Daily Papers

Recent research-level physics-reasoning benchmarks for LLMs reveal a failure mode that lies not in knowledge or execution, but in modeling the world being reasoned about. Models often silently alter given quantities, fabricate laws, or inject unstated assumptions to force a problem into familiar patterns, and then reason inside this corrupted world. We define this premise-level divergence as modeling drift: the gap between a model's internal axiomatic world model (AWM) and the true physical world specified in the problem. Although RLVR and PRM have yielded substantial gains in mathematics and code, their reward shapes do not directly supervise world modeling in axiomatic domains such as physics. We propose Reinforcement Learning with Axiomatic World Modeling (RLAWM), which optimizes the policy by penalizing divergence between its inferred axiomatic world model and the true physics world. RLAWM probes physics reasoning at two hierarchical levels (modeling and solving), each scored by a physically grounded reward. The modeling reward targets abstract knowledge formulation, evaluating whether the model captures the true axiomatic world before attempting calculation. The solving reward targets instantiated knowledge reasoning, checking whether the model's concrete derivation remains consistent with the axiomatic world. This two-level structure separates what world the model believes it is reasoning in from how it reasons within that world. The framework operates exclusively during training, with no extra cost during inference. RLAWM improves performance by up to +12.2 points on PhysReason and +5.2 on PHYSICS over the baseline. It also generalizes zero-shot across difficulty, source, and domain, with a 2.45x gain and +10 points over the strongest baseline on olympiad-level physics and math.

Reinforcement learning usually uses the feedback rewards of environmental to train agents. But the rewards in the actual environment are sparse, and even some environments will not rewards. Most of the current methods are difficult to get good performance in sparse reward or non-reward environments. Although using shaped rewards is effective when solving sparse reward tasks, it is limited to specific problems and learning is also susceptible to local optima. We propose a model-free method that does not rely on environmental rewards to solve the problem of sparse rewards in the general environment. Our method use the minimum number of transitions between states as the distance to replace the rewards of environmental, and proposes a goal-distance gradient to achieve policy improvement. We also introduce a bridge point planning method based on the characteristics of our method to improve exploration efficiency, thereby solving more complex tasks. Experiments show that our method performs better on sparse reward and local optimal problems in complex environments than previous work.

Learning to solve tasks from a sparse reward signal is a major challenge for standard reinforcement learning (RL) algorithms. However, in the real world, agents rarely need to solve sparse reward tasks entirely from scratch. More often, we might possess prior experience to draw on that provides considerable guidance about which actions and outcomes are possible in the world, which we can use to explore more effectively for new tasks. In this work, we study how prior data without reward labels may be used to guide and accelerate exploration for an agent solving a new sparse reward task. We propose a simple approach that learns a reward model from online experience, labels the unlabeled prior data with optimistic rewards, and then uses it concurrently alongside the online data for downstream policy and critic optimization. This general formula leads to rapid exploration in several challenging sparse-reward domains where tabula rasa exploration is insufficient, including the AntMaze domain, Adroit hand manipulation domain, and a visual simulated robotic manipulation domain. Our results highlight the ease of incorporating unlabeled prior data into existing online RL algorithms, and the (perhaps surprising) effectiveness of doing so.

In deep reinforcement learning (RL) research, there has been a concerted effort to design more efficient and productive exploration methods while solving sparse-reward problems. These exploration methods often share common principles (e.g., improving diversity) and implementation details (e.g., intrinsic reward). Prior work found that non-stationary Markov decision processes (MDPs) require exploration to efficiently adapt to changes in the environment with online transfer learning. However, the relationship between specific exploration characteristics and effective transfer learning in deep RL has not been characterized. In this work, we seek to understand the relationships between salient exploration characteristics and improved performance and efficiency in transfer learning. We test eleven popular exploration algorithms on a variety of transfer types -- or ``novelties'' -- to identify the characteristics that positively affect online transfer learning. Our analysis shows that some characteristics correlate with improved performance and efficiency across a wide range of transfer tasks, while others only improve transfer performance with respect to specific environment changes. From our analysis, make recommendations about which exploration algorithm characteristics are best suited to specific transfer situations.

Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been proposed to address some of these problems. Specifically, spiking neural networks are suitable for efficient hardware implementations. However, effective learning algorithms for spiking networks remain elusive, although it is suspected that effective plasticity mechanisms could alleviate the problem of data efficiency. Here, we present a new framework for spiking neural networks - Spark - built upon the idea of modular design, from simple components to entire models. The aim of this framework is to provide an efficient and streamlined pipeline for spiking neural networks. We showcase this framework by solving the sparse-reward cartpole problem with simple plasticity mechanisms. We hope that a framework compatible with traditional ML pipelines may accelerate research in the area, specifically for continuous and unbatched learning, akin to the one animals exhibit.

Large Language Models (LLMs) have achieved remarkable progress through Reinforcement Learning with Verifiable Rewards (RLVR), yet still rely heavily on external supervision (e.g., curated labels). Adversarial learning, particularly through self-play, offers a promising alternative that enables models to iteratively learn from themselves - thus reducing reliance on external supervision. Dual-play extends adversarial learning by assigning specialized roles to two models and training them against each other, fostering sustained competition and mutual evolution. Despite its promise, adapting dual-play training to LLMs remains limited, largely due to their susceptibility to reward hacking and training instability. In this paper, we introduce PasoDoble, a novel LLM dual-play framework. PasoDoble adversarially trains two models initialized from the same base model: a Proposer, which generates challenging questions with ground-truth answers, and a Solver, which attempts to solve them. We enrich the Proposer with knowledge from a pre-training dataset to ensure the questions' quality and diversity. To avoid reward hacking, the Proposer is rewarded for producing only valid questions that push the Solver's limit, while the Solver is rewarded for solving them correctly, and both are updated jointly. To further enhance training stability, we introduce an optional offline paradigm that decouples Proposer and Solver updates, alternately updating each for several steps while holding the other fixed. Notably, PasoDoble operates without supervision during training. Experimental results show that PasoDoble can improve the reasoning performance of LLMs. Our project page is available at https://hcy123902.github.io/PasoDoble.

Large Language Models (LLMs) have demonstrated strong potential in complex reasoning, yet their progress remains fundamentally constrained by reliance on massive high-quality human-curated tasks and labels, either through supervised fine-tuning (SFT) or reinforcement learning (RL) on reasoning-specific data. This dependence renders supervision-heavy training paradigms increasingly unsustainable, with signs of diminishing scalability already evident in practice. To overcome this limitation, we introduce CPMöbius (CPMobius), a collaborative Coach-Player paradigm for data-free reinforcement learning of reasoning models. Unlike traditional adversarial self-play, CPMöbius, inspired by real world human sports collaboration and multi-agent collaboration, treats the Coach and Player as independent but cooperative roles. The Coach proposes instructions targeted at the Player's capability and receives rewards based on changes in the Player's performance, while the Player is rewarded for solving the increasingly instructive tasks generated by the Coach. This cooperative optimization loop is designed to directly enhance the Player's mathematical reasoning ability. Remarkably, CPMöbius achieves substantial improvement without relying on any external training data, outperforming existing unsupervised approaches. For example, on Qwen2.5-Math-7B-Instruct, our method improves accuracy by an overall average of +4.9 and an out-of-distribution average of +5.4, exceeding RENT by +1.5 on overall accuracy and R-zero by +4.2 on OOD accuracy.

Self-evolving Large Language Models (LLMs) offer a scalable path toward super-intelligence by autonomously generating, refining, and learning from their own experiences. However, existing methods for training such models still rely heavily on vast human-curated tasks and labels, typically via fine-tuning or reinforcement learning, which poses a fundamental bottleneck to advancing AI systems toward capabilities beyond human intelligence. To overcome this limitation, we introduce R-Zero, a fully autonomous framework that generates its own training data from scratch. Starting from a single base LLM, R-Zero initializes two independent models with distinct roles, a Challenger and a Solver. These models are optimized separately and co-evolve through interaction: the Challenger is rewarded for proposing tasks near the edge of the Solver capability, and the Solver is rewarded for solving increasingly challenging tasks posed by the Challenger. This process yields a targeted, self-improving curriculum without any pre-existing tasks and labels. Empirically, R-Zero substantially improves reasoning capability across different backbone LLMs, e.g., boosting the Qwen3-4B-Base by +6.49 on math-reasoning benchmarks and +7.54 on general-domain reasoning benchmarks.

TaskGen is an open-sourced agentic framework which uses an Agent to solve an arbitrary task by breaking them down into subtasks. Each subtask is mapped to an Equipped Function or another Agent to execute. In order to reduce verbosity (and hence token usage), TaskGen uses StrictJSON that ensures JSON output from the Large Language Model (LLM), along with additional features such as type checking and iterative error correction. Key to the philosophy of TaskGen is the management of information/memory on a need-to-know basis. We empirically evaluate TaskGen on various environments such as 40x40 dynamic maze navigation with changing obstacle locations (100% solve rate), TextWorld escape room solving with dense rewards and detailed goals (96% solve rate), web browsing (69% of actions successful), solving the MATH dataset (71% solve rate over 100 Level-5 problems), Retrieval Augmented Generation on NaturalQuestions dataset (F1 score of 47.03%)

One of the challenges in applying reinforcement learning in a complex real-world environment lies in providing the agent with a sufficiently detailed reward function. Any misalignment between the reward and the desired behavior can result in unwanted outcomes. This may lead to issues like "reward hacking" where the agent maximizes rewards by unintended behavior. In this work, we propose to disentangle the reward into two distinct parts. A simple task-specific reward, outlining the particulars of the task at hand, and an unknown common-sense reward, indicating the expected behavior of the agent within the environment. We then explore how this common-sense reward can be learned from expert demonstrations. We first show that inverse reinforcement learning, even when it succeeds in training an agent, does not learn a useful reward function. That is, training a new agent with the learned reward does not impair the desired behaviors. We then demonstrate that this problem can be solved by training simultaneously on multiple tasks. That is, multi-task inverse reinforcement learning can be applied to learn a useful reward function.

Reinforcement learning (RL) has become a central paradigm for post-training large language models (LLMs), particularly for complex reasoning tasks, yet it often suffers from exploration collapse: policies prematurely concentrate on a small set of dominant reasoning patterns, improving pass@1 while limiting rollout-level diversity and gains in pass@k. We argue that this failure stems from regularizing local token behavior rather than diversity over sets of solutions. To address this, we propose Uniqueness-Aware Reinforcement Learning, a rollout-level objective that explicitly rewards correct solutions that exhibit rare high-level strategies. Our method uses an LLM-based judge to cluster rollouts for the same problem according to their high-level solution strategies, ignoring superficial variations, and reweights policy advantages inversely with cluster size. As a result, correct but novel strategies receive higher rewards than redundant ones. Across mathematics, physics, and medical reasoning benchmarks, our approach consistently improves pass@k across large sampling budgets and increases the area under the pass@k curve (AUC@K) without sacrificing pass@1, while sustaining exploration and uncovering more diverse solution strategies at scale.

With the rapid development of large language models (LLMs), generative reward models (GRMs) have been widely adopted for reward modeling and evaluation. Previous studies have primarily focused on training specialized GRMs by optimizing them on preference datasets with the judgment correctness as supervision. While it's widely accepted that GRMs with stronger problem-solving capabilities typically exhibit superior judgment abilities, we first identify a significant solve-to-judge gap when examining individual queries. Specifically, the solve-to-judge gap refers to the phenomenon where GRMs struggle to make correct judgments on some queries (14%-37%), despite being fully capable of solving them. In this paper, we propose the Solve-to-Judge (S2J) approach to address this problem. Specifically, S2J simultaneously leverages both the solving and judging capabilities on a single GRM's output for supervision, explicitly linking the GRM's problem-solving and evaluation abilities during model optimization, thereby narrowing the gap. Our comprehensive experiments demonstrate that S2J effectively reduces the solve-to-judge gap by 16.2%, thereby enhancing the model's judgment performance by 5.8%. Notably, S2J achieves state-of-the-art (SOTA) performance among GRMs built on the same base model while utilizing a significantly smaller training dataset. Moreover, S2J accomplishes this through self-evolution without relying on more powerful external models for distillation.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

The reward hypothesis posits that, "all of what we mean by goals and purposes can be well thought of as maximization of the expected value of the cumulative sum of a received scalar signal (reward)." We aim to fully settle this hypothesis. This will not conclude with a simple affirmation or refutation, but rather specify completely the implicit requirements on goals and purposes under which the hypothesis holds.

Solving open-ended science questions remains challenging for large language models, particularly due to inherently unreliable supervision and evaluation. The bottleneck lies in the data construction and reward design for scientific post-training. We develop a large-scale, systematic data processing pipeline that transforms heterogeneous open-source science data into Dr. SCI dataset, which comprises of 1M questions across eight STEM subjects, with explicit verifiable/open-ended splits, scalable difficulty annotation, and fine-grained rubrics that operationalize evaluation for open-ended answers. Building on this dataset, we propose the Dr. SCI post-training pipeline, which redesigns the standard SFT -> RL workflow through three components: (i) Exploration-Expanding SFT, which broadens the model's reasoning pattern coverage prior to RL; (ii) Dynamic Difficulty Curriculum, which adapts training data to the model's evolving scientific capability; and (iii) SciRubric-Guided RL, which enables stable reinforcement learning on open-ended scientific questions via rubric-based evaluation with explicit answer correctness. Qwen3-4B-Base trained using Dr. SCI pipeline achieves 63.2 on GPQA-diamond and 32.4 on GPQA-general, consistently improves over strong post-trained baselines such as o1-mini and GPT-4o, demonstrating substantial gains in scientific reasoning, especially in open-ended settings.

The standard paradigm for solving coding tasks via large language models (LLMs) is to generate-then-rank programs, where the latter step uses a verifier in the ranking process. The growing consensus is that a comprehensive verifier (e.g., a full test suite) should be prioritized over an outcome reward model (ORM) whenever possible, with little consideration given to the trade-offs involved. We aim to challenge this assumption by systematically exploring the tradeoff between speed and accuracy. We find that ORMs play a crucial role in scaling verification through trading accuracy for speed, even when a comprehensive verifier is available. Their value becomes especially apparent when used in a generate-prune-then-rank approach, where a faster but less accurate verifier removes incorrect solutions prior to ranking -- leading to a system that is 11.65x faster while only being 8.33% less accurate than the full test suite. We analyze the generate-prune-then-rank approach and show that it works by filtering out incorrect but highly ranked solutions. These findings enable the design of scalable and accurate program ranking systems.

