Generative RL 进展

Multi-turn visual search agents answer questions about high-resolution images by iteratively deciding where to look. Reinforcement learning for these agents rewards only the final answer, leaving the search process unsupervised. Consequently, faulty routes in which the reasoning process is erroneous yet the final result is correct arise frequently, which in turn leads to ineffective training, i.e., scaling along the wrong paths. In this paper, we introduce HaPRL, the first framework to reinforce the search process with human search behavior. We first build an annotation platform and collect 1K+ human-annotated data with fine-grained behavioral signals. During training, a carefully designed judge scores each rollout with task-adaptive weights, anchored on the distilled trace of how a human annotator actually searched the same image. Extensive experiments show that HaPRL consistently outperforms outcome-based RL, and early-stage process supervision yields 6.7x more improvement in subsequent outcome-based scaling. Our results also demonstrate the importance of aligning model behavior with human process annotation signals, which offer new insight into the training of foundation models.

Large language models (LLMs) are increasingly deployed for natural-language logical reasoning, where the final answer is easy to check but the proof behind it is not. In natural-language logical reasoning, an intermediate conclusion should follow from its premises, and the resulting derivation should support the final answer. Existing methods lack machine-checkable verification of intermediate conclusions and answer-supporting proof dependencies, so they may assign credit to invalid or answer-irrelevant steps. We propose Proof-R1, an RL framework from formal verification that trains LLMs to construct verifiable proofs for natural-language logical reasoning. Proof-R1 admits a generated conclusion into the verified proof state only when the corresponding reasoning action satisfies the proof obligations through UNSAT-based machine-checkable formal verification. Proof-R1 also recovers the answer-supporting dependency closure to trace the proof structure of the final answer and align outcome credit with the proof dependencies. Experiments demonstrate that Proof-R1 improves answer accuracy across three logical reasoning benchmarks and four backbone models and outperforms training-free agents and training-based methods in terms of reasoning-process verifiability.

Vision-Language Navigation (VLN) requires agents to continuously ground task progress from long-horizon instructions and partial egocentric observations. Existing VLM-based navigation agents typically reason only over available observations and may remain confident even when task-relevant evidence is missing. For example, an agent may confidently proceed forward and get lost even though the landmark indicating the next turn lies outside its current field of view. We term this failure mode Progress Myopia: the agent fails to recognize unreliable progress grounding and continues acting on insufficient evidence. To address it, we propose SeekVLN, an evidence-seeking framework that couples semantic progress reasoning with active acquisition of task-relevant observations. SeekVLN is trained in two stages: First, Future-guided Reverse Generation (FRG) uses future expert actions to augment offline expert trajectories with supplementary views and evidence annotations. Supervised fine-tuning on these trajectories establishes a prior for evidence seeking and progress reasoning without additional expert interaction. However, imitation alone does not reveal whether seeking improves subsequent navigation. We therefore introduce Counterfactual Contrastive Policy Optimization (C2PO) for reinforcement fine-tuning. By comparing each evidence-seeking branch with a counterfactual direct-navigation branch from the same state, C2PO uses a contrastive reward to assign credit to seeking decisions based on subsequent navigation benefit. Experiments on simulated benchmarks show that SeekVLN achieves state-of-the-art performance, improving success rate by 12.7% and 7.5% over the base model on R2R-CE and RxR-CE, respectively. Both simulated and real-world evaluations exhibit human-like evidence-seeking behaviors for more reliable progress grounding.

Reinforcement learning (RL) has recently delivered substantial gains in multimodal reasoning, opening a promising route for fine-grained visual perception. Yet for multi-image reasoning grounding (MRG), reasoning over real-world multi-image contexts toward pixel-precise localization, existing RL-based approaches overlook two characteristics intrinsic to this paradigm: a coarse-to-fine hierarchical reasoning pattern, and heterogeneously distributed task--sample difficulties. In this work, we present MG-Thinker, a post-training RL framework that advances a new MRG paradigm featuring such hierarchical reasoning, supported by a curated 25K MRG dataset with task-adaptive Chain-of-Thought (CoT) annotations that elicit multi-perspective evidence before conclusion. To remedy the heterogeneous task--sample difficulties, we further propose Bi-Axial DAPO (BiA-DAPO), which decomposes rollout advantages along an intra-group signal axis and an inter-group competence axis through two complementary mechanisms, both grounded on our defined candidate pool for stable group-level statistics. Extensive experiments show that MG-Thinker achieves state-of-the-art performance on multi-image reasoning grounding while consistently improving generalization across multi-image understanding and diverse multimodal benchmarks.

