Group Relative Policy Optimization

This paper investigates large language model (LLM) abstention learning, specifically using ternary reward, which incentivize truthfulness in large language models. This paper extends that idea by moving from a ternary reward to a Trajectory-Informed advantage reweighting, dynamically re-weights the abstention reward during Group Relative Policy Optimization (GRPO) training. The objective of this work focuses on abstention learning instead of improving truthfulness, serving as an exploration into hallucination reduction. The novelty of this paper lies in methodological innovation, advantage re-weighting, and benchmark selection. Leveraging GRPO's multiple trajectories as a natural abstention signal, this method uses a reward signal to explore knowledge boundaries and encourage consistency. By demonstrating that trajectories can be used as a confidence indicator of the policy relative to the query, they are then used to dynamically calculate the abstention advantage. AbstentionBench is used as the evaluation benchmark, as this work aims to contribute to the field of abstention learning. All datasets on the benchmark were tested against this method and various baselines. Empirical results demonstrate that TIAR achieves state-of-the-art abstention F1 scores across five of six evaluation categories, outperforming the static ternary baseline on 17 of 31 benchmark datasets while fully preserving baseline accuracy.

Multi-trait essay scoring aims to provide fine-grained evaluation of writing quality across multiple dimensions. However, how to effectively post-train autoregressive scoring models remains underexplored. In this paper, we propose Trait-Aware Policy Optimization (TAPO), a post-training framework tailored to autoregressive multi-trait scoring. Our method decomposes rewards along both the sample and trait dimensions, combining global scoring consistency, trait-level accuracy, format validity, and inter-trait dependency preservation. In addition, we use enhanced prompts throughout training by incorporating original prompt texts and trait descriptions, providing richer semantic information for trait-specific score generation. Experiments across multiple backbone models show that our method consistently improves multi-trait scoring performance over supervised fine-tuning and scalar-reward optimization baselines, demonstrating the effectiveness and transferability of trait-aware post-training for essay scoring.

Reinforcement Learning has become a standard paradigm for aligning Large Language Models with human intent and task requirements. While Group Relative Policy Optimization offers an efficient, value-model-free alternative to Proximal Policy Optimization, adapting it to real-world multi-reward settings remains challenging. Standard scalarization practices, such as Reward Combination and Advantage Combination, suffer from significant drawbacks: Reward Combination frequently generates advantages with excessively large squared magnitudes that lead to training instability, while Advantage Combination relies on static hyperparameters and ignores cross-objective correlations. To address these limitations, we propose Dynamic Variance-adaptive Advantage Optimization (DVAO), which dynamically adjusts combination weights based on the empirical reward variance of each objective within a rollout group, effectively up-weighting objectives with a stronger learning signal while suppressing noisy ones. We mathematically prove that DVAO maintains bounded advantage magnitudes for stable training and introduces a self-adaptive cross-objective regularization mechanism. Extensive experiments on mathematical reasoning and tool-use benchmarks using Qwen3 and Qwen2.5 models demonstrate that DVAO significantly outperforms baseline methods, achieving a superior multi-objective Pareto frontier and robust training stability.

This paper studies reinforcement learning for high-frequency trading on limit order books by pairing an Order-Flow-based state model with policy-gradient methods. Instead of value-based RL techniques like tabular Q-learning, our approach deploys policy-based methods like vanilla PPO and DeepSeekMath-inspired variants like GRPO and GSPO, that use group-normalized updates and downside-aware shaping. On backtests with financial assets AMZN, AAPL, and GOOG under a simplified backtesting setup based on spread-scaled rewards, these new policies improve net average PnL, profitability, and drawdown over the Q-Learning baseline. Our results show that (1) Order-Flow signals are an adequate state for policy RL and (2) group-aware PPO surrogates are preferable over value-based baselines.

Recent advancements in Reinforcement Learning (RL), particularly Group Relative Policy Optimization (GRPO), have significantly enhanced the reasoning capabilities of Large Language Models. However, applying these problem-centric optimization methods to role-playing agents often leads to a loss of character fidelity and style collapse, as they prioritize context-specific utility over persona alignment. To address this, we propose Character-Centric Group Relative Policy Optimization (CRPO), a framework designed to realign RL objectives with the role-playing task. CRPO improves character distinctiveness through three mechanisms: decoupling task logic from stylistic rewards to resolve gradient conflicts, dynamically adapting optimization constraints based on character complexity, and utilizing generic responses as negative baselines to prevent the model from reverting to a common distribution. Extensive experiments demonstrate that CRPO outperforms existing methods in consistency, emotion and others.