Collecting high-quality preference datasets for reinforcement learning from human feedback (RLHF) is resource-intensive and challenging. As a result, researchers often train reward models on extensive offline datasets which aggregate diverse generation sources and scoring/alignment policies. We hypothesize that this aggregation has an averaging effect on reward model scores, which limits signal and impairs the alignment process. Inspired by the field of inverse RL, we define the 'inverse alignment problem' in language model training, where our objective is to optimize the critic's reward for a fixed actor and a fixed offline preference dataset. We hypothesize that solving the inverse alignment problem will improve reward model quality by providing clearer feedback on the policy's current behavior. To that end, we investigate whether repeatedly fine-tuning a reward model on subsets of the offline preference dataset aligned with a periodically frozen policy during RLHF improves upon vanilla RLHF. Our empirical results demonstrate that this approach facilitates superior alignment and faster convergence compared to using an unaligned or out-of-distribution reward model relative to the LLM policy.

Large language models (LLMs) can transform education, but their optimization for direct question-answering often undermines effective pedagogy which requires strategically withholding answers. To mitigate this, we propose an online reinforcement learning (RL)-based alignment framework that can quickly adapt LLMs into effective tutors using simulated student-tutor interactions by emphasizing pedagogical quality and guided problem-solving over simply giving away answers. We use our method to train a 7B parameter tutor model without human annotations which reaches similar performance to larger proprietary models like LearnLM. We introduce a controllable reward weighting to balance pedagogical support and student solving accuracy, allowing us to trace the Pareto frontier between these two objectives. Our models better preserve reasoning capabilities than single-turn SFT baselines and can optionally enhance interpretability through thinking tags that expose the model's instructional planning.

Intrinsic reward shaping has emerged as a prevalent approach to solving hard-exploration and sparse-rewards environments in reinforcement learning (RL). While single intrinsic rewards, such as curiosity-driven or novelty-based methods, have shown effectiveness, they often limit the diversity and efficiency of exploration. Moreover, the potential and principle of combining multiple intrinsic rewards remains insufficiently explored. To address this gap, we introduce HIRE (Hybrid Intrinsic REward), a flexible and elegant framework for creating hybrid intrinsic rewards through deliberate fusion strategies. With HIRE, we conduct a systematic analysis of the application of hybrid intrinsic rewards in both general and unsupervised RL across multiple benchmarks. Extensive experiments demonstrate that HIRE can significantly enhance exploration efficiency and diversity, as well as skill acquisition in complex and dynamic settings.

A generally intelligent agent must be able to teach itself how to solve problems in complex domains with minimal human supervision. Recently, deep reinforcement learning algorithms combined with self-play have achieved superhuman proficiency in Go, Chess, and Shogi without human data or domain knowledge. In these environments, a reward is always received at the end of the game, however, for many combinatorial optimization environments, rewards are sparse and episodes are not guaranteed to terminate. We introduce Autodidactic Iteration: a novel reinforcement learning algorithm that is able to teach itself how to solve the Rubik's Cube with no human assistance. Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves -- less than or equal to solvers that employ human domain knowledge.

Process Reward Models (PRMs) are crucial in complex reasoning and problem-solving tasks (e.g., LLM agents with long-horizon decision-making) by verifying the correctness of each intermediate reasoning step. In real-world scenarios, LLMs may apply various reasoning patterns (e.g., decomposition) to solve a problem, potentially suffering from errors under various reasoning patterns. Therefore, PRMs are required to identify errors under various reasoning patterns during the reasoning process. However, existing benchmarks mainly focus on evaluating PRMs with stepwise correctness, ignoring a systematic evaluation of PRMs under various reasoning patterns. To mitigate this gap, we introduce Socratic-PRMBench, a new benchmark to evaluate PRMs systematically under six reasoning patterns, including Transformation, Decomposition, Regather, Deduction, Verification, and Integration. Socratic-PRMBench}comprises 2995 reasoning paths with flaws within the aforementioned six reasoning patterns. Through our experiments on both PRMs and LLMs prompted as critic models, we identify notable deficiencies in existing PRMs. These observations underscore the significant weakness of current PRMs in conducting evaluations on reasoning steps under various reasoning patterns. We hope Socratic-PRMBench can serve as a comprehensive testbed for systematic evaluation of PRMs under diverse reasoning patterns and pave the way for future development of PRMs.

Reinforcement learning (RL) is a framework for solving sequential decision-making problems. In this work, we demonstrate that, surprisingly, RL emerges during the inference time of large language models (LLMs), a phenomenon we term in-context RL (ICRL). To reveal this capability, we introduce a simple multi-round prompting framework, we call ICRL prompting, for inference-time self-improvement. The goal of ICRL prompting is to guide LLMs to perform reinforcement learning during inference for self-improvement on a given task. After each response, the model receives numerical scalar feedback, denoted as a reward. In the next round, we prompt the LLM again together with a context that concatenates all prior responses and their associated rewards. We consistently observe that response quality improves as the context grows. In other words, the LLM can optimize scalar reward signals during inference, exhibiting behavior analogous to reinforcement learning. We evaluate ICRL prompting on Game of 24, creative writing, ScienceWorld, and Olympiad-level math competitions (AIME and HMMT), demonstrating significant improvements over baselines such as Self-Refine and Reflexion. Notably, even when the reward signals are generated by the same LLM, ICRL prompting still improves performance, highlighting a promising new paradigm for test-time scaling.

In this paper, we investigate the obstacle avoidance and navigation problem in the robotic control area. For solving such a problem, we propose revised Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization algorithms with an improved reward shaping technique. We compare the performances between the original DDPG and PPO with the revised version of both on simulations with a real mobile robot and demonstrate that the proposed algorithms achieve better results.

One obstacle to applying reinforcement learning algorithms to real-world problems is the lack of suitable reward functions. Designing such reward functions is difficult in part because the user only has an implicit understanding of the task objective. This gives rise to the agent alignment problem: how do we create agents that behave in accordance with the user's intentions? We outline a high-level research direction to solve the agent alignment problem centered around reward modeling: learning a reward function from interaction with the user and optimizing the learned reward function with reinforcement learning. We discuss the key challenges we expect to face when scaling reward modeling to complex and general domains, concrete approaches to mitigate these challenges, and ways to establish trust in the resulting agents.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Reinforcement Learning from Human Feedback (RLHF) has become a popular approach to align language models (LMs) with human preferences. This method involves collecting a large dataset of human pairwise preferences across various text generations and using it to infer (implicitly or explicitly) a reward model. Numerous methods have been proposed to learn the reward model and align a LM with it. However, the costly process of collecting human preferences has received little attention and could benefit from theoretical insights. This paper addresses this issue and aims to formalize the reward training model in RLHF. We frame the selection of an effective dataset as a simple regret minimization task, using a linear contextual dueling bandit method. Given the potentially large number of arms, this approach is more coherent than the best-arm identification setting. We then propose an offline framework for solving this problem. Under appropriate assumptions - linearity of the reward model in the embedding space, and boundedness of the reward parameter - we derive bounds on the simple regret. Finally, we provide a lower bound that matches our upper bound up to constant and logarithmic terms. To our knowledge, this is the first theoretical contribution in this area to provide an offline approach as well as worst-case guarantees.

In order to solve a task using reinforcement learning, it is necessary to first formalise the goal of that task as a reward function. However, for many real-world tasks, it is very difficult to manually specify a reward function that never incentivises undesirable behaviour. As a result, it is increasingly popular to use reward learning algorithms, which attempt to learn a reward function from data. However, the theoretical foundations of reward learning are not yet well-developed. In particular, it is typically not known when a given reward learning algorithm with high probability will learn a reward function that is safe to optimise. This means that reward learning algorithms generally must be evaluated empirically, which is expensive, and that their failure modes are difficult to anticipate in advance. One of the roadblocks to deriving better theoretical guarantees is the lack of good methods for quantifying the difference between reward functions. In this paper we provide a solution to this problem, in the form of a class of pseudometrics on the space of all reward functions that we call STARC (STAndardised Reward Comparison) metrics. We show that STARC metrics induce both an upper and a lower bound on worst-case regret, which implies that our metrics are tight, and that any metric with the same properties must be bilipschitz equivalent to ours. Moreover, we also identify a number of issues with reward metrics proposed by earlier works. Finally, we evaluate our metrics empirically, to demonstrate their practical efficacy. STARC metrics can be used to make both theoretical and empirical analysis of reward learning algorithms both easier and more principled.

In the last decade, Deep Reinforcement Learning has evolved into a powerful tool for complex sequential decision-making problems. It combines deep learning's proficiency in processing rich input signals with reinforcement learning's adaptability across diverse control tasks. At its core, an RL agent seeks to maximize its cumulative reward, enabling AI algorithms to uncover novel solutions previously unknown to experts. However, this focus on reward maximization also introduces a significant difficulty: improper reward specification can result in unexpected, misaligned agent behavior and inefficient learning. The complexity of accurately specifying the reward function is further amplified by the sequential nature of the task, the sparsity of learning signals, and the multifaceted aspects of the desired behavior. In this thesis, we survey the literature on effective reward specification strategies, identify core challenges relating to each of these approaches, and propose original contributions addressing the issue of sample efficiency and alignment in deep reinforcement learning. Reward specification represents one of the most challenging aspects of applying reinforcement learning in real-world domains. Our work underscores the absence of a universal solution to this complex and nuanced challenge; solving it requires selecting the most appropriate tools for the specific requirements of each unique application.

The Rubiks Cube, with its vast state space and sparse reward structure, presents a significant challenge for reinforcement learning (RL) due to the difficulty of reaching rewarded states. Previous research addressed this by propagating cost-to-go estimates from the solved state and incorporating search techniques. These approaches differ from human strategies that start from fully scrambled cubes, which can be tricky for solving a general sparse-reward problem. In this paper, we introduce a novel RL algorithm using policy gradient methods to solve the Rubiks Cube without relying on near solved-state sampling. Our approach employs a neural network to predict cost patterns between states, allowing the agent to learn directly from scrambled states. Our method was tested on the 2x2x2 Rubiks Cube, where the cube was scrambled 50,000 times, and the model successfully solved it in over 99.4% of cases. Notably, this result was achieved using only the policy network without relying on tree search as in previous methods, demonstrating its effectiveness and potential for broader applications in sparse-reward problems.

Social intelligence, the ability to navigate complex interpersonal interactions, presents a fundamental challenge for language agents. Training such agents via reinforcement learning requires solving the credit assignment problem: determining how individual utterances contribute to multi-turn dialogue outcomes. Existing approaches directly employ language models to distribute episode-level rewards, yielding attributions that are retrospective and lack theoretical grounding. We propose SAVOIR (ShApley Value fOr SocIal RL), a novel principled framework grounded in cooperative game theory. Our approach combines two complementary principles: expected utility shifts evaluation from retrospective attribution to prospective valuation, capturing an utterance's strategic potential for enabling favorable future trajectories; Shapley values ensure fair credit distribution with axiomatic guarantees of efficiency, symmetry, and marginality. Experiments on the SOTOPIA benchmark demonstrate that SAVOIR achieves new state-of-the-art performance across all evaluation settings, with our 7B model matching or exceeding proprietary models including GPT-4o and Claude-3.5-Sonnet. Notably, even large reasoning models consistently underperform, suggesting social intelligence requires qualitatively different capabilities than analytical reasoning.

Reward hacking arises when a model improves a proxy reward by exploiting shortcuts rather than solving the intended task. We study this failure mode through the geometry of reinforcement learning updates in language models and argue that hacking emerges when optimization drifts away from a stable low-dimensional learning trajectory. We analyze this drift through dominant singular directions of parameter updates and show that reward-hacking runs exhibit substantially larger directional change than clean runs. Motivated by this observation, we introduce trusted-direction projection, which constrains gradients to remain within a clean reference subspace. Across reward-hacking experiments on mathematical reasoning, the proposed approach delays shortcut exploitation and better preserves task performance.

We study test-time evolution for humanoid loco-manipulation: solving tasks that a controller was never trained for by repurposing its existing skills, improving from its own attempts, and retaining what it learns, without retraining. Our key insight is that a broad controller already holds much of the competence a new task needs, and that this competence becomes accessible through an interface between planning and control that is expressive enough to specify contact-rich, multi-stage interactions, yet executable and measurable enough that execution feedback can guide planning from experience. InterEvolve realizes this interface with two components. First, we develop an object-aware forward-backward (FB) behavioral foundation model, whose object residuals on a frozen body prior turn a new reward about the body or objects into loco-manipulation behavior at test time. Second, we specify tasks as reward programs: staged rewards with completion conditions and tunable constants. A large language model (LLM) agent revises the program structure in context, drawing on execution feedback and a skill library of verified programs, while a numerical optimizer tunes its constants. With every candidate verified across parallel simulation scenarios, the program explores new ways to induce, repurpose, and compose the controller's existing motor competence for the task at hand, and thus improves over iterations. Experiments show that human-designed rewards leave much of the FB model's loco-manipulation competence untapped, whereas the programs InterEvolve evolves release it, sometimes through novel strategies. It further produces behaviors for diverse tasks, complex scenes, and long-horizon compositions in simulation, and evolved skills run autonomously on a physical Unitree G1 from egocentric onboard perception.

Reward hacking is a form of misalignment in which models overoptimize proxy rewards without genuinely solving the underlying task. Precisely measuring reward hacking occurrence remains challenging because true task rewards are often expensive or impossible to compute. We introduce Countdown-Code, a minimal environment where models can both solve a mathematical reasoning task and manipulate the test harness. This dual-access design creates a clean separation between proxy rewards (test pass/fail) and true rewards (mathematical correctness), enabling accurate measurement of reward-hacking rates. Using this environment, we study reward hacking in open-weight LLMs and find that such behaviors can be unintentionally learned during supervised fine-tuning (SFT) when even a small fraction of reward-hacking trajectories leak into training data. As little as 1\% contamination in distillation SFT data is sufficient for models to internalize reward hacking which resurfaces during subsequent reinforcement learning (RL). We further show that RL amplifies misalignment and drives its generalization beyond the original domain. We open-source our environment and code to facilitate future research on reward hacking in LLMs. Our results reveal a previously underexplored pathway through which reward hacking can emerge and persist in LLMs, underscoring the need for more rigorous validation of synthetic SFT data. Code is available at https://github.com/zohaib-khan5040/Countdown-Code.

To facilitate research in the direction of fine-tuning foundation models from human feedback, we held the MineRL BASALT Competition on Fine-Tuning from Human Feedback at NeurIPS 2022. The BASALT challenge asks teams to compete to develop algorithms to solve tasks with hard-to-specify reward functions in Minecraft. Through this competition, we aimed to promote the development of algorithms that use human feedback as channels to learn the desired behavior. We describe the competition and provide an overview of the top solutions. We conclude by discussing the impact of the competition and future directions for improvement.

Recent work has shown that asking language models to generate reasoning steps improves performance on many reasoning tasks. When moving beyond prompting, this raises the question of how we should supervise such models: outcome-based approaches which supervise the final result, or process-based approaches which supervise the reasoning process itself? Differences between these approaches might naturally be expected not just in final-answer errors but also in reasoning errors, which can be difficult to detect and are problematic in many real-world domains such as education. We run the first comprehensive comparison between process- and outcome-based approaches trained on a natural language task, GSM8K. We find that pure outcome-based supervision produces similar final-answer error rates with less label supervision. However, for correct reasoning steps we find it necessary to use process-based supervision or supervision from learned reward models that emulate process-based feedback. In total, we improve the previous best results from 16.8% to 12.7% final-answer error and 14.0% to 3.4% reasoning error among final-answer-correct solutions.