The common paradigm of reinforcement learning with verifiable rewards (RLVR) is to let agents make multiple attempts at a task, and optimize towards the successful ones. This becomes problematic in the realms of self-improvement, where tasks are so difficult that the agent has a low or even no chance of success, and where there are no teacher models or example solutions to distill from. In this paper, we introduce RLTL;DR. After each failed attempt, we show the policy the verifier outputs and let it write its own feedback, in the form of a single TL;DR insight. The next rollout is conditioned on all previous insights, and we sequentially sample rollouts until a solution is found. Moreover, we enable backpropagation on the in-context insights to internalize a direct task to insight mapping. On challenging tool-calling and coding datasets (filtered to Pass@128=0), standard GRPO training of a Qwen 3.5 9B Thinking policy stays flat at a Pass@1 of 0% to 1%. RLTL;DR breaks through this learning barrier, achieving a Pass@1 of 14-31% with insights in context during training and, crucially, 12-13% when no insight is in context at eval time. We identify that the key is the task to insight internalization. To study this further, we reduce our approach to SFTL;DR, training only on (task, insight) tuples, without showing or backpropagating on any rollouts. Training on only 4k of these tuples recovers almost the full performance of RLTL;DR and classical SFT on full rollouts. This demonstrates a promising compacted training paradigm of the form "on this sort of task, keep this sort of thing in mind", which we hope to inspire future research on.

Assigning credit to intermediate steps remains a central challenge in training Large Language Models (LLMs) on multi-step reasoning tasks with sparse terminal rewards, and actor-critic methods such as PPO address this by learning value functions to construct token-level advantages. Their effectiveness, however, hinges on reliable value estimation, a difficult task requiring the critic to both assess progress toward a correct solution and anticipate an evolving policy's future behavior; errors in either can compromise credit assignment and destabilize online training. In this paper, we revisit the standard state-only formulation of value estimation and propose $π$PPO, a self-privileged actor-critic framework. By reusing verified same-prompt rollouts as contrastive evidence, $π$PPO helps the critic assess intermediate reasoning against successful and failed attempts, while preserving standard policy optimization and the deployment interface. Experiments show that $π$PPO consistently improves value-estimation quality by a substantial margin and outperforms representative actor-critic and critic-free RLVR baselines on challenging mathematical reasoning benchmarks, while remaining effective even when paired with substantially smaller asymmetric critics.

Reinforcement Learning with Verifiable Rewards (RLVR) methods such as GRPO rely on successful self-generated trajectories, but finite rollout budgets can produce all-fail groups with no reward-based policy-gradient signal. While additional rollouts improve the chance of success at higher cost, successful trajectories missing from one model's rollouts may already have been discovered by another. Indeed, we observe that heterogeneous models often succeed on complementary prompts, creating opportunities for mutual learning without a designated stronger teacher. To exploit this complementarity, we propose GRAFT (Gated Replacement of Answer-Failed groups with peer Trajectories), an off-policy-aware framework that replaces all-fail groups with informative peer groups. GRAFT transfers both successful and unsuccessful peer responses with peer-computed advantages, while controlling cross-model mismatch through sequence-level compatibility weighting and token-level importance ratio clipping. Across three heterogeneous model pairs and five mathematical reasoning benchmarks, GRAFT consistently improves both models over GRPO with the same per-model rollout budget, gaining 2.1 points on average and up to 4.5 points in model-level average performance. Stored peer trajectories preserve most of the gains, improving over GRPO by 1.8 points on average without simultaneous co-training.

Recent progress in large language model reasoning has been driven by benchmarks and reinforcement learning environments with automatically verifiable rewards, particularly in mathematics, code, and formal logic. These settings make model accuracy easier to evaluate and optimize, but it remains unclear how far success under fixed problem specifications and stable evaluation criteria transfers to reasoning outside such domains. Real-world reasoning often proceeds under incomplete and revisable information: conclusions may be supported provisionally, defeated by counter-evidence, reinstated by further arguments, or revised when stronger reasons become available. Reasoning of this kind is generally referred to as defeasible reasoning. We introduce ArgGYM, a procedural benchmark and RLVR-compatible training environment for structured defeasible reasoning. ArgGYM decomposes this reasoning into twelve tasks and grounds task-specific scoring in a symbolic argumentation engine that computes the formal states used to evaluate model outputs. It includes a frozen benchmark of 1,440 verified instances across fifteen curriculum configurations, two argument preference orderings (weakest-link and last-link), and two set orderings (elitist and democratic), while the same generators and verifiers can produce fresh instances for evaluation that reduces dependence on static test sets and for verifiable-reward training. On the frozen benchmark, frontier and open-weight models show sharply different reasoning profiles: they can recover substantial parts of structured answers without solving the complete task, and performance declines in later curriculum configurations with longer dependencies and more interacting structures. We release the benchmark, generators, and verifiers for reproducible evaluation and RLVR training.