Contemporary reinforcement learning with verifiable reward methods post-train language models on multi-step reasoning by assigning a single outcome reward uniformly across all tokens in a trajectory. Such uniform assignment ignores which steps contributed to success or failure. Improving credit assignment can address this limitation by enabling targeted refinement of faulty reasoning steps, rather than updating entire trajectories uniformly. Resets are one such simple mechanism, enabling more precise credit assignment by returning to an intermediate state and resampling counterfactual continuations, so that outcome differences can be attributed to decisions made at that point. We propose two such methods: Random-Reset Policy Optimization (RRPO), where reset states are drawn randomly from reasoning steps, and Self-Reset Policy Optimization (SRPO), where the model self-localizes the erroneous step in an incorrect trajectory and resets there. We analyze these methods within the Conservative Policy Iteration (CPI) framework. Extending CPI with a credit-assignment oracle that targets improvable states yields provable improvements over random resets. Across models and reasoning benchmarks, SRPO consistently outperforms standard GRPO and RRPO by sampling multiple suffix continuations at a self-localized reset and learning from their rewards, using only the model itself with no external supervision.

Large language models~(LLMs) are trained on heterogeneous multilingual corpora, yet existing policy optimization methods often implicitly restrict each training question to a single response language or rely on a fixed dominant language for supervision. We propose language-routed policy optimization (LRPO), an online policy optimization framework that treats language as a selectable variable. LRPO elicits multilingual rollouts for each training question and integrates their relative quality into preference-based policy updates, increasing the diversity and informativeness of training signals under the fixed rollout budget. To adaptively determine which languages to explore during reinforcement learning, we introduce a trainable language router formulated as a multi-armed bandit, balancing exploration of underutilized languages with exploitation of more informative ones. Extensive experiments show that LRPO consistently improves multilingual performance, demonstrating that adaptive language routing enables effective cross-lingual knowledge exploitation for training. We release all the resources at https://github.com/Guochry/LRPO.

Reinforcement learning with verifiable rewards (RLVR) has become a powerful paradigm for improving language models on reasoning-intensive tasks, but its effectiveness is often limited by exploration. For example, models often fail on hard problems, leaving little useful reward signal. External expert traces offer a natural source of guidance, yet they may also expose reward-relevant content along the critical path to the verifier target, such as final answers, intermediate values, executable implementations, or answer-related entities. This content can create an unintended reward hacking channel, allowing the policy to obtain reward by copying the trace rather than learning the underlying reasoning or agentic behavior. Existing guided-RL methods reduce this risk by using partial trajectories, but they mainly control how much expert information is shown heuristically rather than which parts should be hidden. To this end, we propose Semantic Masked Expert Policy Optimization (SMEPO), a fine-grained semantic masking strategy for expert-guided RLVR. Instead of truncating traces coarsely or revealing them unchanged, SMEPO masks reward-relevant semantic spans along the critical path while preserving the expert's decomposition, plan, and procedural structure. This turns hard problems from reasoning from scratch into a fill-in-the-blank process: the policy can follow the expert's problem-solving route, but must still reconstruct the missing values, code, or entities by itself. SMEPO is simple to apply and requires no changes to the reward function or RL objective. Across diverse domains, including math, code, and agentic search, SMEPO improves accuracy by up to 3.2 points over GRPO and reduces training time by up to 4.2x. The code is available at https://github.com/mit-han-lab/SMEPO.

