage, higher aggregate response accuracy, and strong coverage at large sampling budgets. A controlled multi-answer evaluation further demonstrates increased correct-mode yield and gains in diversity among verified-correct responses. Code is available at https://github.com/jinhangzhan/ExPPO

Policy-based reinforcement learning algorithms are widely used in various fields. Among them, mainstream policy optimization algorithms such as TRPO and PPO introduce importance sampling into policy iteration, which allows the reuse of historical data. However, this can also lead to a high variance of the surrogate objective and indirectly affects the stability and convergence of the algorithm. In this paper, we first derived an upper bound of the surrogate objective variance, which can grow quadratically with the increase of the surrogate objective. Next, we proposed the dropout technique to avoid the excessive increase of the surrogate objective variance caused by importance sampling. Then, we introduced a general reinforcement learning framework applicable to mainstream policy optimization methods, and applied the dropout technique to the PPO algorithm to obtain the D-PPO variant. Finally, we conduct comparative experiments between D-PPO and PPO algorithms in the Atari 2600 environment, and the results show that D-PPO achieved significant performance improvements compared to PPO, and effectively limited the excessive increase of the surrogate objective variance during training.

Large Language Models (LLMs) have shown promise in solving complex mathematical problems, yet they still fall short of producing accurate and consistent solutions. Reinforcement Learning (RL) is a framework for aligning these models with task-specific rewards, improving overall quality and reliability. Group Relative Policy Optimization (GRPO) is an efficient, value-function-free alternative to Proximal Policy Optimization (PPO) that leverages group-relative reward normalization. We introduce Iterative Group Relative Policy Optimization (iGRPO), a two-stage extension of GRPO that adds dynamic self-conditioning through model-generated drafts. In Stage 1, iGRPO samples multiple exploratory drafts and selects the highest-reward draft using the same scalar reward signal used for optimization. In Stage 2, it appends this best draft to the original prompt and applies a GRPO-style update on draft-conditioned refinements, training the policy to improve beyond its strongest prior attempt. Under matched rollout budgets, iGRPO consistently outperforms GRPO across base models (e.g., Nemotron-H-8B-Base-8K and DeepSeek-R1 Distilled), validating its effectiveness on diverse reasoning benchmarks. Moreover, applying iGRPO to OpenReasoning-Nemotron-7B trained on AceReason-Math achieves new state-of-the-art results of 85.62\% and 79.64\% on AIME24 and AIME25, respectively. Ablations further show that the refinement wrapper generalizes beyond GRPO variants, benefits from a generative judge, and alters learning dynamics by delaying entropy collapse. These results underscore the potential of iterative, self-feedback-based RL for advancing verifiable mathematical reasoning.

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

In neural combinatorial optimization (CO), reinforcement learning (RL) can turn a deep neural net into a fast, powerful heuristic solver of NP-hard problems. This approach has a great potential in practical applications because it allows near-optimal solutions to be found without expert guides armed with substantial domain knowledge. We introduce Policy Optimization with Multiple Optima (POMO), an end-to-end approach for building such a heuristic solver. POMO is applicable to a wide range of CO problems. It is designed to exploit the symmetries in the representation of a CO solution. POMO uses a modified REINFORCE algorithm that forces diverse rollouts towards all optimal solutions. Empirically, the low-variance baseline of POMO makes RL training fast and stable, and it is more resistant to local minima compared to previous approaches. We also introduce a new augmentation-based inference method, which accompanies POMO nicely. We demonstrate the effectiveness of POMO by solving three popular NP-hard problems, namely, traveling salesman (TSP), capacitated vehicle routing (CVRP), and 0-1 knapsack (KP). For all three, our solver based on POMO shows a significant improvement in performance over all recent learned heuristics. In particular, we achieve the optimality gap of 0.14% with TSP100 while reducing inference time by more than an order of magnitude.

Direct Preference Optimization (DPO) has emerged as a popular alternative to Reinforcement Learning from Human Feedback (RLHF), offering theoretical equivalence with simpler implementation. We prove this equivalence is conditional rather than universal, depending on an implicit assumption frequently violated in practice: the RLHF-optimal policy must prefer human-preferred responses. When this assumption fails, DPO optimizes relative advantage over the reference policy rather than absolute alignment with human preferences, leading to pathological convergence where policies decrease DPO loss while preferring dispreferred responses. We characterize when this assumption is violated, show the existence of an undesirable solution space, and prove that DPO and RLHF optimize fundamentally different objectives in such cases. To address this, we introduce Constrained Preference Optimization (CPO), augmenting RLHF with constraints for provable alignment. We further provide a geometric interpretation through soft margin ranking, revealing that DPO implements margin ranking with potentially negative targets. Our theoretical analysis establishes when DPOs' guarantees hold and provides solutions preserving simplicity with provable alignment. Comprehensive experiments on standard benchmarks demonstrate that CPO achieves state-of-the-art performance. Code is available at: https://github.com/visitworld123/CPO.