Multi-reward guided reinforcement learning (i.e., RL) offers a promising way to improve joint audio-video diffusion models along several complementary objectives, including modality-specific quality, cross-modal semantic alignment, and temporal synchronization. Its effectiveness, however, depends on two quantities that change during training: where reward-driven updates should act, and how competing rewards should be combined. Existing methods tend to rely on fixed routing and reward weights, failing to track evolving model functions. To address these limitations, we propose Adaptive Reward Routing to jointly adapt update locations and reward coordination during forward-process RL (i.e., DiffusionNFT) of joint audio-video diffusion models. Our method consists of two components. (i) Cross-Modal Influence-Guided Routing (Localizing Updates): We use bidirectional cross-attention responses as an efficient proxy for evolving cross-modal influence, dynamically reweighting token-aware losses and scaling gradients across cross-modal layers without additional model interventions. (ii) Preference-Preserving Modality-Aware Reweighting (Coordinating Rewards): We preserve predefined weights as preference priors and use branch-specific reward-gradient interactions as residual corrections after warm-up. This resolves evolving conflicts without letting dominant rewards suppress weak but essential objectives. Extensive experiments demonstrate consistent improvements in modality quality, semantic consistency, and audio-video synchronization over strong RL baselines. Ablations and mechanism analyses further validate the complementary benefits of adaptive update routing and reward coordination.

Language model agents can be improved by updating their model weights or refining the harness that guides task execution. These components are coupled: weight updates change how the model uses the harness, while harness updates change the trajectories used for training. We propose VACE, Validation-Gated Alternating CoEvolution, which alternates agentic reinforcement learning with trajectory-driven harness refinement. After each RL stage, VACE reuses the collected trajectories to propose a harness revision and evaluates the incumbent and candidate with the updated model held fixed. The candidate guides subsequent training only if it improves validation performance. With Qwen3.5-9B, VACE achieves 45.26% test accuracy on OfficeQA and a mean partial-credit score of 75.19% on AutomationBench, exceeding weight-only RL by 6.43 and 9.09 percentage points and ungated alternation by 4.59 and 6.95 points, respectively. Across 44 harness proposals, 17 reduce validation performance at the updated checkpoint and are rejected before subsequent RL training, highlighting the importance of validation gating.

Maximum Likelihood Reinforcement Learning (MaxRL) targets prompt-wise log-success and has shown strong performance on reasoning tasks. Under finite rollout budgets, however, the estimator used by MaxRL attenuates each prompt's likelihood gradient by a factor that depends on its success probability and rollout count. Under uniform rollout allocation, the common rollout count fails to compensate for success-dependent attenuation, leaving low-success prompts more strongly attenuated and distorting their relative contributions to the expected aggregate gradient. We introduce SERA (Scale-Equalized Rollout Allocation), which redistributes a fixed rollout budget to approximately equalize these finite-rollout scaling factors. Building on our theoretical analysis of how finite rollouts distort prompt-wise likelihood gradients, we formulate the allocation as a fixed-budget max--min problem, derive a waterline solution to its continuous relaxation, and introduce a multiplicity correction to remove the additional prompt weighting induced by heterogeneous rollout counts. Experiments show stronger alignment with exact likelihood gradients in a controlled ImageNet setting and improved multi-sample solution coverage over MaxRL on maze navigation and mathematical reasoning under matched training rollout budgets.

Large language models (LLMs) exhibit strong general capabilities that mechanistic interpretability has attributed to sparse computational circuits. However, existing circuit studies emphasize preserving functionality or explaining safety, leaving the mechanisms underlying failures across a broader range of tasks largely unexplored. Extending circuit analysis from abilities to errors, we explore the perspective that such failures may likewise arise from erroneous internal computations and that targeted tuning of the corresponding parameters can correct such errors while largely preserving other capabilities. Motivated by this insight, we introduce RESCUE (Reasoning-Error Sparse-Circuit Uncovering and Editing), a framework that localizes error-associated circuits and surgically repairs them for performance enhancement. General tasks typically involve multi-step reasoning and long-form generation, where early deviations can cause prefixes to drift from supervised references, leading SFT-based mask optimization to overlook circuits involved in generation-time errors. RESCUE therefore refines these masks through reinforcement learning with multiple masked-model rollouts, improving their relevance to observed task failures. Finally, RESCUE introduces a pruning technique and precisely fine-tunes error circuits to correct task failures, thereby translating error localization into a sparse and targeted model update. We validate RESCUE on heterogeneous repair sets across two domains: (1) mathematical reasoning, identifying a math error circuit of 1.40% density whose repair raises accuracy from 6.0% to 75.5%; and (2) medical QA, where a similarly compact 1.44% circuit improves repair-set accuracy from 0% to 81%. Our code is available at: https://github.com/chuanpupig/RESCUE.