Self-improvement training enables the large reasoning models (LRMs) to improve themselves by self-generating reasoning trajectories as training data without external supervision. However, we find that this method often falls short in complex reasoning tasks and even leads to model collapse. Through a series of preliminary analyses, we reveal two problems: (1) data imbalance, where most training samples are simple, but the challenging yet crucial samples are scarce; (2) overthinking, where many undesired samples with redundant reasoning steps are used for self-training. To this end, we propose HSIR, which effectively Harnesses Self-Improvement in large Reasoning models via two simple-yet-effective approaches. Specifically, HSIR introduces a verify-then-exit sampling strategy to mitigate data imbalance by efficiently collecting more accurate solutions for difficult queries, and designs an Intrinsic Diversity score to quantify overthinking and filter out the undesired solutions. We apply HSIR to various post-training paradigms, among which we further propose H-GRPO, an enhanced GRPO algorithm that leverages the intrinsic diversity as an external reward to encourage concise and diverse reasoning via reinforcement learning. Extensive results show that HSIR not only effectively enhances the reasoning performance, i.e., bringing up to +10.9% average performance gains, but also significantly improves the reasoning efficiency by reducing up to 42.4% relative inference overhead.

Proximal Policy Optimization (PPO) has become the de facto standard for training legged robots, thanks to its robustness and scalability in massively parallel simulation environments like IsaacLab. However, its on-policy nature makes it inherently sample-inefficient, preventing its use for continuous adaptation and fine-tuning on real hardware. Soft Actor-Critic (SAC), by contrast, is an off-policy algorithm that can reuse past experience, making it a natural candidate for sim-to-real transfer workflows where the same algorithm can be used both in simulation and for online learning on the real robot. Despite these advantages, SAC has consistently failed to match PPO's empirical performance in massively parallel training settings. This work identifies the root causes of this gap and introduces targeted modifications, covering policy initialization, timeout-aware critic targets, and multi-step return estimation, that enable SAC to train stably at scale. Evaluated across multiple legged robot platforms and diverse locomotion tasks, our approach closes the performance gap with PPO entirely.

We study the global convergence of policy gradient for infinite-horizon entropy-regularized Markov decision processes (MDPs) with continuous state and action spaces. We consider log-linear softmax policies with linear function approximation, which extend the tabular softmax parameterization while retaining a tractable policy class. Under $Q^π_τ$-realizability for the regularized state-action value function, we first establish a non-uniform Polyak--Łojasiewicz (PŁ) inequality. The non-uniformity arises through degeneracy of constants associated with the policy geometry, namely the Fisher information matrix or an uncentered feature covariance matrix. We then identify two feature regimes under which this non-uniform constant can be bounded along the gradient flow. For full-affine-span features, we prove radial unboundedness of the KL regularizer and show that the smallest eigenvalue of the Fisher information matrix remains bounded below by an initialization-dependent positive constant. For simplex-valued features, we prove an analogous radial unboundedness result in the subspace orthogonal to the all-ones vector and obtain a uniform lower bound for the smallest eigenvalue of the uncentered covariance matrix. These results imply global linear convergence of the regularized objective along the gradient flow, i.e. suboptimality decaying as $\mathcal{O}(e^{-Ct})$ for some $C>0$. Our analysis extends the global convergence theory of entropy-regularized softmax policy gradient beyond the tabular setting of Agarwal et al. (2020); Bhandari and Russo (2024); Mei et al. (2020).

Text-to-Image (T2I) models have made significant strides in visual realism and semantic consistency, yet they often perpetuate and amplify societal biases. Existing evaluation methods typically address only single-dimensional biases, lacking perspectives to uncover model biases at social-related deeper semantic levels. We introduce HoloFair, a comprehensive benchmark framework for multidimensional demographic bias analysis. Built upon our large-scale fairness-oriented dataset and the SpaFreq (Spatial-Frequency) attribute classifier, this framework proposes the Multi-attribute, Group-wise Bias Index (MGBI) metric, designed to assess both intrinsic diversity and conditional biases. Beyond evaluation, we further introduce Fair-GRPO, a reinforcement-learning-based debiasing method that alters the distribution of generative models through a designed multi-objective reward function. E.g., experiments on the SD3.5-Medium model demonstrate that Fair-GRPO significantly improves multidimensional fairness while maintaining high image quality. We also analyze potential reward hacking phenomena and provide corresponding mitigation strategies. Code and dataset are available at https://github.com/1059684669/HoloFair

Android malware detectors often degrade after deployment because of concept drift, while full retraining at each maintenance step is costly. We propose a chronological adaptive maintenance framework that models deployment-time maintenance as a sequential decision problem. The framework learns a stable latent representation through self-supervised learning during initialization, freezes the encoder, measures latent drift in the fixed representation space, and performs lightweight downstream adaptation using a trainable adapter and classification head. A proximal policy optimization controller selects low-cost maintenance actions based on the detector state, including current utility, retention on a fixed memory set, latent drift indicators, and update cost. We evaluate the framework under a causal deployment-style protocol on emulator and real Android malware datasets with static and dynamic features. Results show that the RL controller provides a strong cost-aware adaptation strategy, consistently remaining among the top-performing policies while achieving a favorable balance between temporal performance, memory retention, and maintenance cost under non-stationary deployment conditions.