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts. This paper proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through Outcome REwArd-based reinforcement Learning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible. We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments. This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples. To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning. With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500. Our investigation also indicates the importance of initial policy models and training queries for RL. Code, models, and data will be released to benefit future researchhttps://github.com/InternLM/OREAL.

Large Reasoning Models (LRMs) have shown remarkable capabilities in solving complex problems through reinforcement learning (RL), particularly by generating long reasoning traces. However, these extended outputs often exhibit substantial redundancy, which limits the efficiency of LRMs. In this paper, we investigate RL-based approaches to promote reasoning efficiency. Specifically, we first present a unified framework that formulates various efficient reasoning methods through the lens of length-based reward shaping. Building on this perspective, we propose a novel Length-bAsed StEp Reward shaping method (LASER), which employs a step function as the reward, controlled by a target length. LASER surpasses previous methods, achieving a superior Pareto-optimal balance between performance and efficiency. Next, we further extend LASER based on two key intuitions: (1) The reasoning behavior of the model evolves during training, necessitating reward specifications that are also adaptive and dynamic; (2) Rather than uniformly encouraging shorter or longer chains of thought (CoT), we posit that length-based reward shaping should be difficulty-aware i.e., it should penalize lengthy CoTs more for easy queries. This approach is expected to facilitate a combination of fast and slow thinking, leading to a better overall tradeoff. The resulting method is termed LASER-D (Dynamic and Difficulty-aware). Experiments on DeepSeek-R1-Distill-Qwen-1.5B, DeepSeek-R1-Distill-Qwen-7B, and DeepSeek-R1-Distill-Qwen-32B show that our approach significantly enhances both reasoning performance and response length efficiency. For instance, LASER-D and its variant achieve a +6.1 improvement on AIME2024 while reducing token usage by 63%. Further analysis reveals our RL-based compression produces more concise reasoning patterns with less redundant "self-reflections". Resources are at https://github.com/hkust-nlp/Laser.

Large language models (LLMs) exhibit remarkable problem-solving abilities, but struggle with complex tasks due to static internal knowledge. Retrieval-Augmented Generation (RAG) enhances access to external information, yet remains limited in multi-hop reasoning and strategic search due to rigid workflows. Recent advancements in agentic deep research empower LLMs to autonomously reason, search, and synthesize information. However, current approaches relying on outcome-based reinforcement learning (RL) face critical issues such as conflicting gradients and reward sparsity, limiting performance gains and training efficiency. To address these, we first propose Atomic Thought, a novel LLM thinking paradigm that decomposes reasoning into fine-grained functional units. These units are supervised by Reasoning Reward Models (RRMs), which provide Atomic Thought Rewards (ATR) for fine-grained guidance. Building on this, we propose Atom-Searcher, a novel RL framework for agentic deep research that integrates Atomic Thought and ATR. Atom-Searcher uses a curriculum-inspired reward schedule, prioritizing process-level ATR early and transitioning to outcome rewards, accelerating convergence on effective reasoning paths. Experiments on seven benchmarks show consistent improvements over the state-of-the-art. Key advantages include: (1) Atom-Searcher scales computation at test-time. (2) Atomic Thought provides supervision anchors for RRMs, bridging deep research tasks and RRMs. (3) Atom-Searcher exhibits more interpretable, human-like reasoning patterns.

Large Language Models (LLMs) are increasingly relied upon for solving complex reasoning tasks in domains such as mathematics, logic, and multi-step question answering. A growing line of work seeks to improve reasoning quality by scaling inference time compute particularly through Process Reward Models (PRMs), used to reward the reasoning at intermediate steps. While effective, these methods introduce substantial computational overhead, especially when generating large numbers of solutions in parallel. In this paper, we investigate whether PRMs can be used mid-generation to provide early signals that enable the rejection of suboptimal candidates before full generation of step is complete. We introduce the hypothesis that PRMs are also Partial Reward Models, meaning that the scores they assign to partially completed reasoning step are predictive of final output quality. This allows for principled early rejection based on intermediate token-level signals. We support this hypothesis both theoretically, by proving that the risk of discarding optimal beams decreases exponentially with generation length and empirically, by demonstrating a strong correlation between partial and final rewards across multiple reward models. On math reasoning benchmarks, our method achieves up to 1.4times-9times reduction in inference FLOPs without degrading final performance. These results suggest that early rejection is a powerful mechanism for improving the compute-efficiency of reasoning in LLMs.

Multimodal large language models (MLLMs) still perform poorly on scientific tasks, particularly those requiring multi-step and interpretable reasoning. Their limitations include insufficient scientific reasoning patterns, lack of global coherence in multi-step inference, and the absence of reflective self-correction, making them unreliable in structured scientific contexts. We introduce EduFlow, the first end-to-end framework that covers the full pipeline of educational scientific reasoning, including data selection, MCTS-based trajectory construction, model training, and output optimization. At its core is EduPRM, a process-aware reward model that critiques reasoning steps with tags and justifications. EduPRM is trained via curriculum learning on three complementary supervision sources: MCTS-guided trajectories, error-injected critiques, and teacher-student dialogues, enabling dynamic adaptation to multi-stage problem solving and iterative refinement during inference. We further propose EduMCTS, a domain-adapted search framework that introduces bootstrapping actions specifically designed for educational reasoning, such as a self-reflection mechanism that promotes reflective error correction. It further leverages EduPRM's fine-grained feedback to guide the search toward higher-quality reasoning trajectories. By applying self-consistency and rejection sampling, we constructed EduMCTS-160K, a large-scale dataset of educational reasoning trajectories. Extensive experiments demonstrate that EduFlow enhances reasoning consistency and coherence. Code, data, and models will be released.

Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate and executable code generation to produce visual renderings of the auxiliary lines for subsequent reasoning. However, in complex solid geometry settings, such a strong dependence on precise specifications substantially restricts the robustness of this strategy. Alternatively, we turn to a simpler and more stable solution, representing auxiliary-line constructions as structured textual descriptions. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. The core is a cross-modal reward model that evaluates how well the generated auxiliary-line description matches the ground-truth auxiliary-line diagram. The reward signal drives a GRPO-based RL stage to yield informative auxiliary-line descriptions for the reasoning. To support the training and evaluation, we develop a scalable data pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. Based on this framework, we derive GeoVLMath, an LVLM for solving complex solid geometry.

Multi-agent systems (MAS) have emerged as a promising approach for enhancing the reasoning capabilities of large language models in complex problem-solving; however, current MAS frameworks suffer from poor flexibility and scalability with underdeveloped optimization strategies. To address these challenges, we propose ReSo, which integrates task graph generation with a reward-driven two-stage agent selection process centered on our Collaborative Reward Model that provides fine-grained reward signals to optimize MAS cooperation. We also introduce an automated data synthesis framework for generating MAS benchmarks without any human annotations. Experimental results show that ReSo matches or outperforms existing methods, achieving 33.7 percent accuracy on Math-MAS and 32.3 percent accuracy on SciBench-MAS, where other approaches completely fail.

Advances in the coding capabilities of LLM agents allow them to inspect and modify their own instructions, tools, and execution procedures. Existing approaches use this ability to search for improved agents through repeated downstream evaluation, which incurs substantial costs and ties the search to the evaluated tasks. We introduce SelfSearch, a reward-free search procedure in which agents modify themselves using records of previous self-improvement episodes. These records capture the reasoning, tool actions, and outcomes of earlier modification attempts, providing concrete experience for improving both task solving and self-modification. Without downstream reward signals during search, SelfSearch improves population-mean success over the initial agent in all six model--benchmark settings, with individual agents gaining up to 11.2 percentage points on Terminal-Bench 2.1. On SWE-bench Multilingual, an agent improves success by 5.0 percentage points while reducing execution cost by 38.5\% on tasks solved by both the initial and evolved agents. SelfSearch achieves competitive task success with evaluation-guided search baselines at lower search cost. With only \$4.03 in search cost, it produces a harness that solves 82.0\% of Terminal-Bench 2.1 tasks with DeepSeek V4 Flash under the settings of a public nine-harness comparison, matching the top-scoring harness, Codex. These results suggest that experience gained through self-modification can improve agents' downstream capabilities and efficiency.

Large Language Models have achieved remarkable success in natural language processing tasks, with Reinforcement Learning playing a key role in adapting them to specific applications. However, obtaining ground truth answers for training LLMs in mathematical problem-solving is often challenging, costly, and sometimes unfeasible. This research delves into the utilization of format and length as surrogate signals to train LLMs for mathematical problem-solving, bypassing the need for traditional ground truth answers.Our study shows that a reward function centered on format correctness alone can yield performance improvements comparable to the standard GRPO algorithm in early phases. Recognizing the limitations of format-only rewards in the later phases, we incorporate length-based rewards. The resulting GRPO approach, leveraging format-length surrogate signals, not only matches but surpasses the performance of the standard GRPO algorithm relying on ground truth answers in certain scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through systematic exploration and experimentation, this research not only offers a practical solution for training LLMs to solve mathematical problems and reducing the dependence on extensive ground truth data collection, but also reveals the essence of why our label-free approach succeeds: base model is like an excellent student who has already mastered mathematical and logical reasoning skills, but performs poorly on the test paper, it simply needs to develop good answering habits to achieve outstanding results in exams , in other words, to unlock the capabilities it already possesses.

Despite significant progress, multimodal large language models continue to struggle with visual mathematical problem solving. Some recent works recognize that visual perception is a bottleneck in visual mathematical reasoning, but their solutions are limited to improving the extraction and interpretation of visual inputs. Notably, they all ignore the key issue of whether the extracted visual cues are faithfully integrated and properly utilized in subsequent reasoning. Motivated by this, we present CogFlow, a novel cognitive-inspired three-stage framework that incorporates a knowledge internalization stage, explicitly simulating the hierarchical flow of human reasoning: perceptionRightarrowinternalizationRightarrowreasoning. Inline with this hierarchical flow, we holistically enhance all its stages. We devise Synergistic Visual Rewards to boost perception capabilities in parametric and semantic spaces, jointly improving visual information extraction from symbols and diagrams. To guarantee faithful integration of extracted visual cues into subsequent reasoning, we introduce a Knowledge Internalization Reward model in the internalization stage, bridging perception and reasoning. Moreover, we design a Visual-Gated Policy Optimization algorithm to further enforce the reasoning is grounded with the visual knowledge, preventing models seeking shortcuts that appear coherent but are visually ungrounded reasoning chains. Moreover, we contribute a new dataset MathCog for model training, which contains samples with over 120K high-quality perception-reasoning aligned annotations. Comprehensive experiments and analysis on commonly used visual mathematical reasoning benchmarks validate the superiority of the proposed CogFlow.

Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments. Recent work has begun to frame PDE solving as a code-generation task for large language models (LLMs), yet existing approaches operate primarily at inference time: relying on prompting, debugging, self-refinement, and test-time scaling rather than adapting the model itself. In parallel, reinforcement learning with verifiable rewards has emerged as a post-training paradigm for code and math reasoning, but its verifiers are typically binary: a compiler runs, or a test passes. Such signals discard the graded structure of scientific correctness, where two solvers may both execute and yet differ in solution accuracy by orders of magnitude. In this work, we introduce RLVP: Reinforcement Learning with Verifiable Physics, an RL post-training framework for multi-PDE solver code generation. RLVP addresses this verifiability gap with a hybrid verifier: hard program-validity checks ensure executability, while continuous physics rewards score function-space accuracy and PDE-residual consistency. A single policy is post-trained across diverse PDE families spanning hyperbolic, parabolic, elliptic, and incompressible-flow systems. RLVP improves over both pre-trained and supervised-only baselines on PDE benchmarks, and shows zero-shot improvement transfer to held-out PDEs. We show that a smaller LLM post-trained with RLVP can outperform prompting a frontier model on in-distribution PDE solver generation. The trained policy shows evidence of compositionality in numerical motifs: it recombines stencils, time-stepping schemes, and boundary-handling primitives learned from the PDEs used in training into generated solvers for unseen PDE problems.

Text-to-Image (T2I) models have made significant advancements in recent years, but they still struggle to accurately capture intricate details specified in complex compositional prompts. While fine-tuning T2I models with reward objectives has shown promise, it suffers from "reward hacking" and may not generalize well to unseen prompt distributions. In this work, we propose Reward-based Noise Optimization (ReNO), a novel approach that enhances T2I models at inference by optimizing the initial noise based on the signal from one or multiple human preference reward models. Remarkably, solving this optimization problem with gradient ascent for 50 iterations yields impressive results on four different one-step models across two competitive benchmarks, T2I-CompBench and GenEval. Within a computational budget of 20-50 seconds, ReNO-enhanced one-step models consistently surpass the performance of all current open-source Text-to-Image models. Extensive user studies demonstrate that our model is preferred nearly twice as often compared to the popular SDXL model and is on par with the proprietary Stable Diffusion 3 with 8B parameters. Moreover, given the same computational resources, a ReNO-optimized one-step model outperforms widely-used open-source models such as SDXL and PixArt-alpha, highlighting the efficiency and effectiveness of ReNO in enhancing T2I model performance at inference time. Code is available at https://github.com/ExplainableML/ReNO.

Scaling test-time compute has emerged as a key strategy for enhancing the reasoning capabilities of large language models (LLMs), particularly in tasks like mathematical problem-solving. A traditional approach, Self-Consistency (SC), generates multiple solutions to a problem and selects the most common answer via majority voting. Another common method involves scoring each solution with a reward model (verifier) and choosing the best one. Recent advancements in Generative Reward Models (GenRM) reframe verification as a next-token prediction task, enabling inference-time scaling along a new axis. Specifically, GenRM generates multiple verification chains-of-thought to score each solution. Under a limited inference budget, this introduces a fundamental trade-off: should you spend the budget on scaling solutions via SC or generate fewer solutions and allocate compute to verification via GenRM? To address this, we evaluate GenRM against SC under a fixed inference budget. Interestingly, we find that SC is more compute-efficient than GenRM for most practical inference budgets across diverse models and datasets. For instance, GenRM first matches SC after consuming up to 8x the inference compute and requires significantly more compute to outperform it. Furthermore, we derive inference scaling laws for the GenRM paradigm, revealing that compute-optimal inference favors scaling solution generation more aggressively than scaling the number of verifications. Our work provides practical guidance on optimizing test-time scaling by balancing solution generation and verification. The code is available at https://github.com/nishadsinghi/sc-genrm-scaling.