We study the learning dynamics of fine-tuning a policy model on self-generated and reward-weighted data, with particular focus on a generalized version of REINFORCE — referred to as RE(S) — that updates the rollout distribution once every $S \ge 1$ gradient steps. Prior work in bandits and reinforcement learning has developed rich theory for policy gradient methods, and on-policy sampling (i.e., a small $S$, ideally $1$) is often viewed as crucial to their success; yet in prominent application like post-training large language models, reward-guided self-training has proved to be effective even when the rollout distribution is updated infrequently, but theoretical understanding remains limited for the convergence properties of these off-policy methods. To bridge these gaps, we develop a unified theory for RE(S) that covers the full spectrum of $S \ge 1$: it can be interpreted as a stage-wise optimization process, where each stage takes $S$ gradient steps for minimizing the Kullback-Leibler distance to a fixed reward-weighted rollout distribution. For multi-arm bandits with softmax policies, our in-depth analysis and numerical experiments reveal three key findings: (1) for any fixed $S$, RE(S) enjoys global convergence to the optimal policy as the number of rollout distribution updates $B = \lfloor T / S \rfloor \rightarrow \infty$, where $T$ denotes the number of gradient steps; (2) we prove tight two-sided bounds showing that the suboptimality gap of RE(S) achieves an asymptotic $Θ(1 / T)$ convergence rate, while $S$ only affects the length of a burn-in phase; (3) when initialized at a weak policy with a small optimal-action probability, RE(1) gets trapped around suboptimal policies for a long period, whereas RE(S) with a suitable $S$ avoids the detour and achieves significantly faster convergence to the global optimum, highlighting the benefits of off-policyness in this case.

Looped reasoning models repeatedly apply a shared set of parameters, enabling more computation without increasing the model size. These models also support input-dependent computation by dynamically deciding when to stop looping. Motivated by the recent success of looped transformers in language modeling and reasoning, we investigate whether dynamic looping can similarly benefit sequential decision-making. We provide a complexity-theoretic motivation for this approach by showing that there exist Markov decision processes in which a state-adaptive policy achieves the optimal return with asymptotically less expected computation than any optimal fixed-runtime policy. To learn compute-adaptive policies in practice, we introduce Looped Actor, a transformer-based policy that repeatedly refines a latent representation toward a fixed point using a shared computational block. This allows the model to allocate computation adaptively by varying the number of loops based on the current state. We evaluate Looped Actor on 22 tasks across six environments, ranging from combinatorial puzzles to robotic manipulation and spanning online and offline reinforcement learning (RL) with discrete and continuous actions. Looped Actor matches or exceeds the performance of an untied baseline with 16$\times$ more parameters, with the largest gains in environments where action selection requires substantial multistep planning. For the Boxoban environment, we find that the computation allocation is structured: the number of loops increases with the number of remaining pushes and future optimal pushes become increasingly predictable from the latent state over successive loops. Together, these results highlight actor looping as a simple and efficient way to equip RL agents with adaptive computation and improve their planning capabilities. Code is available at https://github.com/camail-official/LoopedActor

Distilling the reasoning capabilities of large language models (LLMs) into smaller students is a central challenge for efficient deployment. Current approaches face a fundamental tension: optimizing purely for verifiable task rewards (e.g., via GRPO) leads to reward hacking, where students arrive at correct final answers through flawed intermediate logic, while regularizing with soft divergence penalties against a teacher (e.g., KL-based distillation) dilutes task performance and, critically, allows the student to compensate for severe logical violations at one step with high teacher agreement at others. We argue that this averaging is fundamentally misaligned with the nature of reasoning: a chain-of-thought is only as valid as its weakest link. Motivated by this observation, we formulate reasoning distillation as a constrained reinforcement learning problem in which the task reward is maximized subject to a worst-case constraint on the teacher log-likelihood along every prefix of the trajectory. To avoid the prohibitive cost of dual Lagrangian solvers and the test-time teacher dependence of state-augmented methods such as Saute, we derive an unaugmented constrained MDP whose reward transformation preserves the hard-constraint semantics, admits a low-variance policy gradient decomposition into single-step and long-term terms, and provably satisfies the worst-case constraint almost surely in the penalty limit. Through extensive experiments on mathematical reasoning and code generation tasks, we demonstrate that our method significantly expands the accuracy-fidelity Pareto front. By matching the high Final Answer Correctness of pure RL and drastically reducing teacher constraint violations, we ultimately achieve the highest rigorous Reasoning Success Rate across all evaluated settings.