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO is essentially a drop-in replacement for the GRPO advantage estimator, but it trains the LLM to output a set of solutions where individual solutions specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes more standardized, optimizing for diversity may need to become the default post-training objective.

The Flexible Job Shop Scheduling Problem (FJSP) is the optimal allocation of a set of jobs to machines. Two primary challenges persist in FJSP: the unpredictable arrival of future jobs and the combinatorial complexity of the problem, rendering it intractable for conventional mixed-integer linear programming solvers. This paper proposes an event-based \gls{DRL} approach to solve FJSP with random job arrivals. Specifically, we employ the Proximal Policy Optimization algorithm and use lightweight Multi-Layer Perceptrons to train the \gls{DRL} agent for minimizing the total completion time of all jobs. We design the state representation to be directly accessible from the environment, and limit the learning agent to selecting from among a set of well-established dispatching rules. Simulations show that our \gls{DRL} approach outperforms any of the individual dispatching rules on datasets with varying heterogeneity and job arrival rates. We benchmark our \gls{DRL} against an arrival-triggered mixed-integer linear programming solution and show that our method achieves good performance especially when the datasets are heterogeneous.

Reinforcement learning methods such as GRPO have seen great popularity in LLM post-training. In GRPO, models produce completions to a set of prompts, which are rewarded, and the policy is updated towards the relatively high reward completions. Due to the auto-regressive nature of models, the generation phase of such style of training can be extremely time consuming. As a solution, prior work has sought to distribute the inference step across many nodes, working parallel. These works assume primarily homogeneous models in the training in order to keep samples as close to on-policy as possible. This assumption may be impractical in decentralized systems, where parties with various computes and preferences may wish to collaborate on the same task. Thus, decentralized training requires an approach that can handle heterogeneous models - different models collaborating on the same tasks. However, this leads to highly off-policy samples presented during training, which prior work has identified that off-policy samples can hurt GRPO convergence. To enable heterogeneity, we propose Filtered Truncated Importance Sampling (F-TIS) - a GRPO-style training paradigm that can use off-policy samples to improve local model's learning. Our framework allows various models to collaborate in the same RL training run while being communication efficient. We extensively evaluate F-TIS in various heterogeneous setups and we show that it exhibits identical final model convergence to purely on-sample training. Furthermore, we observe in some setups better generalization on out-of-distribution tasks than on-policy training, increasing model's performance by up to 12%.

Ranking systems used in decision-support settings should not only order candidates but also expose evidence that can be independently checked. We study evidence-certified candidate ranking: given an intent_id, a predefined plan skeleton, a window-local candidate roster, and text-derived candidate trajectories with span provenance, a system must output a Top-K list together with doc_id:span evidence certificates whose cited spans are sufficient to recover the decision. We instantiate this task on MAVEN-ERE and RAMS with fixed upstream extraction, window-local randomized candidate identifiers, skeleton-aligned trajectory supervision, hard negatives, and audit references. We introduce Evidence-Coupled Policy Optimization (ECPO), a listwise policy-optimization objective whose action is the joint object of ranking and evidence certificate. ECPO first learns an interpretable trajectory reward from skeleton alignment, argument consistency, and optional graph features; it then optimizes a constrained policy with three coupled rewards: listwise ranking utility, span-level certificate validity, and an evidence-cycle reward computed by a label-free deterministic verifier that reconstructs candidate support from claim-stripped cited spans. This reframes the goal from maximizing ordinary NDCG alone to maximizing CertNDCG and decision-evidence coupling. The evaluation compares ECPO against zero-shot, SFT, and GRPO policies, RM-only scoring with deterministic evidence attachment, grammar/JSON-constrained decoding, validator retry, best-of-N RM selection, and post-hoc evidence rationalization under closed-roster, predicted-roster, and hybrid-roster settings.