The development of reasoning capabilities represents a critical frontier in large language models (LLMs) research, where reinforcement learning (RL) and process reward models (PRMs) have emerged as predominant methodological frameworks. Contrary to conventional wisdom, empirical evidence from DeepSeek-R1 demonstrates that pure RL training focused on mathematical problem-solving can progressively enhance reasoning abilities without PRM integration, challenging the perceived necessity of process supervision. In this study, we conduct a systematic investigation of the relationship between RL training and PRM capabilities. Our findings demonstrate that problem-solving proficiency and process supervision capabilities represent complementary dimensions of reasoning that co-evolve synergistically during pure RL training. In particular, current PRMs underperform simple baselines like majority voting when applied to state-of-the-art models such as DeepSeek-R1 and QwQ-32B. To address this limitation, we propose Self-PRM, an introspective framework in which models autonomously evaluate and rerank their generated solutions through self-reward mechanisms. Although Self-PRM consistently improves the accuracy of the benchmark (particularly with larger sample sizes), analysis exposes persistent challenges: The approach exhibits low precision (<10\%) on difficult problems, frequently misclassifying flawed solutions as valid. These analyses underscore the need for continued RL scaling to improve reward alignment and introspective accuracy. Overall, our findings suggest that PRM may not be essential for enhancing complex reasoning, as pure RL not only improves problem-solving skills but also inherently fosters robust PRM capabilities. We hope these findings provide actionable insights for building more reliable and self-aware complex reasoning models.

Heuristic algorithms play a vital role in solving combinatorial optimization (CO) problems, yet traditional designs depend heavily on manual expertise and struggle to generalize across diverse instances. We introduce HeurAgenix, a two-stage hyper-heuristic framework powered by large language models (LLMs) that first evolves heuristics and then selects among them automatically. In the heuristic evolution phase, HeurAgenix leverages an LLM to compare seed heuristic solutions with higher-quality solutions and extract reusable evolution strategies. During problem solving, it dynamically picks the most promising heuristic for each problem state, guided by the LLM's perception ability. For flexibility, this selector can be either a state-of-the-art LLM or a fine-tuned lightweight model with lower inference cost. To mitigate the scarcity of reliable supervision caused by CO complexity, we fine-tune the lightweight heuristic selector with a dual-reward mechanism that jointly exploits singals from selection preferences and state perception, enabling robust selection under noisy annotations. Extensive experiments on canonical benchmarks show that HeurAgenix not only outperforms existing LLM-based hyper-heuristics but also matches or exceeds specialized solvers. Code is available at https://github.com/microsoft/HeurAgenix.

Large Language Models and multi-agent systems have shown promise in decomposing complex tasks, yet they struggle with long-horizon reasoning tasks and escalating computation cost. This work introduces a hierarchical multi-agent architecture that distributes reasoning across a 64*64 grid of lightweight agents, supported by a selective oracle. A spatial curriculum progressively expands the operational region of the grid, ensuring that agents master easier central tasks before tackling harder peripheral ones. To improve reliability, the system integrates Negative Log-Likelihood as a measure of confidence, allowing the curriculum to prioritize regions where agents are both accurate and well calibrated. A Thompson Sampling curriculum manager adaptively chooses training zones based on competence and NLL-driven reward signals. We evaluate the approach on a spatially grounded Tower of Hanoi benchmark, which mirrors the long-horizon structure of many robotic manipulation and planning tasks. Results demonstrate improved stability, reduced oracle usage, and stronger long-range reasoning from distributed agent cooperation.

Video-to-Audio (V2A) generation requires balancing four critical perceptual dimensions: semantic consistency, audio-visual temporal synchrony, aesthetic quality, and spatial accuracy; yet existing methods suffer from objective entanglement that conflates competing goals in single loss functions and lack human preference alignment. We introduce PrismAudio, the first framework to integrate Reinforcement Learning into V2A generation with specialized Chain-of-Thought (CoT) planning. Our approach decomposes monolithic reasoning into four specialized CoT modules (Semantic, Temporal, Aesthetic, and Spatial CoT), each paired with targeted reward functions. This CoT-reward correspondence enables multidimensional RL optimization that guides the model to jointly generate better reasoning across all perspectives, solving the objective entanglement problem while preserving interpretability. To make this optimization computationally practical, we propose Fast-GRPO, which employs hybrid ODE-SDE sampling that dramatically reduces the training overhead compared to existing GRPO implementations. We also introduce AudioCanvas, a rigorous benchmark that is more distributionally balanced and covers more realistically diverse and challenging scenarios than existing datasets, with 300 single-event classes and 501 multi-event samples. Experimental results demonstrate that PrismAudio achieves state-of-the-art performance across all four perceptual dimensions on both the in-domain VGGSound test set and out-of-domain AudioCanvas benchmark. The project page is available at https://PrismAudio-Project.github.io.

Integrating Large Language Models (LLMs) with external tools via multi-agent systems offers a promising new paradigm for decomposing and solving complex problems. However, training these systems remains notoriously difficult due to the credit assignment challenge, as it is often unclear which specific functional agent is responsible for the success or failure of decision trajectories. Existing methods typically rely on sparse or globally broadcast rewards, failing to capture individual contributions and leading to inefficient reinforcement learning. To address these limitations, we introduce the Shapley-based Hierarchical Attribution for Reinforcement Policy (SHARP), a novel framework for optimizing multi-agent reinforcement learning via precise credit attribution. SHARP effectively stabilizes training by normalizing agent-specific advantages across trajectory groups, primarily through a decomposed reward mechanism comprising a global broadcast-accuracy reward, a Shapley-based marginal-credit reward for each agent, and a tool-process reward to improve execution efficiency. Extensive experiments across various real-world benchmarks demonstrate that SHARP significantly outperforms recent state-of-the-art baselines, achieving average match improvements of 23.66% and 14.05% over single-agent and multi-agent approaches, respectively.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for enhancing reasoning in Large Language Models (LLMs). However, it frequently encounters challenges such as entropy collapse, excessive verbosity, and insufficient exploration for hard problems. Crucially, existing reward schemes fail to distinguish between the need for extensive search during problem-solving and the efficiency required for mastered knowledge. In this work, we introduce T2T(Thickening-to-Thinning), a dynamic reward framework inspired by human learning processes. Specifically, it implements a dual-phase mechanism: (1) On incorrect attempts, T2T incentivizes "thickening" (longer trajectories) to broaden the search space and explore novel solution paths; (2) Upon achieving correctness, it shifts to "thinning", imposing length penalties to discourage redundancy, thereby fostering model confidence and crystallizing reasoning capabilities. Extensive experiments on mathematical benchmarks (MATH-500, AIME, AMC) across Qwen-series and Deepseek models demonstrate that T2T significantly outperforms standard GRPO and recent baselines, achieving superior performance.

Reinforcement Learning from Verifiable Rewards (RLVR) has been widely adopted as the de facto method for enhancing the reasoning capabilities of large language models and has demonstrated notable success in verifiable domains like math and competitive programming tasks. However, the efficacy of RLVR diminishes significantly when applied to agentic environments. These settings, characterized by multi-step, complex problem solving, lead to high failure rates even for frontier LLMs, as the reward landscape is too sparse for effective model training via conventional RLVR. In this work, we introduce Agent-RLVR, a framework that makes RLVR effective in challenging agentic settings, with an initial focus on software engineering tasks. Inspired by human pedagogy, Agent-RLVR introduces agent guidance, a mechanism that actively steers the agent towards successful trajectories by leveraging diverse informational cues. These cues, ranging from high-level strategic plans to dynamic feedback on the agent's errors and environmental interactions, emulate a teacher's guidance, enabling the agent to navigate difficult solution spaces and promotes active self-improvement via additional environment exploration. In the Agent-RLVR training loop, agents first attempt to solve tasks to produce initial trajectories, which are then validated by unit tests and supplemented with agent guidance. Agents then reattempt with guidance, and the agent policy is updated with RLVR based on the rewards of these guided trajectories. Agent-RLVR elevates the pass@1 performance of Qwen-2.5-72B-Instruct from 9.4% to 22.4% on SWE-Bench Verified. We find that our guidance-augmented RLVR data is additionally useful for test-time reward model training, shown by further boosting pass@1 to 27.8%. Agent-RLVR lays the groundwork for training agents with RLVR in complex, real-world environments where conventional RL methods struggle.

Assistance games are a promising alternative to reinforcement learning from human feedback (RLHF) for training AI assistants. Assistance games resolve key drawbacks of RLHF, such as incentives for deceptive behavior, by explicitly modeling the interaction between assistant and user as a two-player game where the assistant cannot observe their shared goal. Despite their potential, assistance games have only been explored in simple settings. Scaling them to more complex environments is difficult because it requires both solving intractable decision-making problems under uncertainty and accurately modeling human users' behavior. We present the first scalable approach to solving assistance games and apply it to a new, challenging Minecraft-based assistance game with over 10^{400} possible goals. Our approach, AssistanceZero, extends AlphaZero with a neural network that predicts human actions and rewards, enabling it to plan under uncertainty. We show that AssistanceZero outperforms model-free RL algorithms and imitation learning in the Minecraft-based assistance game. In a human study, our AssistanceZero-trained assistant significantly reduces the number of actions participants take to complete building tasks in Minecraft. Our results suggest that assistance games are a tractable framework for training effective AI assistants in complex environments. Our code and models are available at https://github.com/cassidylaidlaw/minecraft-building-assistance-game.

Large language model (LLM)-based agents trained with reinforcement learning (RL) have shown strong potential on complex interactive tasks. However, standard RL paradigms favor static problem-solving over continuous adaptation: agents often converge to suboptimal strategies due to insufficient exploration, while learned knowledge remains implicit within parameters rather than explicitly retrievable, limiting effective experiential learning. To address these limitations, we introduce RetroAgent, an online RL framework that empowers agents to master complex interactive environments not just by solving, but by evolving. Concretely, RetroAgent features a hindsight self-reflection mechanism that produces dual intrinsic feedback: (1) intrinsic numerical feedback that that tracks incremental subtask completion relative to prior attempts, rewarding promising explorations, and (2) intrinsic language feedback that distills reusable lessons into a memory buffer, retrieved via our proposed Similarity & Utility-Aware Upper Confidence Bound (SimUtil-UCB) strategy balancing relevance, utility, and exploration to effectively leverage past experiences. Extensive experiments on two model families across four challenging agentic tasks demonstrate that RetroAgent significantly outperforms existing methods, achieving state-of-the-art results -- e.g., surpassing Group Relative Policy Optimization (GRPO)-trained agents by +18.3% on ALFWorld, +15.4% on WebShop, +27.1% on Sokoban, and +8.9% on MineSweeper -- while exhibiting strong test-time adaptation and generalization to out-of-distribution scenarios.

Human-written agent skills encode rich workflows for real-world problem solving, but are typically used as external inference-time instructions rather than internalized as reusable model capabilities. We introduce SkillGym, a framework that transforms these skills into executable, verifiable training environments for large language model agents. Its skill-to-task pipeline instantiates concrete tasks, verifies outcomes with code-based checkers, and assesses empirical skill dependence through contrastive executions. We construct and release 2,756 environments across 12 categories and collect 8,364 successful trajectories from multiple models and harnesses, averaging 49 tool calls and over 60k logged text tokens. These resources support supervised fine-tuning on verified workflows and reinforcement learning with outcome-based rewards. Under Claude Code, supervised fine-tuning improves Qwen3.5-35B-A3B by 199 Elo on GDPval-AA v2, 19.10 percentage points on Terminal-Bench 2.1, and 28.13 and 12.38 points on SkillsBench v1.1 with and without skills, respectively. Our 35B SkillGym-Agent reaches 51.47\% on skill-assisted SkillsBench, exceeding reported scores for Claude Sonnet 4.6, GPT-5.4 Mini, and DeepSeek V4 Pro. Without skills, it also surpasses skill-assisted bases under Codex and Claude Code, suggesting reusable procedural competence.

Reinforcement learning is increasingly used for code-centric tasks. These tasks include code generation, summarization, understanding, repair, testing, and optimization. This trend is growing faster with large language models and autonomous agents. A key challenge is how to design reward signals that make sense for software. In many RL problems, the reward is a clear number. In software, this is often not possible. The goal is rarely a single numeric objective. Instead, rewards are usually proxies. Common proxies check if the code compiles, passes tests, or satisfies quality metrics. Many reward designs have been proposed for code-related tasks. However, the work is scattered across areas and papers. There is no single survey that brings these approaches together and shows the full landscape of reward design for RL in software. In this survey, we provide the first systematic and comprehensive review of reward engineering for RL in software tasks. We focus on existing methods and techniques. We structure the literature along three complementary dimensions, summarizing the reward-design choices within each. We conclude with challenges and recommendations in the reward design space for SE tasks.

Despite recent advances in large language models, open-source models often struggle to consistently perform well on complex reasoning tasks. Existing ensemble methods, whether applied at the token or output levels, fail to address these challenges. In response, we present Language model Ensemble with Monte Carlo Tree Search (LE-MCTS), a novel framework for process-level ensembling of language models. LE-MCTS formulates step-by-step reasoning with an ensemble of language models as a Markov decision process. In this framework, states represent intermediate reasoning paths, while actions consist of generating the next reasoning step using one of the language models selected from a predefined pool. Guided by a process-based reward model, LE-MCTS performs a tree search over the reasoning steps generated by different language models, identifying the most accurate reasoning chain. Experimental results on five mathematical reasoning benchmarks demonstrate that our approach outperforms both single language model decoding algorithms and language model ensemble methods. Notably, LE-MCTS improves performance by 3.6% and 4.3% on the MATH and MQA datasets, respectively, highlighting its effectiveness in solving complex reasoning problems.

Recent progress in large-scale reinforcement learning (RL) has notably enhanced the reasoning capabilities of large language models (LLMs), especially in mathematical domains. However, current multimodal LLMs (MLLMs) for mathematical reasoning often rely on one-to-one image-text pairs and single-solution supervision, overlooking the diversity of valid reasoning perspectives and internal reflections. In this work, we introduce MathV-DP, a novel dataset that captures multiple diverse solution trajectories for each image-question pair, fostering richer reasoning supervision. We further propose Qwen-VL-DP, a model built upon Qwen-VL, fine-tuned with supervised learning and enhanced via group relative policy optimization (GRPO), a rule-based RL approach that integrates correctness discrimination and diversity-aware reward functions. Our method emphasizes learning from varied reasoning perspectives and distinguishing between correct yet distinct solutions. Extensive experiments on the MathVista's minitest and Math-V benchmarks demonstrate that Qwen-VL-DP significantly outperforms prior base MLLMs in both accuracy and generative diversity, highlighting the importance of incorporating diverse perspectives and reflective reasoning in multimodal mathematical reasoning.