While modern language models demonstrate impressive generative capabilities, they often struggle with constrained, counter-intuitive creative tasks. To address this limitation, we explore chess puzzle generation as a rigorous testbed for computational creativity and reasoning, a domain where altering a single piece can invalidate an entire solution. We propose a novel approach for conditional generation of creative chess puzzles using masked diffusion models. Unlike previous methods, our non-directional diffusion approach allows for conditioning on specific tactical themes and partial board positions. We introduce a novel auxiliary task of simultaneous best-move prediction, which improves solution uniqueness by 11.6% and theme-conditioning accuracy by 2.5%. To further optimize solution uniqueness and theme conditioning, we establish a reinforcement learning framework adapted from Denoising Diffusion Policy Optimization (DDPO). This RL training increases the yield of unique and theme-matching positions by 89.1%. Finally, we release the first open-weights models (Appendix B) for chess puzzle generation, offering a new pathway for controllable, creative generation.

Group-relative RL methods such as Flow-GRPO post-train image generators by exploring with isotropic Gaussian noise added at every denoising step. This noise decides which rollouts the model learns from, yet it perturbs every channel and spatial position of the latent equally. In this paper, we instead show that latent elements differ in how much they change the generated image, so exploration should adapt to these differences. We introduce EXPLORENET to learn an adaptive exploration distribution. EXPLORENET is a policy that predicts a noise scale for every latent element from the current latent, the denoising step, and the prompt, before any reward is observed; it is trained on the reward spread of each rollout group and discarded after training, leaving inference unchanged. On Stable Diffusion 3.5 Medium, EXPLORENET improves held-out GenEval2 by 14% over Flow-GRPO, transfers to two independent compositional benchmarks and five preference and image-quality models, and reaches a 67.2% human preference win-rate. Overall, across our group-relative diffusion RL experiments, we find that exploration is learnable, the shape of the exploration distribution outweighs its magnitude, and rollout quality is more effective than rollout quantity.

Direct preference optimization (DPO) models binary preferences through a Bradley-Terry model with a common noise scale, without explicitly accounting for preference strength or prompt-dependent uncertainty from human feedback. We introduce uncertainty-normalized margin DPO (UNM-DPO), which combines strength-dependent margins with a learned prompt scale. Motivated by a heteroskedastic Bradley-Terry model, we develop two training objectives. Both compare the implicit rewards of preferred and rejected responses, derived from response log-probability ratios to a reference policy. Advantage-only (AO) divides this reward difference by the prompt scale before subtracting the margin; whole-residual (WR) subtracts the margin before dividing by the scale. For the WR comparison model, we establish a necessary and sufficient condition under which known margins make the prompt scale identifiable. We introduce a practical procedure for learning the scale. Building on WR, we introduce ULNM-DPO-WR, which normalizes each response's implicit reward by its length. We evaluate our methods against DPO and related baselines on HelpSteer2 and HelpSteer3, using the Skywork reward model as a judge. With Llama-3.1-8B-Instruct, ULNM-DPO-WR achieves tie-adjusted win rates against matched DPO of 68.00% and 65.31% on evaluation panels, with higher mean rewards and shorter responses on average. On AlpacaEval with a GPT-4.1 judge and GPT-4-Turbo reference answers, the same 8B policy achieves a length-controlled win rate of 21.62%, compared with 16.39% for DPO and 15.30% for SimPO. These results demonstrate the potential of combining preference-strength margins, learned prompt scales, and length normalization for policy optimization.

Scaling laws for optimization against reward models in AI alignment have pinned down how performance depends on optimization effort---measured by a KL-divergence budget relative to a reference policy. Beyond a certain budget, over-optimization (or reward hacking) can arise: because we optimize against a proxy reward model (distinct from true rewards), performance can plateau or degrade. Naturally, the proxy reward's accuracy depends on how much preference data (often in the form of pairwise comparisons) was used to train it. However, existing research does not cleanly identify how performance jointly scales with the amount of training data and the divergence budget. Our main contribution is to provide an empirically accurate and theoretically grounded scaling law in such context. Performance roughly scales as $Θ(\sqrt{\min\{\log(M),K\}})$, where $M$ is the number of comparisons in training data and $K$ is the policy's divergence budget. We develop an information-theoretic model to establish this upper bound and prove it is tightly achievable through a constructive procedure. Informed by this, we conduct extensive empirical evaluations using a real-world annotation setup, whereby a large 70B gold reward model generates feedback data and proxy reward models are trained from less capable models (0.6B to 4B). Our scaling law provides an excellent fit (R2 from 97% to 99%), outperforms alternative specifications, and remains robust across model sizes, noise, and optimization procedures (best-of-$N$ or policy tilting). Our evidence suggests that reward optimization is analogous to a surprisingly simple selection task: choosing from a sequence of IID Gaussian random variables using noisy preference feedback.