Reinforcement learning with verifiable rewards has become the standard recipe for improving LLM reasoning, but the dominant algorithm GRPO assigns a single trajectory-level advantage to every token, diluting the signal at pivotal reasoning steps and injecting noise at uninformative ones. Critic-free alternatives derived from on-policy distillation supply per-token signals through oracle-conditioned likelihood ratios, yet apply each signal in isolation from the trajectory-level evidence accumulated up to that position. We propose Oracle-Prompted Policy Optimization (OPPO), which rests on a single observation: the oracle signal used by prior distillation-style methods for local discrimination is also the natural Bayesian update of the model's belief about eventual success. Accumulating the signal along a trajectory yields, in closed form and at the cost of one extra forward pass, a running estimate of the success probability at every position, together with a token-level advantage that requires no learned value network and no additional rollouts. A first-order analysis factorizes the advantage into the per-token discrimination signal used by distillation methods modulated by a state weight that concentrates credit on genuinely pivotal tokens, with a directional variance-reduction guarantee. The framework admits two estimators differing only in which model scores the evidence: a \textit{self-oracle} that reuses the student and recovers the on-policy distillation reward as a strict special case, and a \textit{teacher-oracle} that delegates scoring to a stronger frozen model. On two base LLMs across seven mathematics, science, and code reasoning benchmarks, OPPO improves over GRPO, DAPO, and SDPO by up to $+6.0$ points on AMC'23 and $+5.2$ points on AIME'24, with gains that widen monotonically with response length.

Post-training has become central to improving reasoning and alignment in large language models, where critic-free models enable scalable learning from model-generated outputs but lack principled mechanisms to distinguish informative from noisy signals. Recent approaches leverage response-level measures as uncertainty signals to regulate group-based optimization methods such as GRPO. Yet their empirical success remains unstable and unclear in how they influence optimization dynamics. In this paper, we provide, to our knowledge, the first principled formulation that interprets uncertainty signals as mechanisms for characterizing and regulating gradient variance and learning signal quality. Based on both empirical and theoretical analysis, we identify two critical gaps of current entropy-based estimators: The anisotropic gap and The calibration gap. Motivated by this analysis, we propose Geometric-aware Calibrated Policy Optimization (GCPO), a novel framework integrating geometry-aware measures to capture semantic disagreement with reward-based calibration to align uncertainty with learning signal strength. Experiments on multiple benchmarks show that our approach more faithfully tracks gradient variability and consistently improves post-training performance. Our results highlight the importance of designing uncertainty signals that are aligned with optimization dynamics, offering a principled perspective for robust post-training.

Reinforcement learning substantially improves pretrained language models, but it remains understudied why critic-free methods such as PPO and GRPO work as well as they do, and when they should provide the largest gains. We develop a value-gradient perspective of critic-free RL for LLM post-training. First, under a differentiable rollout and additive-noise parameterization, we show that the actor update is value-gradient-like in expectation: the backward pass propagates costates whose conditional expectation equals the value gradient. Second, for discrete transformer policies, we show that autodifferentiation through attention produces empirical costates that approximate this value signal, with an error controlled by the sampling gap and policy entropy. These results motivate a decomposition of RL impact into value gradient signal and reachable reward headroom, yielding a criterion for when RL should be most effective along a pretraining trajectory.