Reinforcement learning fine-tuning has become the dominant approach for aligning diffusion models with human preferences. However, assessing images is intrinsically a multi-dimensional task, and multiple evaluation criteria need to be optimized simultaneously. Existing practice deal with multiple rewards by training one specialist model per reward, optimizing a weighted-sum reward R(x)=sum_k w_k R_k(x), or sequentially fine-tuning with a hand-crafted stage schedule. These approaches either fail to produce a unified model that can be jointly trained on all rewards or necessitates heavy manually tuned sequential training. We find that the failure stems from using a naive weighted-sum reward aggregation. This approach suffers from a sample-level mismatch because most rollouts are specialist samples, highly informative for certain reward dimensions but irrelevant for others; consequently, weighted summation dilutes their supervision. To address this issue, we propose MARBLE (Multi-Aspect Reward BaLancE), a gradient-space optimization framework that maintains independent advantage estimators for each reward, computes per-reward policy gradients, and harmonizes them into a single update direction without manually-tuned reward weighting, by solving a Quadratic Programming problem. We further propose an amortized formulation that exploits the affine structure of the loss used in DiffusionNFT, to reduce the per-step cost from K+1 backward passes to near single-reward baseline cost, together with EMA smoothing on the balancing coefficients to stabilize updates against transient single-batch fluctuations. On SD3.5 Medium with five rewards, MARBLE improves all five reward dimensions simultaneously, turns the worst-aligned reward's gradient cosine from negative under weighted summation in 80% of mini-batches to consistently positive, and runs at 0.97X the training speed of baseline training.

Assistive agents should make humans' lives easier. Classically, such assistance is studied through the lens of inverse reinforcement learning, where an assistive agent (e.g., a chatbot, a robot) infers a human's intention and then selects actions to help the human reach that goal. This approach requires inferring intentions, which can be difficult in high-dimensional settings. We build upon prior work that studies assistance through the lens of empowerment: an assistive agent aims to maximize the influence of the human's actions such that they exert a greater control over the environmental outcomes and can solve tasks in fewer steps. We lift the major limitation of prior work in this area--scalability to high-dimensional settings--with contrastive successor representations. We formally prove that these representations estimate a similar notion of empowerment to that studied by prior work and provide a ready-made mechanism for optimizing it. Empirically, our proposed method outperforms prior methods on synthetic benchmarks, and scales to Overcooked, a cooperative game setting. Theoretically, our work connects ideas from information theory, neuroscience, and reinforcement learning, and charts a path for representations to play a critical role in solving assistive problems.

Recent advances in large multimodal models (LMMs) have enabled impressive reasoning and perception abilities, yet most existing training pipelines still depend on human-curated data or externally verified reward models, limiting their autonomy and scalability. In this work, we strive to improve LMM reasoning capabilities in a purely unsupervised fashion (without any annotated data or reward distillation). To this end, we propose a self-evolving framework, named EvoLMM, that instantiates two cooperative agents from a single backbone model: a Proposer, which generates diverse, image-grounded questions, and a Solver, which solves them through internal consistency, where learning proceeds through a continuous self-rewarding process. This dynamic feedback encourages both the generation of informative queries and the refinement of structured reasoning without relying on ground-truth or human judgments. When using the popular Qwen2.5-VL as the base model, our EvoLMM yields consistent gains upto sim3\% on multimodal math-reasoning benchmarks, including ChartQA, MathVista, and MathVision, using only raw training images. We hope our simple yet effective approach will serve as a solid baseline easing future research in self-improving LMMs in a fully-unsupervised fashion. Our code and models are available at https://github.com/mbzuai-oryx/EvoLMM.

Large language models (LLMs) have achieved significant progress in solving complex reasoning tasks by Reinforcement Learning with Verifiable Rewards (RLVR). This advancement is also inseparable from the oversight automated by reliable verifiers. However, current outcome-based verifiers (OVs) are unable to inspect the unreliable intermediate steps in the long reasoning chains of thought (CoTs). Meanwhile, current process-based verifiers (PVs) have difficulties in reliably detecting errors in the complex long CoTs, limited by the scarcity of high-quality annotations due to the prohibitive costs of human annotations. Therefore, we propose the Outcome-based Process Verifier (OPV), which verifies the rationale process of summarized outcomes from long CoTs to achieve both accurate and efficient verification and enable large-scale annotation. To empower the proposed verifier, we adopt an iterative active learning framework with expert annotations to progressively improve the verification capability of OPV with fewer annotation costs. Specifically, in each iteration, the most uncertain cases of the current best OPV are annotated and then subsequently used to train a new OPV through Rejection Fine-Tuning (RFT) and RLVR for the next round. Extensive experiments demonstrate OPV's superior performance and broad applicability. It achieves new state-of-the-art results on our held-out \thisbench, outperforming much larger open-source models such as Qwen3-Max-Preview with an F1 score of 83.1 compared to 76.3. Furthermore, OPV effectively detects false positives within synthetic dataset, closely align with expert assessment. When collaborating with policy models, OPV consistently yields performance gains, e.g., raising the accuracy of DeepSeek-R1-Distill-Qwen-32B from 55.2\% to 73.3\% on AIME2025 as the compute budget scales.

While large-scale unsupervised language models (LMs) learn broad world knowledge and some reasoning skills, achieving precise control of their behavior is difficult due to the completely unsupervised nature of their training. Existing methods for gaining such steerability collect human labels of the relative quality of model generations and fine-tune the unsupervised LM to align with these preferences, often with reinforcement learning from human feedback (RLHF). However, RLHF is a complex and often unstable procedure, first fitting a reward model that reflects the human preferences, and then fine-tuning the large unsupervised LM using reinforcement learning to maximize this estimated reward without drifting too far from the original model. In this paper, we leverage a mapping between reward functions and optimal policies to show that this constrained reward maximization problem can be optimized exactly with a single stage of policy training, essentially solving a classification problem on the human preference data. The resulting algorithm, which we call Direct Preference Optimization (DPO), is stable, performant and computationally lightweight, eliminating the need for fitting a reward model, sampling from the LM during fine-tuning, or performing significant hyperparameter tuning. Our experiments show that DPO can fine-tune LMs to align with human preferences as well as or better than existing methods. Notably, fine-tuning with DPO exceeds RLHF's ability to control sentiment of generations and improves response quality in summarization and single-turn dialogue while being substantially simpler to implement and train.

In this paper, we introduce AceMath, a suite of frontier math models that excel in solving complex math problems, along with highly effective reward models capable of evaluating generated solutions and reliably identifying the correct ones. To develop the instruction-tuned math models, we propose a supervised fine-tuning (SFT) process that first achieves competitive performance across general domains, followed by targeted fine-tuning for the math domain using a carefully curated set of prompts and synthetically generated responses. The resulting model, AceMath-72B-Instruct greatly outperforms Qwen2.5-Math-72B-Instruct, GPT-4o and Claude-3.5 Sonnet. To develop math-specialized reward model, we first construct AceMath-RewardBench, a comprehensive and robust benchmark for evaluating math reward models across diverse problems and difficulty levels. After that, we present a systematic approach to build our math reward models. The resulting model, AceMath-72B-RM, consistently outperforms state-of-the-art reward models. Furthermore, when combining AceMath-72B-Instruct with AceMath-72B-RM, we achieve the highest average rm@8 score across the math reasoning benchmarks. We will release model weights, training data, and evaluation benchmarks at: https://research.nvidia.com/labs/adlr/acemath

LLMs exhibit advanced reasoning capabilities, offering the potential to transform natural language questions into mathematical models. However, existing open-source datasets in operations research domain lack detailed annotations of the modeling process, such as variable definitions, focusing solely on objective values, which hinders reinforcement learning applications. To address this, we release the StructuredOR dataset, annotated with comprehensive labels that capture the complete mathematical modeling process. We further propose BPP-Search, a algorithm that integrates reinforcement learning into a tree-of-thought structure using Beam search, a Process reward model, and a pairwise Preference algorithm. This approach enables efficient exploration of tree structures, avoiding exhaustive search while improving accuracy. Extensive experiments on StructuredOR, NL4OPT, and MAMO-ComplexLP datasets show that BPP-Search significantly outperforms state-of-the-art methods. In tree-based reasoning, BPP-Search excels in accuracy and efficiency, enabling faster retrieval of correct solutions.

The foundation of reproducible science lies in protocols that are precise, logically ordered, and executable. The autonomous generation of these protocols through natural language queries could greatly improve the efficiency of the reproduction process. However, current leading large language models (LLMs) often generate incomplete or inconsistent protocols, limiting their utility. To address this limitation, we first introduce SciRecipe, a large-scale dataset of over 12K structured protocols spanning 27 biological subfields and encompassing both comprehension and problem-solving tasks. To further improve protocol generation, we propose the "Sketch-and-Fill" paradigm, which separates analysis, structuring, and expression to ensure each step is explicit and verifiable. Complementing this, the structured component-based reward mechanism evaluates step granularity, action order, and semantic fidelity, aligning model optimization with experimental reliability. Building on these components, we develop Thoth, trained through a staged Knowledge-to-Action process that progresses from knowledge acquisition to operational reasoning and ultimately to robust, executable protocol generation. Across multiple benchmarks, Thoth consistently surpasses both proprietary and open-source LLMs, achieving significant improvements in step alignment, logical sequencing, and semantic accuracy. Our approach paves the way for reliable scientific assistants that bridge knowledge with experimental execution. All data, code, and models will be released publicly.

Recent studies on post-training large language models (LLMs) for reasoning through reinforcement learning (RL) typically focus on tasks that can be accurately verified and rewarded, such as solving math problems. In contrast, our research investigates the impact of reward noise, a more practical consideration for real-world scenarios involving the post-training of LLMs using reward models. We found that LLMs demonstrate strong robustness to substantial reward noise. For example, manually flipping 40% of the reward function's outputs in math tasks still allows a Qwen-2.5-7B model to achieve rapid convergence, improving its performance on math tasks from 5% to 72%, compared to the 75% accuracy achieved by a model trained with noiseless rewards. Surprisingly, by only rewarding the appearance of key reasoning phrases (namely reasoning pattern reward, RPR), such as ``first, I need to''-without verifying the correctness of answers, the model achieved peak downstream performance (over 70% accuracy for Qwen-2.5-7B) comparable to models trained with strict correctness verification and accurate rewards. Recognizing the importance of the reasoning process over the final results, we combined RPR with noisy reward models. RPR helped calibrate the noisy reward models, mitigating potential false negatives and enhancing the LLM's performance on open-ended tasks. These findings suggest the importance of improving models' foundational abilities during the pre-training phase while providing insights for advancing post-training techniques. Our code and scripts are available at https://github.com/trestad/Noisy-Rewards-in-Learning-to-Reason.

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models fail to robustly verify their own outputs. We introduce RISE (Reinforcing Reasoning with Self-Verification), a novel online RL framework designed to tackle this. RISE explicitly and simultaneously trains an LLM to improve both its problem-solving and self-verification abilities within a single, integrated RL process. The core mechanism involves leveraging verifiable rewards from an outcome verifier to provide on-the-fly feedback for both solution generation and self-verification tasks. In each iteration, the model generates solutions, then critiques its own on-policy generated solutions, with both trajectories contributing to the policy update. Extensive experiments on diverse mathematical reasoning benchmarks show that RISE consistently improves model's problem-solving accuracy while concurrently fostering strong self-verification skills. Our analyses highlight the advantages of online verification and the benefits of increased verification compute. Additionally, RISE models exhibit more frequent and accurate self-verification behaviors during reasoning. These advantages reinforce RISE as a flexible and effective path towards developing more robust and self-aware reasoners.

Large language models (LLMs) demonstrate significant reasoning capabilities, particularly through long chain-of-thought (CoT) processes, which can be elicited by reinforcement learning (RL). However, prolonged CoT reasoning presents limitations, primarily verbose outputs due to excessive introspection. The reasoning process in these LLMs often appears to follow a trial-and-error methodology rather than a systematic, logical deduction. In contrast, tree-of-thoughts (ToT) offers a conceptually more advanced approach by modeling reasoning as an exploration within a tree structure. This reasoning structure facilitates the parallel generation and evaluation of multiple reasoning branches, allowing for the active identification, assessment, and pruning of unproductive paths. This process can potentially lead to improved performance and reduced token costs. Building upon the long CoT capability of LLMs, we introduce tree-of-thoughts RL (ToTRL), a novel on-policy RL framework with a rule-based reward. ToTRL is designed to guide LLMs in developing the parallel ToT strategy based on the sequential CoT strategy. Furthermore, we employ LLMs as players in a puzzle game during the ToTRL training process. Solving puzzle games inherently necessitates exploring interdependent choices and managing multiple constraints, which requires the construction and exploration of a thought tree, providing challenging tasks for cultivating the ToT reasoning capability. Our empirical evaluations demonstrate that our ToTQwen3-8B model, trained with our ToTRL, achieves significant improvement in performance and reasoning efficiency on complex reasoning tasks.

Large vision language models exhibit notable limitations on Geometry Problem Solving (GPS) because of their unreliable diagram interpretation and pure natural-language reasoning. A recent line of work mitigates this by using symbolic solvers: the model directly generates a formal program that a geometry solver can execute. However, this direct program generation lacks intermediate reasoning, making the decision process opaque and prone to errors. In this work, we explore a new approach that integrates Chain-of-Thought (CoT) with formal language. The model interleaves natural language reasoning with incremental emission of solver-executable code, producing a hybrid reasoning trace in which critical derivations are expressed in formal language. To teach this behavior at scale, we combine (1) supervised fine-tuning on an 11K newly developed synthetic dataset with interleaved natural language reasoning and automatic formalization, and (2) solver-in-the-loop reinforcement learning that jointly optimizes both the CoT narrative and the resulting program through outcome-based rewards. Built on Qwen2.5-VL-7B, our new model, named GF-Reasoner, achieves up to 15% accuracy improvements on standard GPS benchmarks, surpassing both 7B-scale peers and the much larger model Qwen2.5-VL-72B. By exploiting high-order geometric knowledge and offloading symbolic computation to the solver, the generated reasoning traces are noticeably shorter and cleaner. Furthermore, we present a comprehensive analysis of method design choices (e.g., reasoning paradigms, data synthesis, training epochs, etc.), providing actionable insights for future research.

As machine learning has moved towards leveraging large models as priors for downstream tasks, the community has debated the right form of prior for solving reinforcement learning (RL) problems. If one were to try to prefetch as much computation as possible, they would attempt to learn a prior over the policies for some yet-to-be-determined reward function. Recent work (forward-backward (FB) representation learning) has tried this, arguing that an unsupervised representation learning procedure can enable optimal control over arbitrary rewards without further fine-tuning. However, FB's training objective and learning behavior remain mysterious. In this paper, we demystify FB by clarifying when such representations can exist, what its objective optimizes, and how it converges in practice. We draw connections with rank matching, fitted Q-evaluation, and contraction mapping. Our analysis suggests a simplified unsupervised pre-training method for RL that, instead of enabling optimal control, performs one step of policy improvement. We call our proposed method one-step forward-backward representation learning (one-step FB). Experiments in didactic settings, as well as in 10 state-based and image-based continuous control domains, demonstrate that one-step FB converges to errors 10^5 smaller and improves zero-shot performance by +24% on average. Our project website is available at https://chongyi-zheng.github.io/onestep-fb.