Beam-search-based test-time methods provide an effective way to improve large language model (LLM) performance on long-horizon generation by pruning invalid reasoning paths early, leading to significantly improved reasoning efficiency and more favorable test-time cost scaling. Despite strong empirical success, the theoretical understanding of beam search remains limited. In this paper, we study the test-time compute guarantee of the commonly used beam search framework that uses the model's internal log-likelihood for intermediate scoring, while relying on an external reward model only after a complete response is generated. We first establish a lower bound for vanilla beam search, showing that at least $Ω(C^\star(x)^2)$ samples are required for the optimal response to survive, where $C^\star(x)$ is the token-level coverage coefficient for prompt $x$. This motivates our modified confidence-filtered beam search (CF-Beam), which reduces the sufficient coverage dependence from quadratic to nearly linear under prefix competitiveness, for fixed horizon, gap, and target accuracy. We then show that the regret of CF-Beam is upper-bounded by the probability of rare failure events and the reward estimation error scaled by a path-level coverage coefficient, where the rare-failure term vanishes as per-step sampling increases. Our results highlight a fundamental advantage of beam search over sequence-level inference methods such as Best-of-N and Best-of-Majority. While the guarantees of these approaches typically involve coverage coefficients that grow exponentially with the horizon $L$, CF-Beam controls the dominant search-induced term through a token-level coverage coefficient that scales polynomially with $L$. Our numerical experiments further confirm that beam search is more robust on hard instances and under increasing reasoning horizons.

Long-horizon LLM agents require reinforcement learning methods that can assign credit to intermediate decisions under sparse and delayed rewards. Existing group-based methods such as GRPO and GiGPO alleviate this issue by comparing rollout returns or repeated anchor states, but they still fail when the compared returns have no variation. We identify this failure mode as zero-credit failure: during early training, many failed rollouts contain useful prefixes, yet existing methods assign them no task-discriminative advantage. To address this issue, we propose Milestone Viability Potential Policy Optimization (MVPO), a potential-routed policy optimization algorithm that learns from viable failure prefixes. MVPO estimates prefix potential over Union-Find viability regions, repairs zero-credit groups with potential-difference advantages, and attenuates the potential branch according to relative performance progress. Experiments with Qwen2.5-1.5B-Instruct show that MVPO outperforms eight strong baselines, including GRPO and GiGPO. Under the same training length, MVPO improves over the GiGPO baseline by +4.4 success points on ALFWorld and +5.3 on WebShop, while adding only 0.16%-0.20% advantage-construction overhead.

Group-relative methods for reinforcement learning with verifiable rewards (RLVR) learn from differences in rollout outcomes. Independently sampling complete trajectories is costly and does not explicitly explore the decision space at critical positions. Feedback on a completed trajectory can reveal which earlier choices the policy reconsiders, suggesting where to sample alternative continuations. We introduce Hindsight-Divergence Localization (HDL), which uses hindsight-induced changes in token log-likelihoods to select branch points. HDL generates a small number of complete root trajectories and fills each training group with continuations from the selected positions under the original task context. Each continuation reuses its root prefix and contributes policy updates only through its newly generated suffix, reducing generation cost while focusing additional exploration and learning on decisions after branching. Experiments with three models across math, code, and agent tasks show gains in both rollout efficiency and task performance. Compared with GRPO at matched group sizes and training steps, HDL yields up to a 2.5$\times$ reduction in generated tokens and a 1.8$\times$ speedup in rollout wall-clock time. Despite this reduced generation budget, HDL improves performance across all three domains, with gains of up to 12.5 points on agent tasks.

GUI agents automate tasks on digital devices by grounding language instructions in visual interfaces. Existing group-relative reinforcement learning improves GUI action prediction by comparing the rewards of multiple responses sampled from the same GUI state. However, binary evaluation treats spatially different failed clicks as identical and provides no relative signal when all sampled clicks fail. To address these limitations, we propose Spatial Credit Assignment (SCA), which uses the screen coordinates of sampled clicks to refine group-relative credit. Specifically, SCA predicts each held-out response's reward from the other responses in groups containing both successes and failures, then uses the prediction residual to adjust credit. When all sampled clicks fail, SCA instead orders them by distance to the annotated target. These spatial references are used only to construct the training update; the deployed policy remains unchanged. We evaluate whether this correction improves the policy update itself by comparing its error and directional alignment with the exact return gradient in a controlled synthetic study. Across GUI grounding and offline action-prediction benchmarks, SCA improves grounding across professional domains and achieves the strongest results among reinforcement-fine-tuned models on most action-prediction metrics, with consistent gains across the reported GUI suites.