Reinforcement learning from verifiable rewards (RLVR) has emerged as a central technique for improving the reasoning capabilities of large language models. Despite its effectiveness, how response-level rewards translate into token-level probability changes remains poorly understood. We introduce a discriminator view of RLVR updates, showing that the policy-gradient update direction implicitly acts as a linear discriminator over token-gradient vectors and thereby determines which token probabilities are increased or decreased during learning. Under standard sequence-level RLVR, this discriminator is constructed from positive- and negative-side centroids formed by advantage-weighted averaging of token-gradient vectors. However, such centroid construction can be dominated by shared high-frequency patterns, such as formatting tokens, diluting sparse yet discriminative directions that better distinguish high-reward responses from low-reward ones. To address this limitation, we propose $\textbf{DelTA}$, a discriminative token credit assignment method that estimates token coefficients to amplify side-specific token-gradient directions and downweight shared or weakly discriminative ones. These coefficients reweight a self-normalized RLVR surrogate, making the effective side-wise centroids more contrastive and thereby reshaping the RLVR update direction. On seven mathematical benchmarks, DelTA outperforms the strongest same-scale baselines by 3.26 and 2.62 average points on Qwen3-8B-Base and Qwen3-14B-Base, respectively. Additional results on code generation, a different backbone, and out-of-domain evaluations further demonstrate the generalization ability of DelTA.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for reasoning in language models, with GRPO as its primary example. However, GRPO requires continuous online rollout generation, making it computationally expensive and difficult to scale. While Direct Preference Optimization (DPO) offers a stable and efficient offline alternative, it is typically expected to underperform w.r.t. online RL methods such as GRPO when trained on rollouts from a cold supervised fine-tuned (SFT) policy. We introduce G2D (GRPO to DPO)}, a three-stage pipeline that performs a short GRPO warm-up, constructs a static preference dataset, and fine-tunes a model offline with DPO. Across a set of values of the number of online steps (K) in GRPO on Qwen2.5-7B and Llama-3.1-8B, we find that offline DPO with moderate warm-up matches or outperforms GRPO at substantially lower compute cost in our setting. On Qwen2.5-7B, G2D at K=150 achieves 62.4% on MATH-500, outperforming GRPO (51.6%) by 10.8% at ~4x lower compute. On Llama-3.1-8B, G2D at K=500 achieves 49.4%, surpassing GRPO in our experimental setting. We show that performance is not governed by the number of preference pairs, which does not vary much w.r.t. K, but by their informativeness. Moderate warm-up produces rollouts with calibrated uncertainty, yielding stronger contrastive signal, while excessive warm-up leads to overconfident policies and less informative data. Our results recast the offline-online gap in RLVR as primarily a data informativeness problem, and identify short online RL warm-up with appropriate difficulty calibration of the fine-tuning dataset as a compute-efficient alternative to online RL.

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose \textbf{LamPO}, a \textbf{Lambda-Style Policy Optimization} method that replaces scalar group advantages with a \emph{Pairwise Decomposed Advantage}. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.

Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models (LLMs). However, GRPO is prone to advantage collapse, a failure mode where homogeneous rewards within a group (e.g., all correct or all incorrect answers) yield near-zero advantages and vanishing gradients. To address this, we introduce the Advantage Collapse Rate (ACR), the first diagnostic metric quantifying the proportion of training batches with ineffective gradients. Across models from 0.5B to 14B parameters on mathematical reasoning benchmarks, we show that ACR strongly predicts training stagnation and final performance. We then propose Adaptive Virtual Sample Policy Optimization (AVSPO), a lightweight extension of GRPO that injects virtual reward samples, guided by real-time ACR monitoring, to enable learning from homogeneous groups without additional model rollouts. AVSPO reduces advantage collapse by 58-63% relative to GRPO and yields consistent accuracy gains of 4-6 percentage points across all model scales, while maintaining generalization on the evaluated out-of-domain task. Code and datasets are available at https://github.com/hexixiang/Advantage-Collapse-Rate.

Most value-based and actor--critic reinforcement learning methods rely on Bellman-style recursions, yet these recursions collapse under non-exponential discounting common in human preferences and survival processes. We show the breakdown is structural: exponential discounting sits at a fragile intersection of multiplicativity and time homogeneity, and violating either property breaks standard dynamic programming. To overcome this, we propose Pontryagin-Guided Direct Policy Optimization (PG-DPO), a variational framework that abandons recursion and couples the Pontryagin Maximum Principle with Monte Carlo rollouts via an Adjoint-MC projection enforcing pointwise Hamiltonian maximization. Across multi-dimensional hyperbolic and survival-discount benchmarks, PG-DPO improves accuracy and stability where equation-driven solvers and critic-based baselines diverge.