Recent advances in large language models (LLMs) have predominantly focused on maximizing accuracy and reasoning capabilities, often overlooking crucial computational efficiency considerations. While this approach has yielded impressive accuracy improvements, it has led to methods that may be impractical for real-world deployment due to computational overhead and latency constraints. This paper investigates the potential synergy between reasoning enhancement and computational efficiency by analyzing the integration of two contrasting approaches: Quiet-STaR (Self-Taught Reasoner) and REBASE (REward BAlanced SEarch). Through comprehensive empirical analysis using the Mistral-7B model on the GSM8K dataset, we demonstrate that while each method excels in its primary objective-Quiet-STaR achieving superior accuracy (32.03%) despite high computational cost (554.66s runtime, 12.73T FLOPs), and REBASE providing exceptional efficiency (8.47s runtime, 2.35T FLOPs) while maintaining baseline-comparable accuracy (10.94%)-their integration reveals fundamental challenges in reconciling reasoning depth with computational efficiency. The combined approach unexpectedly results in degraded performance (9.38% accuracy, 143.66s runtime), highlighting critical insights about the complex interplay between reasoning enhancement and efficiency optimization in LLMs. Our findings illuminate the need for novel architectures and algorithms specifically designed to bridge the gap between these competing objectives, while providing concrete directions for future research in compute-efficient reasoning methods.

State-of-the-art large language models (LLMs) exhibit impressive problem-solving capabilities but may struggle with complex reasoning and factual correctness. Existing methods harness the strengths of chain-of-thought and retrieval-augmented generation (RAG) to decompose a complex problem into simpler steps and apply retrieval to improve factual correctness. These methods work well on straightforward reasoning tasks but often falter on challenging tasks such as competitive programming and mathematics, due to frequent reasoning errors and irrelevant knowledge retrieval. To address this, we introduce Critic-guided planning with Retrieval-augmentation, CR-Planner, a novel framework that leverages fine-tuned critic models to guide both reasoning and retrieval processes through planning. CR-Planner solves a problem by iteratively selecting and executing sub-goals. Initially, it identifies the most promising sub-goal from reasoning, query generation, and retrieval, guided by rewards given by a critic model named sub-goal critic. It then executes this sub-goal through sampling and selecting the optimal output based on evaluations from another critic model named execution critic. This iterative process, informed by retrieved information and critic models, enables CR-Planner to effectively navigate the solution space towards the final answer. We employ Monte Carlo Tree Search to collect the data for training the critic models, allowing for a systematic exploration of action sequences and their long-term impacts. We validate CR-Planner on challenging domain-knowledge-intensive and reasoning-heavy tasks, including competitive programming, theorem-driven math reasoning, and complex domain retrieval problems. Our experiments demonstrate that CR-Planner significantly outperforms baselines, highlighting its effectiveness in addressing challenging problems by improving both reasoning and retrieval.

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

Designing rewards for Reinforcement Learning (RL) is challenging because it needs to convey the desired task, be efficient to optimize, and be easy to compute. The latter is particularly problematic when applying RL to robotics, where detecting whether the desired configuration is reached might require considerable supervision and instrumentation. Furthermore, we are often interested in being able to reach a wide range of configurations, hence setting up a different reward every time might be unpractical. Methods like Hindsight Experience Replay (HER) have recently shown promise to learn policies able to reach many goals, without the need of a reward. Unfortunately, without tricks like resetting to points along the trajectory, HER might require many samples to discover how to reach certain areas of the state-space. In this work we investigate different approaches to incorporate demonstrations to drastically speed up the convergence to a policy able to reach any goal, also surpassing the performance of an agent trained with other Imitation Learning algorithms. Furthermore, we show our method can also be used when the available expert trajectories do not contain the actions, which can leverage kinesthetic or third person demonstration. The code is available at https://sites.google.com/view/goalconditioned-il/.

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

Reward models are key in reinforcement learning from human feedback (RLHF) systems, aligning the model behavior with human preferences. Particularly in the math domain, there have been plenty of studies using reward models to align policies for improving reasoning capabilities. Recently, as the importance of reward models has been emphasized, RewardBench is proposed to understand their behavior. However, we figure out that the math subset of RewardBench has different representations between chosen and rejected completions, and relies on a single comparison, which may lead to unreliable results as it only see an isolated case. Therefore, it fails to accurately present the robustness of reward models, leading to a misunderstanding of its performance and potentially resulting in reward hacking. In this work, we introduce a new design for reliable evaluation of reward models, and to validate this, we construct RewardMATH, a benchmark that effectively represents the robustness of reward models in mathematical reasoning tasks. We demonstrate that the scores on RewardMATH strongly correlate with the results of optimized policy and effectively estimate reward overoptimization, whereas the existing benchmark shows almost no correlation. The results underscore the potential of our design to enhance the reliability of evaluation, and represent the robustness of reward model. We make our code and data publicly available.

Reward design plays a pivotal role in aligning large language models (LLMs) with human values, serving as the bridge between feedback signals and model optimization. This survey provides a structured organization of reward modeling and addresses three key aspects: mathematical formulation, construction practices, and interaction with optimization paradigms. Building on this, it develops a macro-level taxonomy that characterizes reward mechanisms along complementary dimensions, thereby offering both conceptual clarity and practical guidance for alignment research. The progression of LLM alignment can be understood as a continuous refinement of reward design strategies, with recent developments highlighting paradigm shifts from reinforcement learning (RL)-based to RL-free optimization and from single-task to multi-objective and complex settings.

Reinforcement learning (RL) in long horizon and sparse reward tasks is notoriously difficult and requires a lot of training steps. A standard solution to speed up the process is to leverage additional reward signals, shaping it to better guide the learning process. In the context of language-conditioned RL, the abstraction and generalisation properties of the language input provide opportunities for more efficient ways of shaping the reward. In this paper, we leverage this idea and propose an automated reward shaping method where the agent extracts auxiliary objectives from the general language goal. These auxiliary objectives use a question generation (QG) and question answering (QA) system: they consist of questions leading the agent to try to reconstruct partial information about the global goal using its own trajectory. When it succeeds, it receives an intrinsic reward proportional to its confidence in its answer. This incentivizes the agent to generate trajectories which unambiguously explain various aspects of the general language goal. Our experimental study shows that this approach, which does not require engineer intervention to design the auxiliary objectives, improves sample efficiency by effectively directing exploration.

In reinforcement learning (RL), an agent learns to perform a task by interacting with an environment and receiving feedback (a numerical reward) for its actions. However, the assumption that rewards are always observable is often not applicable in real-world problems. For example, the agent may need to ask a human to supervise its actions or activate a monitoring system to receive feedback. There may even be a period of time before rewards become observable, or a period of time after which rewards are no longer given. In other words, there are cases where the environment generates rewards in response to the agent's actions but the agent cannot observe them. In this paper, we formalize a novel but general RL framework - Monitored MDPs - where the agent cannot always observe rewards. We discuss the theoretical and practical consequences of this setting, show challenges raised even in toy environments, and propose algorithms to begin to tackle this novel setting. This paper introduces a powerful new formalism that encompasses both new and existing problems and lays the foundation for future research.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn behavior alignment reward functions. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality -- some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

Reward post-training of flow models either reweights the model's own samples under a KL penalty or a frozen reference, often for thousands of updates, or backpropagates the reward and moves every sample without checking that the move is worth its size. We introduce MEND, a reinforcement learning method built on proximal velocity matching. MEND caps rewards within each prompt group, so samples that already score well receive no move. Below the cap, it proposes moves along the reward gradient and accepts one only when its capped reward gain exceeds a quadratic displacement price. The model then regresses onto the resulting velocity targets, with no KL term, frozen reference model, or advantage weights. In 100 updates, MEND outperforms Flow-GRPO (about 4k updates) on five of six evaluators at the same distance to base-model images. Under an equal-budget protocol, it surpasses ReFL and DiffusionNFT at every evaluated update across four training rewards, reaching PickScore 24.03 versus 23.92 and 23.43, respectively. A 300-update three-reward run also surpasses the five-reward DiffusionNFT model on all three rewards it trains on. MEND is general and easy to adopt: it applies to any flow backbone with a differentiable reward.

Large language models for mathematical reasoning are typically trained with outcome-based rewards, which credit only the final answer. In our experiments, we observe that this paradigm is highly susceptible to reward hacking, leading to a substantial overestimation of a model's reasoning ability. This is evidenced by a high incidence of false positives - solutions that reach the correct final answer through an unsound reasoning process. Through a systematic analysis with human verification, we establish a taxonomy of these failure modes, identifying patterns like Miracle Steps - abrupt jumps to a correct output without a valid preceding derivation. Probing experiments suggest a strong association between these Miracle Steps and memorization, where the model appears to recall the answer directly rather than deriving it. To mitigate this systemic issue, we introduce the Rubric Reward Model (RRM), a process-oriented reward function that evaluates the entire reasoning trajectory against problem-specific rubrics. The generative RRM provides fine-grained, calibrated rewards (0-1) that explicitly penalize logical flaws and encourage rigorous deduction. When integrated into a reinforcement learning pipeline, RRM-based training consistently outperforms outcome-only supervision across four math benchmarks. Notably, it boosts Verified Pass@1024 on AIME2024 from 26.7% to 62.6% and reduces the incidence of Miracle Steps by 71%. Our work demonstrates that rewarding the solution process is crucial for building models that are not only more accurate but also more reliable.

Extrinsic rewards can effectively guide reinforcement learning (RL) agents in specific tasks. However, extrinsic rewards frequently fall short in complex environments due to the significant human effort needed for their design and annotation. This limitation underscores the necessity for intrinsic rewards, which offer auxiliary and dense signals and can enable agents to learn in an unsupervised manner. Although various intrinsic reward formulations have been proposed, their implementation and optimization details are insufficiently explored and lack standardization, thereby hindering research progress. To address this gap, we introduce RLeXplore, a unified, highly modularized, and plug-and-play framework offering reliable implementations of eight state-of-the-art intrinsic reward methods. Furthermore, we conduct an in-depth study that identifies critical implementation details and establishes well-justified standard practices in intrinsically-motivated RL. Our documentation, examples, and source code are available at https://github.com/RLE-Foundation/RLeXplore.

Large language models (LLMs) trained to answer questions are natively poor at teaching. Reinforcement Learning (RL) against a simulated student is a promising approach to improve their pedagogy, but existing RL-trained tutors reward the student's success on the tutored problem with the tutor's words still in context. The reward is then easiest to raise by telling the student the answer, and a tuned penalty is needed to reduce telling. Drawing on learning sciences, we introduce a masked near-transfer post-test: the student is tested on an unseen variant of the tutored problem with the tutor's utterances masked, so the reward can rise only through what the student wrote in its own turns. This discourages cognitive offloading by the student and allows the continuous penalty to be replaced by two binary reward gates (factual correctness of tutor response, no solution handover). A leave-one-out ablation shows that the learning-gain reward on its own does not separate teaching from telling: the gates reduce solution handover while the near-transfer post-test improves out-of-domain transfer. Using these reward designs we develop Eduardo, a multi-turn RL recipe for training LLM tutors, and use it to train 4B, 9B, 14B and 27B models from two distinct LLM architectures. Our post-trained Eduardo-27B model matches Gemini-3.1-Pro on MathTutorBench and Claude Opus 4.8 on TutorMoments at 2.4-6.2x fewer thinking tokens than frontier models, which matters for interactive tutoring. Without being named in the reward, the model more than doubles its use of the push-for-justification teacher move while support fading (e.g., assigning independent work), whose payoff lies beyond a single-problem dialog episode, is trained out. We open-source our training environment, an 8,671-problem near-transfer dataset, and trained models for further development.

The aim of Reinforcement Learning (RL) in real-world applications is to create systems capable of making autonomous decisions by learning from their environment through trial and error. This paper emphasizes the importance of reward engineering and reward shaping in enhancing the efficiency and effectiveness of reinforcement learning algorithms. Reward engineering involves designing reward functions that accurately reflect the desired outcomes, while reward shaping provides additional feedback to guide the learning process, accelerating convergence to optimal policies. Despite significant advancements in reinforcement learning, several limitations persist. One key challenge is the sparse and delayed nature of rewards in many real-world scenarios, which can hinder learning progress. Additionally, the complexity of accurately modeling real-world environments and the computational demands of reinforcement learning algorithms remain substantial obstacles. On the other hand, recent advancements in deep learning and neural networks have significantly improved the capability of reinforcement learning systems to handle high-dimensional state and action spaces, enabling their application to complex tasks such as robotics, autonomous driving, and game playing. This paper provides a comprehensive review of the current state of reinforcement learning, focusing on the methodologies and techniques used in reward engineering and reward shaping. It critically analyzes the limitations and recent advancements in the field, offering insights into future research directions and potential applications in various domains.

Outcome-reward reinforcement learning (RL) has proven effective at improving the reasoning capabilities of large language models (LLMs). However, standard RL assigns credit only at the level of the final answer, penalizing entire reasoning traces when the outcome is incorrect and uniformly reinforcing all steps when it is correct. As a result, correct intermediate steps may be discouraged in failed traces, while spurious steps may be reinforced in successful ones. We refer to this failure mode as the problem of credit assignment. While a natural remedy is to train a process reward model, accurately optimizing such models to identify corrective reasoning steps remains challenging. We introduce Intervention Training (InT), a training paradigm in which the model performs fine-grained credit assignment on its own reasoning traces by proposing short, targeted corrections that steer trajectories toward higher reward. Using reference solutions commonly available in mathematical reasoning datasets and exploiting the fact that verifying a model-generated solution is easier than generating a correct one from scratch, the model identifies the first error in its reasoning and proposes a single-step intervention to redirect the trajectory toward the correct solution. We then apply supervised fine-tuning (SFT) to the on-policy rollout up to the point of error concatenated with the intervention, localizing error to the specific step that caused failure. We show that the resulting model serves as a far better initialization for RL training. After running InT and subsequent fine-tuning with RL, we improve accuracy by nearly 14% over a 4B-parameter base model on IMO-AnswerBench, outperforming larger open-source models such as gpt-oss-20b.

Finding meaningful and accurate dense rewards is a fundamental task in the field of reinforcement learning (RL) that enables agents to explore environments more efficiently. In traditional RL settings, agents learn optimal policies through interactions with an environment guided by reward signals. However, when these signals are sparse, delayed, or poorly aligned with the intended task objectives, agents often struggle to learn effectively. Dense reward functions, which provide informative feedback at every step or state transition, offer a potential solution by shaping agent behavior and accelerating learning. Despite their benefits, poorly crafted reward functions can lead to unintended behaviors, reward hacking, or inefficient exploration. This problem is particularly acute in complex or high-dimensional environments where handcrafted rewards are difficult to specify and validate. To address this, recent research has explored a variety of approaches, including inverse reinforcement learning, reward modeling from human preferences, and self-supervised learning of intrinsic rewards. While these methods offer promising directions, they often involve trade-offs between generality, scalability, and alignment with human intent. This proposal explores several approaches to dealing with these unsolved problems and enhancing the effectiveness and reliability of dense reward construction in different RL applications.