A key strength of Proximal Policy Optimization (PPO) is its learned critic, which uses historical trajectories collected during reinforcement learning to estimate expected returns and reduce policy-gradient variance. However, we find that the critic is also a major source of instability in reinforcement learning for large language models (LLMs). We identify two critic failure modes that destabilize PPO. First, filtering truncated rollouts from both actor and critic shifts the policy objective to reward conditioned on completion, allowing truncation to increase even as conditional reward improves. Second, heterogeneous return noise can cause high-variance prompts to dominate critic updates in finite batches. We introduce EasyPPO to address these failures. Actor-only overlong filtering trains the critic on returns from both completed and truncated rollouts. Noise-normalized critic regression weights each prompt's critic loss by the inverse standard deviation of its sampled returns, balancing noise contributions across prompts. Moderately smaller critic mini-batches confine outlier influence to fewer rollouts during gradient clipping. Across continuous-reward coding on FrontierCS, binary-reward mathematical reasoning on AIME24, and multi-turn search on Search-R1, EasyPPO remains stable throughout the full training horizon and consistently outperforms vanilla PPO, VAPO, and HL-Gauss PPO. Its best validation scores show relative gains of 14.89%, 2.28%, and 9.47% over PPO, respectively.

Reward hacking occurs when policy optimization exploits a brittle reward interface or an overly permissive proxy objective, improving the training score without improving the underlying response quality. This phenomenon is amplified in group-relative policy optimization: an unsupported reward can shift the group baseline and alter the updates of other rollouts, while post-hoc or purely relative weighting cannot represent group-wide uncertainty. We propose Self-Tuned Anchored Reliability Group-Relative Policy Optimization (STAR-GRPO), a reliability-first advantage estimator based on paired assessments of the same rollout. STAR separates the quality signal from its learning influence: score disagreement determines rollout reliability, relative reliability enters a self-tuned robust location--scale fit before group normalization, and absolute group reliability attenuates the resulting bounded advantage. The analysis establishes coordinate and second-moment bounds, characterizes exact centering through the weighted location equation, and gives reliability-dependent attenuation guarantees for outlying rewards. We evaluate STAR-GRPO in two complementary reward-hacking regimes. In token-interface exploitation, STAR prevents runaway optimization of the deployed-interface score while improving the canonical quality signal. In rubric-proxy overoptimization for medical reasoning, STAR improves independent semantic evaluation, narrows the proxy--judge discrepancy, and reduces overclaim while optimizing the same task proxy. Together, these results show that reliability-first normalization offers a principled way to limit unsupported reward influence on both group baselines and policy updates, while retaining the task reward as the optimization target.

Group relative policy optimization (GRPO) learns only from prompts whose sampled responses disagree: a group that is entirely correct or entirely incorrect has zero reward variance, contributes no gradient, and still consumes its rollouts. Prompt-selection methods reduce this waste by steering sampling toward intermediate pass rates, but they choose the target, its width, and the uncertainty model heuristically, in raw pass-rate or logit coordinates. We show that GRPO comes with a natural coordinate for pass rates: the arc length $ψ=\arcsin\sqrt{p}$ on the Bernoulli Fisher--Rao manifold. In arc length, the expected GRPO update is uniform up to two boundary ramps; the probability of a zero-variance group is bounded by two Gaussian boundary layers of width $1/\sqrt{2G}$; pass-rate evidence has constant noise; and the gradients of the pass@$k$ and pass$^k$ objectives are Gaussians whose center and width follow from $k$ in closed form. A prompt curriculum for GRPO is therefore a Gaussian in arc length, and choosing its center amounts to choosing the objective. We turn this observation into ARCUS, a drop-in sampler that tracks every prompt with a Kalman filter in arc length, scores prompts by an objective-matched Gaussian kernel times the predicted probability of an informative group, keeps only informative groups for the unchanged GRPO update, and paces the target toward the hardest objective whose predicted yield stays within a small slack of the best. Across six mathematical reasoning benchmarks and three backbones, ARCUS improves the average accuracy of GRPO by 2.8--2.9 points and that of dynamic sampling by 1.1--1.2 points, while generating 48--57% fewer rollouts than dynamic sampling.