Reinforcement learning with verifiable rewards has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models particularly in mathematics. Current approaches in this domain present a clear trade-off: PPO-style methods (e.g., GRPO/DAPO) offer training stability but exhibit slow learning trajectories due to their trust-region constraints on policy updates, while REINFORCE-style approaches (e.g., CISPO) demonstrate improved learning efficiency but suffer from performance instability as they clip importance sampling weights while still permitting non-zero gradients outside the trust-region. To address these limitations, we introduce DISPO, a simple yet effective REINFORCE-style algorithm that decouples the up-clipping and down-clipping of importance sampling weights for correct and incorrect responses, yielding four controllable policy update regimes. Through targeted ablations, we uncover how each regime impacts training: for correct responses, weights >1 increase the average token entropy (i.e., exploration) while weights <1 decrease it (i.e., distillation) -- both beneficial but causing gradual performance degradation when excessive. For incorrect responses, overly restrictive clipping triggers sudden performance collapse through repetitive outputs (when weights >1) or vanishing response lengths (when weights <1). By separately tuning these four clipping parameters, DISPO maintains the exploration-distillation balance while preventing catastrophic failures, achieving 61.04% on AIME'24 (vs. 55.42% CISPO and 50.21% DAPO) with similar gains across various benchmarks and models.

Incorporating safety is an essential prerequisite for broadening the practical applications of reinforcement learning in real-world scenarios. To tackle this challenge, Constrained Markov Decision Processes (CMDPs) are leveraged, which introduce a distinct cost function representing safety violations. In CMDPs' settings, Lagrangian relaxation technique has been employed in previous algorithms to convert constrained optimization problems into unconstrained dual problems. However, these algorithms may inaccurately predict unsafe behavior, resulting in instability while learning the Lagrange multiplier. This study introduces a novel safe reinforcement learning algorithm, Safety Critic Policy Optimization (SCPO). In this study, we define the safety critic, a mechanism that nullifies rewards obtained through violating safety constraints. Furthermore, our theoretical analysis indicates that the proposed algorithm can automatically balance the trade-off between adhering to safety constraints and maximizing rewards. The effectiveness of the SCPO algorithm is empirically validated by benchmarking it against strong baselines.

Post-training with supervised chain-of-thought fine-tuning and reinforcement learning from verifiable rewards has substantially improved the mathematical reasoning capabilities of large language models (LLMs). However, their application to signal processing problems remains relatively under-explored. This report investigates reinforcement fine-tuning strategies for adapting Qwen2.5-3B-Base to graduate-level signal mathematical problems from WirelessMATHBench-XL, a comprehensive benchmark for mathematical reasoning in this domain. We examine two training paradigms: (i) direct reinforcement learning (RL) on WirelessMATHBench-XL with verifiable rewards; and (ii) supervised fine-tuning (SFT) on a distilled wireless-domain chain-of-thought corpus, followed by the same domain-specific RL stage. Across both paradigms, we benchmark Group Relative Policy Optimization (GRPO), Group Sequence Policy Optimization (GSPO), and Geometric-Mean Policy Optimization (GMPO). We aim to assess whether domain-aware CoT SFT serves as an effective initialization for subsequent RL, and whether GSPO or GMPO offer advantages in stability or accuracy over GRPO for signal reasoning tasks. Our best model achieves an overall accuracy of 39.12\%, representing a more than threefold improvement over the untrained Base model (12.37\%).

Among on-policy reinforcement learning algorithms, Proximal Policy Optimization (PPO) demonstrates is widely favored for its simplicity, numerical stability, and strong empirical performance. Standard PPO relies on surrogate objectives defined via importance ratios, which require evaluating policy likelihood that is typically straightforward when the policy is modeled as a Gaussian distribution. However, extending PPO to more expressive, high-capacity policy models such as continuous normalizing flows (CNFs), also known as flow-matching models, is challenging because likelihood evaluation along the full flow trajectory is computationally expensive and often numerically unstable. To resolve this issue, we propose PolicyFlow, a novel on-policy CNF-based reinforcement learning algorithm that integrates expressive CNF policies with PPO-style objectives without requiring likelihood evaluation along the full flow path. PolicyFlow approximates importance ratios using velocity field variations along a simple interpolation path, reducing computational overhead without compromising training stability. To further prevent mode collapse and further encourage diverse behaviors, we propose the Brownian Regularizer, an implicit policy entropy regularizer inspired by Brownian motion, which is conceptually elegant and computationally lightweight. Experiments on diverse tasks across various environments including MultiGoal, PointMaze, IsaacLab and MuJoCo Playground show that PolicyFlow achieves competitive or superior performance compared to PPO using Gaussian policies and flow-based baselines including FPO and DPPO. Notably, results on MultiGoal highlight PolicyFlow's ability to capture richer multimodal action distributions.