Reward functions are central in reinforcement learning (RL), guiding agents towards optimal decision-making. The complexity of RL tasks requires meticulously designed reward functions that effectively drive learning while avoiding unintended consequences. Effective reward design aims to provide signals that accelerate the agent's convergence to optimal behavior. Crafting rewards that align with task objectives, foster desired behaviors, and prevent undesirable actions is inherently challenging. This thesis delves into the critical role of reward signals in RL, highlighting their impact on the agent's behavior and learning dynamics and addressing challenges such as delayed, ambiguous, or intricate rewards. In this thesis work, we tackle different aspects of reward shaping. First, we address the problem of designing informative and interpretable reward signals from a teacher's/expert's perspective (teacher-driven). Here, the expert, equipped with the optimal policy and the corresponding value function, designs reward signals that expedite the agent's convergence to optimal behavior. Second, we build on this teacher-driven approach by introducing a novel method for adaptive interpretable reward design. In this scenario, the expert tailors the rewards based on the learner's current policy, ensuring alignment and optimal progression. Third, we propose a meta-learning approach, enabling the agent to self-design its reward signals online without expert input (agent-driven). This self-driven method considers the agent's learning and exploration to establish a self-improving feedback loop.

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in inefficient optimization process. In this work, we investigate the function of process reward models (PRMs) to accelerate the RL training for LRMs. We propose a novel intrinsic signal-driven generative process evaluation mechanism operating at the thought level to address major bottlenecks in RL-based training. Specifically, instead of requiring PRMs to know how to solve problems, our method uses intrinsic signals in solutions to judge stepwise correctness and aggregate contiguous correct/incorrect steps into coherent 'thought' units. This structured, thought-level rewards enable more reliable credit assignment by reducing ambiguity in step segmentation and alleviating reward hacking. We further introduce a capability-adaptive reward mechanism that dynamically balances exploration and exploitation based on the LRM's current proficiency, guiding learning without stifling creative trial-and-error. These innovations are integrated into a new off-policy RL algorithm, TP-GRPO, which extends grouped proximal optimization with process-based rewards and improves training efficiency. Experiments on 1.5B and 7B parameter LRMs demonstrate that our method achieves higher problem-solving accuracy with significantly fewer training samples than outcome-only reward baselines. The results validate that well-structured process rewards can substantially accelerate LRM optimization in math reasoning tasks. Code is available at https://github.com/cs-holder/tp_grpo.

While recent advances have boosted LM proficiency in linguistic benchmarks, LMs consistently struggle to reason correctly on complex tasks like mathematics. We turn to Reinforcement Learning from Human Feedback (RLHF) as a method with which to shape model reasoning processes. In particular, we explore two reward schemes, outcome-supervised reward models (ORMs) and process-supervised reward models (PRMs), to optimize for logical reasoning. Our results show that the fine-grained reward provided by PRM-based methods enhances accuracy on simple mathematical reasoning (GSM8K) while, unexpectedly, reducing performance in complex tasks (MATH). Furthermore, we show the critical role reward aggregation functions play in model performance. Providing promising avenues for future research, our study underscores the need for further exploration into fine-grained reward modeling for more reliable language models.

Reward function design and exploration time are arguably the biggest obstacles to the deployment of reinforcement learning (RL) agents in the real world. In many real-world tasks, designing a reward function takes considerable hand engineering and often requires additional sensors to be installed just to measure whether the task has been executed successfully. Furthermore, many interesting tasks consist of multiple implicit intermediate steps that must be executed in sequence. Even when the final outcome can be measured, it does not necessarily provide feedback on these intermediate steps. To address these issues, we propose leveraging the abstraction power of intermediate visual representations learned by deep models to quickly infer perceptual reward functions from small numbers of demonstrations. We present a method that is able to identify key intermediate steps of a task from only a handful of demonstration sequences, and automatically identify the most discriminative features for identifying these steps. This method makes use of the features in a pre-trained deep model, but does not require any explicit specification of sub-goals. The resulting reward functions can then be used by an RL agent to learn to perform the task in real-world settings. To evaluate the learned reward, we present qualitative results on two real-world tasks and a quantitative evaluation against a human-designed reward function. We also show that our method can be used to learn a real-world door opening skill using a real robot, even when the demonstration used for reward learning is provided by a human using their own hand. To our knowledge, these are the first results showing that complex robotic manipulation skills can be learned directly and without supervised labels from a video of a human performing the task. Supplementary material and data are available at https://sermanet.github.io/rewards

Reward-based optimization algorithms require both exploration, to find rewards, and exploitation, to maximize performance. The need for efficient exploration is even more significant in sparse reward settings, in which performance feedback is given sparingly, thus rendering it unsuitable for guiding the search process. In this work, we introduce the SparsE Reward Exploration via Novelty and Emitters (SERENE) algorithm, capable of efficiently exploring a search space, as well as optimizing rewards found in potentially disparate areas. Contrary to existing emitters-based approaches, SERENE separates the search space exploration and reward exploitation into two alternating processes. The first process performs exploration through Novelty Search, a divergent search algorithm. The second one exploits discovered reward areas through emitters, i.e. local instances of population-based optimization algorithms. A meta-scheduler allocates a global computational budget by alternating between the two processes, ensuring the discovery and efficient exploitation of disjoint reward areas. SERENE returns both a collection of diverse solutions covering the search space and a collection of high-performing solutions for each distinct reward area. We evaluate SERENE on various sparse reward environments and show it compares favorably to existing baselines.

Reward design in reinforcement learning (RL) is challenging since specifying human notions of desired behavior may be difficult via reward functions or require many expert demonstrations. Can we instead cheaply design rewards using a natural language interface? This paper explores how to simplify reward design by prompting a large language model (LLM) such as GPT-3 as a proxy reward function, where the user provides a textual prompt containing a few examples (few-shot) or a description (zero-shot) of the desired behavior. Our approach leverages this proxy reward function in an RL framework. Specifically, users specify a prompt once at the beginning of training. During training, the LLM evaluates an RL agent's behavior against the desired behavior described by the prompt and outputs a corresponding reward signal. The RL agent then uses this reward to update its behavior. We evaluate whether our approach can train agents aligned with user objectives in the Ultimatum Game, matrix games, and the DealOrNoDeal negotiation task. In all three tasks, we show that RL agents trained with our framework are well-aligned with the user's objectives and outperform RL agents trained with reward functions learned via supervised learning

Reward engineering, the manual specification of reward functions to induce desired agent behavior, remains a fundamental challenge in multi-agent reinforcement learning. This difficulty is amplified by credit assignment ambiguity, environmental non-stationarity, and the combinatorial growth of interaction complexity. We argue that recent advances in large language models (LLMs) point toward a shift from hand-crafted numerical rewards to language-based objective specifications. Prior work has shown that LLMs can synthesize reward functions directly from natural language descriptions (e.g., EUREKA) and adapt reward formulations online with minimal human intervention (e.g., CARD). In parallel, the emerging paradigm of Reinforcement Learning from Verifiable Rewards (RLVR) provides empirical evidence that language-mediated supervision can serve as a viable alternative to traditional reward engineering. We conceptualize this transition along three dimensions: semantic reward specification, dynamic reward adaptation, and improved alignment with human intent, while noting open challenges related to computational overhead, robustness to hallucination, and scalability to large multi-agent systems. We conclude by outlining a research direction in which coordination arises from shared semantic representations rather than explicitly engineered numerical signals.

Reward finetuning has emerged as a promising approach to aligning foundation models with downstream objectives. Remarkable success has been achieved in the language domain by using reinforcement learning (RL) to maximize rewards that reflect human preference. However, in the vision domain, existing RL-based reward finetuning methods are limited by their instability in large-scale training, rendering them incapable of generalizing to complex, unseen prompts. In this paper, we propose Proximal Reward Difference Prediction (PRDP), enabling stable black-box reward finetuning for diffusion models for the first time on large-scale prompt datasets with over 100K prompts. Our key innovation is the Reward Difference Prediction (RDP) objective that has the same optimal solution as the RL objective while enjoying better training stability. Specifically, the RDP objective is a supervised regression objective that tasks the diffusion model with predicting the reward difference of generated image pairs from their denoising trajectories. We theoretically prove that the diffusion model that obtains perfect reward difference prediction is exactly the maximizer of the RL objective. We further develop an online algorithm with proximal updates to stably optimize the RDP objective. In experiments, we demonstrate that PRDP can match the reward maximization ability of well-established RL-based methods in small-scale training. Furthermore, through large-scale training on text prompts from the Human Preference Dataset v2 and the Pick-a-Pic v1 dataset, PRDP achieves superior generation quality on a diverse set of complex, unseen prompts whereas RL-based methods completely fail.

Automatically synthesizing dense rewards from natural language descriptions is a promising paradigm in reinforcement learning (RL), with applications to sparse reward problems, open-ended exploration, and hierarchical skill design. Recent works have made promising steps by exploiting the prior knowledge of large language models (LLMs). However, these approaches suffer from important limitations: they are either not scalable to problems requiring billions of environment samples, due to requiring LLM annotations for each observation, or they require a diverse offline dataset, which may not exist or be impossible to collect. In this work, we address these limitations through a combination of algorithmic and systems-level contributions. We propose \oni, a distributed architecture that simultaneously learns an RL policy and an intrinsic reward function using LLM feedback. Our approach annotates the agent's collected experience via an asynchronous LLM server, which is then distilled into an intrinsic reward model. We explore a range of algorithmic choices for reward modeling with varying complexity, including hashing, classification, and ranking models. By studying their relative tradeoffs, we shed light on questions regarding intrinsic reward design for sparse reward problems. Our approach achieves state-of-the-art performance across a range of challenging, sparse reward tasks from the NetHack Learning Environment in a simple unified process, solely using the agent's gathered experience, without requiring external datasets. We make our code available at https://github.com/facebookresearch/oni.

In the Reinforcement Learning (RL) framework, the learning is guided through a reward signal. This means that in situations of sparse rewards the agent has to focus on exploration, in order to discover which action, or set of actions leads to the reward. RL agents usually struggle with this. Exploration is the focus of Quality-Diversity (QD) methods. In this thesis, we approach the problem of sparse rewards with these algorithms, and in particular with Novelty Search (NS). This is a method that only focuses on the diversity of the possible policies behaviors. The first part of the thesis focuses on learning a representation of the space in which the diversity of the policies is evaluated. In this regard, we propose the TAXONS algorithm, a method that learns a low-dimensional representation of the search space through an AutoEncoder. While effective, TAXONS still requires information on when to capture the observation used to learn said space. For this, we study multiple ways, and in particular the signature transform, to encode information about the whole trajectory of observations. The thesis continues with the introduction of the SERENE algorithm, a method that can efficiently focus on the interesting parts of the search space. This method separates the exploration of the search space from the exploitation of the reward through a two-alternating-steps approach. The exploration is performed through NS. Any discovered reward is then locally exploited through emitters. The third and final contribution combines TAXONS and SERENE into a single approach: STAX. Throughout this thesis, we introduce methods that lower the amount of prior information needed in sparse rewards settings. These contributions are a promising step towards the development of methods that can autonomously explore and find high-performance policies in a variety of sparse rewards settings.

Reward modeling is essential for aligning large language models (LLMs) with human preferences, especially through reinforcement learning from human feedback (RLHF). To provide accurate reward signals, a reward model (RM) should stimulate deep thinking and conduct interpretable reasoning before assigning a score or a judgment. However, existing RMs either produce opaque scalar scores or directly generate the prediction of a preferred answer, making them struggle to integrate natural language critiques, thus lacking interpretability. Inspired by recent advances of long chain-of-thought (CoT) on reasoning-intensive tasks, we hypothesize and validate that integrating reasoning capabilities into reward modeling significantly enhances RM's interpretability and performance. In this work, we introduce a new class of generative reward models -- Reasoning Reward Models (ReasRMs) -- which formulate reward modeling as a reasoning task. We propose a reasoning-oriented training pipeline and train a family of ReasRMs, RM-R1. The training consists of two key stages: (1) distillation of high-quality reasoning chains and (2) reinforcement learning with verifiable rewards. RM-R1 improves LLM rollouts by self-generating reasoning traces or chat-specific rubrics and evaluating candidate responses against them. Empirically, our models achieve state-of-the-art or near state-of-the-art performance of generative RMs across multiple comprehensive reward model benchmarks, outperforming much larger open-weight models (e.g., Llama3.1-405B) and proprietary ones (e.g., GPT-4o) by up to 13.8%. Beyond final performance, we perform thorough empirical analysis to understand the key ingredients of successful ReasRM training. To facilitate future research, we release six ReasRM models along with code and data at https://github.com/RM-R1-UIUC/RM-R1.

Despite their widespread use, the role of reward models in shaping reinforcement learning is poorly understood. Reward models offer a tempting promise: they automatically estimate response quality in the absence of verifiers or human judges. Unlike "verifiable rewards" which typically produce binary scores, reward models typically produce continuous scores, allowing them to be sensitive to fine-grained differences in responses. However, we show this apparent strength is a serious weakness: many popular reward models are oversensitive, assigning different scores to equally good responses. Theoretically, we show that seemingly perfect reward models can be highly oversensitive; empirically, this oversensitivity can lead to bad policies. In place of existing notions of "reward model accuracy," we propose evaluating reward models using distinct measures of "discriminative ability" and "specificity" (the complement of oversensitivity). As a solution, we describe a training-free algorithm that uses Monte Carlo dropout on any neural reward model to produce discrete reward clusters. Theoretically, we prove there exist discretizations that reduce oversensitivity at minimal expense of discriminative ability; empirically we show, in both controlled and natural RL settings, that discretizing rewards leads to less reward hacking and better policies than training on the original rewards.

Reward models (RMs) are crucial for the training and inference-time scaling up of large language models (LLMs). However, existing reward models primarily focus on human preferences, neglecting verifiable correctness signals which have shown strong potential in training LLMs. In this paper, we propose agentic reward modeling, a reward system that combines reward models with verifiable correctness signals from different aspects to provide reliable rewards. We empirically implement a reward agent, named RewardAgent, that combines human preference rewards with two verifiable signals: factuality and instruction following, to provide more reliable rewards. We conduct comprehensive experiments on existing reward model benchmarks and inference time best-of-n searches on real-world downstream tasks. RewardAgent significantly outperforms vanilla reward models, demonstrating its effectiveness. We further construct training preference pairs using RewardAgent and train an LLM with the DPO objective, achieving superior performance on various NLP benchmarks compared to conventional reward models. Our codes are publicly released to facilitate further research (https://github.com/THU-KEG/Agentic-Reward-Modeling).

Intrinsic rewards are designed to guide exploration in reinforcement learning by assigning value to an agent's experience, for example through prediction error or learning progress. However, maximizing these rewards need not produce the most informative experience available. We propose a formal criterion for exploration that compares policies by the counterfactual information they acquire: how well their histories can substitute for experience under alternative policies. We construct a single, simple environment in which specified count-based, prediction-error, empowerment, and information-gain objectives have maximizing policies that are Pareto-suboptimal at acquiring counterfactual information. We explain these failures and establish conditions under which existing intrinsic rewards successfully encourage optimal exploration. We also construct an objective that assigns a higher value whenever exploration strictly improves under our criterion.