Reinforcement learning with verifiable rewards (RLVR) plays a pivotal role in improving the reasoning ability of large language models. However, widely used PPO surrogate objectives are fundamentally local, as they rely on a local approximation of the exact policy gradient objective. While this approximation improves stability by reducing the variance induced by importance sampling, it also introduces structural bias into the surrogate objective, which must be controlled through trust region mechanisms. In this work, we introduce the $N$-step forward trace, which augments the PPO surrogate objective using the cumulative likelihood ratio of the next $N-1$ tokens. Building on this idea, we propose $N$-Step Forward-Trace Policy Optimization (NFPO), a practical RLVR algorithm that integrates the $N$-step forward trace into the masked policy gradient framework. NFPO provides a continuous bridge between the PPO surrogate objective and the exact policy gradient objective, offering a principled mechanism for controlling the bias-variance trade-off. Our theoretical analysis shows that, with an appropriate choice of $N$, the proposed objective yields a tighter policy-improvement bound than the standard PPO surrogate. Experiments on comprehensive reasoning benchmarks demonstrate that NFPO consistently improves performance, supporting our theoretical findings.

Reinforcement learning improves LLM reasoning, but PPO/GRPO typically use fixed clipping and decoding temperature, which makes training brittle and tuning-heavy. We propose Adaptive Group Policy Optimization (AGPO), a critic-free refinement of GRPO that uses group-level statistics to control both update magnitude and exploration. AGPO uses a shared probe-derived statistical state to drive two controllers: (i) adaptive clipping, which sets the trust-region size from reward dispersion and skewness, probe vote entropy, policy entropy, and step-wise KL drift; and (ii) bidirectional adaptive temperature sampling, which heats or cools decoding around a base temperature according to centered uncertainty relative to a running baseline. On nine English and Chinese math/STEM benchmarks, Qwen2.5-14B trained with AGPO outperforms PPO/GRPO under the same generated-token budget, reaching 67.3% on GSM8K and 40.5% on MATH. Gains transfer to Llama-3-8B and Gemma-2-9B, and ablations confirm both modules are complementary. Our implementation is publicly available at https://github.com/wandugu/paper_agpo.

Skill atrophy, the gradual decline of human capability under AI assistance, poses a safety risk in shared-control of semi-autonomous systems, where operators may be unable to distinguish their own inputs from autonomous corrections. We propose Proximal State Nudging (PSN), a shared autonomy algorithm that jointly optimizes for skill development and task performance by nudging users toward states estimated to be most learnable. We first show that PSN outperforms existing shared autonomy baselines in balancing student improvement in unassisted reward with overall shared performance, using simulated students in the classic LunarLander environment. We then present, to the best of our knowledge, the first human subject studies of a planner incorporating learning-compatible shared autonomy: across two driving tasks in the CARLA simulator (High Performance Racing and Parallel Parking, n = 60), PSN produces up to 7x larger gains in unassisted skill than standard blended shared autonomy, while incurring 50% fewer collisions than unassisted self-practice.

Training large multimodal models (LMMs) via reinforcement learning (RL) to natively invoke video-processing tools (e.g., cropping) has become a promising route to long-video understanding. However, existing native-RL methods dispatch tool calls sequentially (i.e., one per turn): a single wrong crop propagates errors without peer correction, multi-turn tool calls corrupt context, and inference cost scales linearly with the number of turns. We introduce ParaVT, the first multi-agent end-to-end RL-trained framework for Parallel Video Tool calling, dispatching multiple time-window crops in a single turn for cleaner context and better fault tolerance. Yet applying standard RL to ParaVT reveals an obstacle we term the Tool Prior Paradox: the pretrained tool priors that enable tool exploration also destabilize cold-started structural format and expose the skip-tool reward shortcut under temperature sampling. A cross-model contrast on a weaker-prior LMM supports this claim: format stays stable but RL elicits zero tool calls, indicating that prior strength is the shared driver of both format collapse and tool exploration. We propose PARA-GRPO (Parseability-Anchored and Ratio-gAted GRPO), which augments standard RL with two complementary mechanisms: (i) a targeted format reward applied only at the structural-token positions most prone to collapse, and (ii) a per-prompt frame-budget randomization that creates training prompts where calling the tool yields a measurable reward signal over skipping it. Across six long-video understanding benchmarks, ParaVT improves over the Qwen3-VL baseline by +7.9% on average, with PARA-GRPO lifting training-time format compliance from 0.13 to 0.64. As tool capabilities become increasingly internalized in modern LMMs, RL must cooperate with the resulting priors, and ParaVT offers a general recipe for agentic RL. Code, data, and model weights are publicly available.