GRPO-based LLM post-training commonly samples multiple trajectories from the same prompt and then trains on the resulting group. In long-context GRPO workloads, this shared prompt-side prefix can contain retrieved passages, visual tokens, tool schemas, system instructions, or task context, while the full rollout group is still too large to pack into one training microbatch. Standard dense trainers therefore recompute the same prefix forward and backward for every trajectory. We present a schedule-level reuse mechanism that decouples prefix and suffix computation. The schedule runs prefix forward once, executes suffixes as ordinary microbatches while reading prefix K/V and accumulating prefix-side gK/gV , and then runs prefix backward once on the accumulated gradient cache. This reordered schedule is equivalent to baseline training over real arithmetic and aligns numerically within finite-precision tolerance. Because only K/V and gK/gV are hot during suffix computation, the approach offloads dormant prefix activations, integrates with TP/EP/CP/PP and DP-style placement at the execution level, and preserves aux-loss-based MoE router semantics through logical prefix-token accounting. On dense Llama3-8B, Qwen3-8B, and MoE Qwen3-MoE-30B-A3B configurations, the schedule matches optimizer updates across TP/CP/PP/EP combinations, aligns on a 100-step real GRPO actor-update trace replay, reaches up to 4.395x speedup (2.930x under a conservative compile-on comparison) as prefix ratio and GRPO group size grow, and reduces Phase-B peak HBM by up to 59.1%, extending the Llama3-8B capacity frontier from 17,920 to 29,696 total tokens.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for post-training reasoning models. However, group-based methods such as Group Relative Policy Optimization (GRPO) face a critical dilemma in sparse-reward settings: pure Reinforcement Learning (RL) suffers from advantage collapse and high-variance gradient estimation, while mixed-policy optimization introduces persistent distributional bias. To resolve this dilemma, we introduce Hindsight-Anchored Policy Optimization (HAPO). HAPO employs the Synthetic Success Injection (SSI) operator, a hindsight mechanism that selectively anchors optimization to teacher demonstrations during failure. This injection is governed by a Thompson sampling-inspired gating mechanism, creating an autonomous, self-paced curriculum. Theoretically, we demonstrate that HAPO achieves asymptotic consistency: by naturally annealing the teacher signal as the policy improves, HAPO recovers the unbiased on-policy gradient. This ensures off-policy guidance acts as a temporary scaffold rather than a persistent ceiling, enabling the model to surpass the limitations of static teacher forcing.

Speculative decoding accelerates inference by using a lightweight draft model to generate candidate tokens in parallel, and are then verified by the target model, enabling lossless acceleration. Recently, diffusion-based speculative decoding further improves parallelism by generating multiple tokens per forward pass via block-level diffusion, achieving state-of-the-art (SOTA) performance. However, existing methods adopt a fixed inference block size and assume a uniform optimal decoding strategy across all inputs. In this paper, we show that this assumption is suboptimal, as the optimal block size varies across samples and plays a critical role in speculative decoding performance. Moreover, these values exhibit a clear local structure, concentrating around the training block size, which reduces the problem to a low-dimensional and structured decision space. Based on these insights, we propose BlockPilot, a sample-adaptive policy that predicts the optimal block size from the prefilling representation. Specifically, we formulate block size selection as a lightweight policy learning problem and propose an instance-adaptive decision mechanism that predicts the optimal block size based on the representation of the prefilling stage. The prediction is performed only once after prefilling, allowing for seamless integration. Extensive experiments demonstrate that our method is plug-and-play, introduces minimal overhead, and consistently improves efficiency, achieving an acceptance length of 5.92 and a 4.20times speedup on Qwen3-4B under temperature T=1.

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

Entropy control has become an effective tool in reinforcement learning (RL) of large language models (LLMs), helping balance exploration-exploitation trade-off during alignment process. Such RL paradigm is often conducted on mixtures of heterogeneous tasks, which induce distinct entropy regimes under the same policy, making global or token-level entropy regulation insufficient to corresponding heterogeneous needs of exploration. This heterogeneity further makes GRPO-style normalized advantages induce an entropy-dependent bias, making advantage signals across prompt groups statistically non-comparable. To address this issue, we propose Group Entropy-Controlled Policy Optimization (GEPO), a lightweight extension to GRPO that uses group entropy, estimated from existing grouped samples to perform entropy-conditioned asymmetric advantage shaping. GEPO attenuates positive advantages in low-entropy groups to reduce over-exploitation, and negative advantages in high-entropy groups to preserve exploration, with adaptive thresholds derived from historical entropy statistics. Extensive experiments on two base models across thirteen benchmarks spanning mathematics, physics, science, code generation, and instruction following show that GEPO consistently outperforms GRPO and recent entropy-controlled methods, delivering balanced cross-task improvements while preserving task-specific exploration levels throughout training.