Although reinforcement learning with verifiable rewards (RLVR) shows promise in improving the reasoning ability of large language models (LLMs), the scaling up dilemma remains due to the reliance on human annotated labels especially for complex tasks. Recent alternatives that explore various self-reward signals exhibit the eliciting potential of LLM reasoning, but suffer from the non-negligible collapse issue. Inspired by the success of self-supervised learning, we propose Co-Reward, a novel RL framework that leverages contrastive agreement across semantically analogical questions as a reward basis. Specifically, we construct a similar question for each training sample (without labels) and synthesize their individual surrogate labels through a simple rollout voting, and then the reward is constructed by cross-referring the labels of each question pair to enforce the internal reasoning consistency across analogical inputs. Intuitively, such a self-supervised reward-shaping mechanism increases the difficulty of learning collapse into a trivial solution, and promotes stable reasoning elicitation and improvement through expanding the input sample variants. Empirically, Co-Reward achieves superior performance compared to other self-reward baselines on multiple reasoning benchmarks and LLM series, and reaches or even surpasses ground-truth (GT) labeled reward, with improvements of up to +6.8% on MATH500 over GT reward on Llama-3.2-3B-Instruct. Our code is publicly available at https://github.com/tmlr-group/Co-Reward.

Reinforcement learning (RL) has significantly improved the reasoning ability of large language models. However, current reward models underperform in challenging reasoning scenarios and predominant RL training paradigms rely on rule-based or reference-based rewards, which impose two critical limitations: 1) the dependence on finely annotated reference answer to attain rewards; and 2) the requirement for constrained output format. These limitations fundamentally hinder further RL data scaling and sustained enhancement of model reasoning performance. To address these limitations, we propose a comprehensive framework for evaluating and improving the performance of reward models in complex reasoning scenarios. We first present a reasoning-oriented benchmark (Libra Bench), systematically constructed from a diverse collection of challenging mathematical problems and advanced reasoning models, to address the limitations of existing reward model benchmarks in reasoning scenarios. We further introduce a novel approach for improving the generative reward model via learning-to-think methodologies. Based on the proposed approach, we develop Libra-RM series, a collection of generative reward models with reasoning capabilities that achieve state-of-the-art results on various benchmarks. Comprehensive downstream experiments are conducted and the experimental results demonstrate the correlation between our Libra Bench and downstream application, and the potential of Libra-RM to further improve reasoning models with unlabeled data.

Recent studies show that LLM hidden states encode reward-related information, such as answer correctness and model confidence. However, existing approaches typically fit black-box probes on the full hidden states, offering little insight into how this information is structured across neurons. In this paper, we show that reward-related information is concentrated in a sparse subset of neurons. Using simple probing, we identify two types of neurons: value neurons, whose activations predict state value, and dopamine neurons, whose activations encode step-level temporal difference (TD) errors. Together, these neurons form a sparse reward subsystem within LLM hidden states. These names are drawn by analogy with neuroscience, where value neurons and dopamine neurons in the biological reward subsystem also encode value and reward prediction errors, respectively. We demonstrate that value neurons are robust and transferable across diverse datasets and models, and provide causal evidence that they encode reward-related information. Finally, we show applications of the reward subsystem: value neurons serve as effective predictors of model confidence, and dopamine neurons can function as a process reward model (PRM) to guide inference-time search.

Exploration in sparse reward environments remains one of the key challenges of model-free reinforcement learning. Instead of solely relying on extrinsic rewards provided by the environment, many state-of-the-art methods use intrinsic rewards to encourage exploration. However, we show that existing methods fall short in procedurally-generated environments where an agent is unlikely to visit a state more than once. We propose a novel type of intrinsic reward which encourages the agent to take actions that lead to significant changes in its learned state representation. We evaluate our method on multiple challenging procedurally-generated tasks in MiniGrid, as well as on tasks with high-dimensional observations used in prior work. Our experiments demonstrate that this approach is more sample efficient than existing exploration methods, particularly for procedurally-generated MiniGrid environments. Furthermore, we analyze the learned behavior as well as the intrinsic reward received by our agent. In contrast to previous approaches, our intrinsic reward does not diminish during the course of training and it rewards the agent substantially more for interacting with objects that it can control.

Large Language Model (LLM) agents increasingly solve long-horizon tasks through multi-turn interactions with users and external tools. In these settings, relevant task information often unfolds over time rather than being fully specified at the initial prompt. Service agents make this challenge especially concrete: users may clarify or revise their goals, while tool responses provide information needed for subsequent decisions. Thus, a final reward alone cannot indicate which actions contributed to resolving the task. Recent methods rely on comparative evidence from other trajectories or resampled continuations, or on separately constructed step-level learning signals, to refine credit. However, a completed rollout already records how information and errors flow between agent actions. We introduce Influence-Aware Policy Optimization (IAPO), which represents each rollout as a typed influence-dependency graph over trainable agent actions, with user and tool observations serving as evidence. IAPO converts support-use and failed-use structure into routing weights that redistribute the same trajectory-level advantage. Experiments with Qwen3-4B and Qwen3-8B demonstrate superior performance over multi-turn reinforcement learning (RL) baselines across three service-agent benchmarks: {τ^2}-Bench, UserBench, and AgentChangeBench. BFCL-v4 Multi-Turn further shows that these gains do not compromise multi-turn function-calling performance. This work advances the understanding of credit assignment in multi-turn user interactions and provides a principled approach to training service agents from sparse outcome feedback.

Reward models (RMs) provide critical feedback signals for LLM post-training, notably in reinforced fine-tuning (RFT) and reinforcement learning (RL) pipelines. However, current reward evaluation relies on heterogeneous criteria such as rule-based verifiers, ground-truth references, procedural checklists, and complex rubrics, where a unified mechanism to integrate all types of evidence remains unexplored. To this end, we propose Skill Reward Model (Skill-RM), a unified framework that reformulates reward modeling as the execution of a reusable Reward-Evaluation Skill. By treating reward computation as a structured agentic task, Skill-RM provides a consistent interface to orchestrate heterogeneous resources, dynamically selecting and aggregating evidence tailored to the specific requirements of each input. This approach enables the reward model to move beyond static evaluation, ensuring consistency and transparency across diverse tasks. Extensive experiments on reward benchmarks and downstream applications, including best-of-N selection and reinforcement learning, demonstrate that Skill-RM consistently outperforms traditional judge baselines. Our findings suggest that Skill-RM not only provides a unified solution for reward modeling but also achieves superior performance through the strategic and dynamic orchestration of evidence. The code is at https://github.com/Qwen-Applications/Skill-RM.

Recent progress in reasoning models suggests that generating plausible attempts for research-level mathematics may be within reach, but verification remains a bottleneck, consuming scarce expert time. We hypothesize that a meaningful solution should contain enough method-level information that, when applied to a neighborhood of related questions, it should yield better downstream performance than incorrect solutions. Building on this idea, we propose Consequence-Based Utility, an oracle-free evaluator that scores each candidate by testing its value as an in-context exemplar in solving related yet verifiable questions. Our approach is evaluated on an original set of research-level math problems, each paired with one expert-written solution and nine LLM-generated solutions. Notably, Consequence-Based Utility consistently outperforms reward models, generative reward models, and LLM judges on ranking quality. Specifically, for GPT-OSS-120B, it improves Acc@1 from 67.2 to 76.3 and AUC from 71.4 to 79.6, with similarly large AUC gains on GPT-OSS-20B (69.0 to 79.2). Furthermore, compared to LLM-Judges, it also exhibits a larger solver-evaluator gap, maintaining a stronger correct-wrong separation even on instances where the underlying solver often fails to solve.

Significant progress in reward modeling over recent years has been driven by a paradigm shift from task-specific designs towards generalist reward models. Despite this trend, developing effective reward models remains a fundamental challenge: the heavy reliance on large-scale labeled preference data. Pre-training on abundant unlabeled data offers a promising direction, but existing approaches fall short of instilling explicit reasoning into reward models. To bridge this gap, we propose a self-training approach that leverages unlabeled data to elicit reward reasoning in reward models. Based on this approach, we develop GRAM-R^2, a generative reward model trained to produce not only preference labels but also accompanying reward rationales. GRAM-R^2 can serve as a foundation model for reward reasoning and can be applied to a wide range of tasks with minimal or no additional fine-tuning. It can support downstream applications such as response ranking and task-specific reward tuning. Experiments on response ranking, task adaptation, and reinforcement learning from human feedback demonstrate that GRAM-R^2 consistently delivers strong performance, outperforming several strong discriminative and generative baselines.

Curiosity-based reward schemes can present powerful exploration mechanisms which facilitate the discovery of solutions for complex, sparse or long-horizon tasks. However, as the agent learns to reach previously unexplored spaces and the objective adapts to reward new areas, many behaviours emerge only to disappear due to being overwritten by the constantly shifting objective. We argue that merely using curiosity for fast environment exploration or as a bonus reward for a specific task does not harness the full potential of this technique and misses useful skills. Instead, we propose to shift the focus towards retaining the behaviours which emerge during curiosity-based learning. We posit that these self-discovered behaviours serve as valuable skills in an agent's repertoire to solve related tasks. Our experiments demonstrate the continuous shift in behaviour throughout training and the benefits of a simple policy snapshot method to reuse discovered behaviour for transfer tasks.

Reward models (RMs) play a critical role in enhancing the reasoning performance of LLMs. For example, they can provide training signals to finetune LLMs during reinforcement learning (RL) and help select the best answer from multiple candidates during inference. In this paper, we provide a systematic introduction to RMs, along with a comprehensive survey of their applications in LLM reasoning. We first review fundamental concepts of RMs, including their architectures, training methodologies, and evaluation techniques. Then, we explore their key applications: (1) guiding generation and selecting optimal outputs during LLM inference, (2) facilitating data synthesis and iterative self-improvement for LLMs, and (3) providing training signals in RL-based finetuning. Finally, we discuss critical open questions regarding the selection, generalization, evaluation, and enhancement of RMs, based on existing research and our own empirical findings. Our analysis aims to provide actionable insights for the effective deployment and advancement of RMs for LLM reasoning.

Reinforcement learning (RL) has been widely used in text generation to alleviate the exposure bias issue or to utilize non-parallel datasets. The reward function plays an important role in making RL training successful. However, previous reward functions are typically task-specific and sparse, restricting the use of RL. In our work, we propose a task-agnostic approach that derives a step-wise reward function directly from a model trained with teacher forcing. We additionally propose a simple modification to stabilize the RL training on non-parallel datasets with our induced reward function. Empirical results show that our method outperforms self-training and reward regression methods on several text generation tasks, confirming the effectiveness of our reward function.

Preference optimization, particularly through Reinforcement Learning from Human Feedback (RLHF), has achieved significant success in aligning Large Language Models (LLMs) to adhere to human intentions. Unlike offline alignment with a fixed dataset, online feedback collection from humans or AI on model generations typically leads to more capable reward models and better-aligned LLMs through an iterative process. However, achieving a globally accurate reward model requires systematic exploration to generate diverse responses that span the vast space of natural language. Random sampling from standard reward-maximizing LLMs alone is insufficient to fulfill this requirement. To address this issue, we propose a bilevel objective optimistically biased towards potentially high-reward responses to actively explore out-of-distribution regions. By solving the inner-level problem with the reparameterized reward function, the resulting algorithm, named Self-Exploring Language Models (SELM), eliminates the need for a separate RM and iteratively updates the LLM with a straightforward objective. Compared to Direct Preference Optimization (DPO), the SELM objective reduces indiscriminate favor of unseen extrapolations and enhances exploration efficiency. Our experimental results demonstrate that when finetuned on Zephyr-7B-SFT and Llama-3-8B-Instruct models, SELM significantly boosts the performance on instruction-following benchmarks such as MT-Bench and AlpacaEval 2.0, as well as various standard academic benchmarks in different settings. Our code and models are available at https://github.com/shenao-zhang/SELM.

We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete diffusion models remain challenging. In this work, we introduce a principled plug-and-play discrete diffusion posterior sampling algorithm based on split Gibbs sampling, which we call SG-DPS. Our algorithm enables reward-guided generation and solving inverse problems in discrete-state spaces. We demonstrate that SG-DPS converges to the true posterior distribution on synthetic benchmarks, and enjoys state-of-the-art posterior sampling performance on a range of benchmarks for discrete data, achieving up to 2x improved performance compared to existing baselines.

Large language models (LLMs) have demonstrated remarkable performance in reasoning tasks, where reinforcement learning (RL) serves as a key algorithm for enhancing their reasoning capabilities. Currently, there are two mainstream reward paradigms: model-based rewards and rule-based rewards. However, both approaches suffer from limitations: rule-based rewards lack robustness, while model-based rewards are vulnerable to reward hacking. To address these issues, we propose Cooper(Co-optimizing Policy Model and Reward Model), a RL framework that jointly optimizes both the policy model and the reward model. Cooper leverages the high precision of rule-based rewards when identifying correct responses, and dynamically constructs and selects positive-negative sample pairs for continued training the reward model. This design enhances robustness and mitigates the risk of reward hacking. To further support Cooper, we introduce a hybrid annotation strategy that efficiently and accurately generates training data for the reward model. We also propose a reference-based reward modeling paradigm, where the reward model takes a reference answer as input. Based on this design, we train a reward model named VerifyRM, which achieves higher accuracy on VerifyBench compared to other models of the same size. We conduct reinforcement learning using both VerifyRM and Cooper. Our experiments show that Cooper not only alleviates reward hacking but also improves end-to-end RL performance, for instance, achieving a 0.54% gain in average accuracy on Qwen2.5-1.5B-Instruct. Our findings demonstrate that dynamically updating reward model is an effective way to combat reward hacking, providing a reference for better integrating reward models into RL.

Text-to-image models are powerful for producing high-quality images based on given text prompts, but crafting these prompts often requires specialized vocabulary. To address this, existing methods train rewriting models with supervision from large amounts of manually annotated data and trained aesthetic assessment models. To alleviate the dependence on data scale for model training and the biases introduced by trained models, we propose a novel prompt optimization framework, designed to rephrase a simple user prompt into a sophisticated prompt to a text-to-image model. Specifically, we employ the large vision language models (LVLMs) as the solver to rewrite the user prompt, and concurrently, employ LVLMs as a reward model to score the aesthetics and alignment of the images generated by the optimized prompt. Instead of laborious human feedback, we exploit the prior knowledge of the LVLM to provide rewards, i.e., AI feedback. Simultaneously, the solver and the reward model are unified into one model and iterated in reinforcement learning to achieve self-improvement by giving a solution and judging itself. Results on two popular datasets demonstrate that our method outperforms other strong competitors.