Reinforcement learning (RL) has become a cornerstone for improving the reasoning capabilities of large language models (LLMs), but the need for on-policy data substantially limits training efficiency. Reusing off-policy data through importance sampling (IS) can improve efficiency but introduce considerable instability. Hence, algorithms such as PPO and GRPO widely adopt IS-ratio clipping to stabilize training. However, training stability and gradient estimate are mainly determined by the product of IS ratio and advantage. To further stabilize training, we propose ACPO, which clips the product of the IS ratio and the advantage, leading to more stable gradient estimates. We also establish a connection between ACPO and gradient clipping in policy mirror descent (PMD), which is a standard technique to stabilize optimization process, and prove the convergence of clipped-PMD under the standard RL setting. Experiments on widely used mathematical reasoning benchmarks show that ACPO consistently outperforms PPO and GRPO in both accuracy and training efficiency, delivering 4-6 percentage points gains on standard math benchmarks, with Qwen3-8B+PPO. Hence, ACPO is a practical and effective alternative to conventional IS-ratio clipping for RL post-training of LLMs.

Chinese Semantic Error Correction (CSEC) targets semantic errors in Chinese text, which are typically more subtle and complex than spelling and grammatical errors but remain relatively underexplored. Existing LLM-based approaches face two recurring obstacles in this task: over-correction, and unclear interaction between Chain-of-Thought (CoT) reasoning and self-consistency decoding, such that the benefits brought by CoT cannot be reliably transferred to final corrections. We propose Vote-guided Advantage Allocation for CSEC (VAA-CSEC), a multi-stage framework that combines CoT distillation, Supervised Fine-Tuning (SFT), Reinforcement Learning (RL) and self-consistency decoding. During RL, we design a task-specific reward function that directly aligned with the minimal-editing principle of CSEC. We further introduce Group-Level Relative Policy Optimization (GLPO), which reallocates GRPO advantages according to the margin between individual rollout rewards and the vote-aggregated group reward, aligning the RL training objective with the self-consistency objective used at inference time. Experiments on CSED-C and NaSGEC-Exam show that VAA-CSEC outperforms all LLM-based baselines on CSED-C with an F0.5 of 47.72%, achieves the highest recall of 42.15% among all methods, and establishes a new state of the art of 41.55% F0.5 on NaSGEC-Exam.

Ensuring the safety of reasoning large language models (LLMs) across languages is essential for their reliable deployment. However, when exposed to jailbreak attacks in non-high-resource languages, these models may generate unsafe responses even when their reasoning traces identify safety risks. To address this issue, we propose aligning cross-lingual thoughts and responses (ACTR), a framework that improves multilingual safety alignment by strengthening the use of existing safety reasoning. Specifically, we first present the think gap score (TGS) to compare the normalized contributions of reasoning traces to attention outputs during response generation across languages, and use reasoning- trace substitution to measure the cross-lingual safety gap. Next, using a corpus of jailbreak queries, we assess neuron importance through changes in response representations caused by neuron masking and compare the high-importance neuron sets obtained with reasoning enabled and disabled to identify safety think neurons that support the use of safety reasoning. Finally, we devise neuron-selective consistency optimization (NSCO), which uses a frozen judge model to reward agreement between the safety categories of reasoning traces and responses while updating only the parameters associated with the selected neurons, requiring no human-annotated responses or preference data. Across two reasoning models, ACTR achieves lower average attack success rates than the evaluated state-of-the-art methods on AdvBench-X and MultiJail, with safety gains extending to unseen languages, while preserving or improving average performance on multilingual knowledge and mathematical reasoning tasks and limiting false refusals of benign requests. Warning: this paper contains examples with unsafe content.

Group Relative Policy Optimization (GRPO) is widely used to train reasoning language models, where it computes advantages by centering and normalizing rewards across rollouts of the same prompt. For multiple rewards, GRPO sums the reward components and normalizes the total reward by its within-group standard deviation. The corresponding variance equals the sum of all pairwise reward covariances. For a fixed centered reward, larger aggregate covariance produces smaller advantages, and vice versa, allowing update magnitudes to adapt to reward dependence. However, correlated rewards with large scales can dominate this normalization and suppress signals from smaller-scale rewards. We propose Correlation-Normalized GRPO (CorrGRPO), which normalizes pairwise covariances into Pearson correlation coefficients. CorrGRPO keeps the centered total reward unchanged while balancing the influence of differently scaled rewards on the correlation-based normalization. This allows advantage magnitudes to adapt to reward correlations without the normalization being dominated by large-scale reward components. We compare CorrGRPO with GRPO and other variants on code generation, tool calling, and agent security, using models ranging from 0.5B to 8B parameters. These tasks all involve multiple rewards that can improve together or present tradeoffs. Results show improvements across three domains, including code generation, tool calling, and agent security. Our code is available at https://github.com/HKUST-KnowComp/CorrGRPO.