Proximal Policy Optimization (PPO) is a ubiquitous on-policy reinforcement learning algorithm but is significantly less utilized than off-policy learning algorithms in multi-agent settings. This is often due to the belief that PPO is significantly less sample efficient than off-policy methods in multi-agent systems. In this work, we carefully study the performance of PPO in cooperative multi-agent settings. We show that PPO-based multi-agent algorithms achieve surprisingly strong performance in four popular multi-agent testbeds: the particle-world environments, the StarCraft multi-agent challenge, Google Research Football, and the Hanabi challenge, with minimal hyperparameter tuning and without any domain-specific algorithmic modifications or architectures. Importantly, compared to competitive off-policy methods, PPO often achieves competitive or superior results in both final returns and sample efficiency. Finally, through ablation studies, we analyze implementation and hyperparameter factors that are critical to PPO's empirical performance, and give concrete practical suggestions regarding these factors. Our results show that when using these practices, simple PPO-based methods can be a strong baseline in cooperative multi-agent reinforcement learning. Source code is released at https://github.com/marlbenchmark/on-policy.

Off-policy learning (OPL) aims at finding improved policies from logged bandit data, often by minimizing the inverse propensity scoring (IPS) estimator of the risk. In this work, we investigate a smooth regularization for IPS, for which we derive a two-sided PAC-Bayes generalization bound. The bound is tractable, scalable, interpretable and provides learning certificates. In particular, it is also valid for standard IPS without making the assumption that the importance weights are bounded. We demonstrate the relevance of our approach and its favorable performance through a set of learning tasks. Since our bound holds for standard IPS, we are able to provide insight into when regularizing IPS is useful. Namely, we identify cases where regularization might not be needed. This goes against the belief that, in practice, clipped IPS often enjoys favorable performance than standard IPS in OPL.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but suffers from advantage collapse on ``hard samples'' where all rollouts fail. This lack of variance eliminates crucial learning signals. For these intractable samples, simply scaling up rollout budgets offers limited gains. We introduce Joint Policy and Prompt Optimization (P^2O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P^2O leverages the GEPA algorithm to discover successful reasoning prompts for intractable instances. Via context distillation, the model internalizes these prompt-induced gains directly into its parameters, removing the need for inference-time prompting. Empirically, P^2O restores critical advantage signals, significantly outperforming standard GRPO and surpassing baselines with doubled rollout budgets, ultimately yielding strong out-of-distribution generalization and an up to 9.5% performance improvement. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates establishes a self-reinforcing paradigm for autonomous LLM alignment.

Provably efficient Model-Based Reinforcement Learning (MBRL) based on optimism or posterior sampling (PSRL) is ensured to attain the global optimality asymptotically by introducing the complexity measure of the model. However, the complexity might grow exponentially for the simplest nonlinear models, where global convergence is impossible within finite iterations. When the model suffers a large generalization error, which is quantitatively measured by the model complexity, the uncertainty can be large. The sampled model that current policy is greedily optimized upon will thus be unsettled, resulting in aggressive policy updates and over-exploration. In this work, we propose Conservative Dual Policy Optimization (CDPO) that involves a Referential Update and a Conservative Update. The policy is first optimized under a reference model, which imitates the mechanism of PSRL while offering more stability. A conservative range of randomness is guaranteed by maximizing the expectation of model value. Without harmful sampling procedures, CDPO can still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic policy improvement and global optimality simultaneously. Empirical results also validate the exploration efficiency of CDPO.

Morphology-control co-design concerns the coupled optimization of an agent's body structure and control policy. This problem exhibits a bi-level structure, where the control dynamically adapts to the morphology to maximize performance. Existing methods typically neglect the control's adaptation dynamics by adopting a single-level formulation that treats the control policy as fixed when optimizing morphology. This can lead to inefficient optimization, as morphology updates may be misaligned with control adaptation. In this paper, we revisit the co-design problem from a game-theoretic perspective, modeling the intrinsic coupling between morphology and control as a novel variant of a Stackelberg game. We propose Stackelberg Proximal Policy Optimization (Stackelberg PPO), which explicitly incorporates the control's adaptation dynamics into morphology optimization. By modeling this intrinsic coupling, our method aligns morphology updates with control adaptation, thereby stabilizing training and improving learning efficiency. Experiments across diverse co-design tasks demonstrate that Stackelberg PPO outperforms standard PPO in both stability and final performance, opening the way for dramatically more efficient robotics designs.