Reinforcement learning with verifiable rewards has made post-training highly effective when correctness can be checked automatically. However, many important model behaviors require satisfying several qualitative criteria at once. Rubric-based rewards address this setting by grading prompt-specific criteria and aggregating them into a scalar reward. Yet standard static aggregations conflate a criterion's human-assigned importance with its current usefulness as an optimization signal. We show that this assumption breaks down in rubric RL: many important criteria are already saturated or currently unreachable, while criteria that distinguish rollouts are not necessarily those with the largest human weights. We introduce POW3R, a policy-aware rubric reward framework that preserves human weights and category balance as the rubric objective while adapting criterion-level reward weights during training. POW3R uses rollout-level contrast to emphasize criteria that currently separate the policy's outputs, making the GRPO reward more informative without changing the underlying evaluation target. Across three base policies on two datasets spanning multimodal and text-only settings, POW3R wins $24$ of $30$ base-policy/metric comparisons, improving both mean rubric reward and strict completion (the fraction of prompts whose response satisfies every required rubric criterion) over vanilla GRPO with rubric rewards, and reaches the same plateau in $2.5$--$4\times$ fewer training steps. Rubric rewards should therefore distinguish what should matter in the final answer from what can teach the current policy.

Vision-Language-Action (VLA) models show promising ability in language-guided robotic tasks. However, making VLA policies reliable remains challenging, because a manipulation task is completed through closed-loop interaction, where each action affects subsequent execution. To analyze this problem, we revisit VLA policy during execution and argue that a VLA policy acts both as a planner, which makes task-oriented decisions that change the direction of execution, and as an executor, which realizes these decisions through dense continuous actions. This view suggests that improving VLA reliability requires particular attention to planning actions. Existing optimization methods can imitate actions or improve complete trajectories, but they usually do not explicitly identify planning actions or measure their importance for task success. To address this issue, we propose Planning-Aware Policy Optimization for VLA models (PAPO-VLA). PAPO-VLA first identifies planning actions by jointly considering action variation and trajectory outcome, then estimates their importance through causal sufficiency and causal necessity, and finally incorporates this importance into GRPO advantage estimation. In this way, more important planning actions receive stronger optimization emphasis, while the whole trajectory is still optimized by trajectory-level feedback. Experiments on multiple benchmarks demonstrate the effectiveness of PAPO-VLA.

Group Relative Policy Optimization(GRPO) has become a cornerstone of modern reinforcement learning alignment, prized for its efficacy in foregoing an explicit value-critic by leveraging reward normalization across sampled trajectory cohorts. However, the method's reliance on a monolithic statistical baseline, such as the group mean, collapses the relational topology of the trajectory space into a single scalar, thereby erasing the fine-grained preference information essential for navigating complex, rank-sensitive reward landscapes. To address this issue, we introduce a novel framework, Lambda Policy Optimization (LambdaPO), that addresses this information-theoretic bottleneck by re-conceptualizing advantage estimation from a scalar value to a decomposed, pairwise preference structure. Specifically, the advantage for any given trajectory is formulated as the integrated sum of reward differentials against all peers in its cohort, where each pairwise comparison is dynamically attenuated by the policy's own probabilistic confidence in the established preference. To further mitigate the sparsity of binary outcome supervision, we augment the objective with a semantic density reward, derived from the precision-recall alignment between generated reasoning traces and ground-truth solutions. As a result, our method can mine more fine-grained optimization signals from a group of rollouts, guiding the LLM to a better optima. Experimental results across challenging math reasoning and question-answering tasks demonstrates that LambdaPO improves performance compared to the baseline methods.

Medical vision-language models (VLMs) have rapidly advanced as general-purpose multimodal assistants, yet their deployment in 3D Computed Tomography (CT) analysis remains constrained by a persistent mismatch between optimization objectives and clinical rigor. Current Reinforcement Learning (RL) paradigms still rely on lexical proxy signals that induce \textit{Evaluation Hallucinations}'', where models optimize linguistic fluency rather than factual clinical correctness, leading to diagnostically critical errors. To bridge this gap, we introduce the \textbf{Clinical Abnormality Benchmarking Substrate (CABS)}, a structured system that decomposes radiology reports into verifiable clinical semantic units. Using CABS, we identify a \textit{Mechanistic Divergence}'' in standard RL, where surface-similarity rewards drive policy gradients to bypass medical facts. We therefore propose \textbf{Trajectory-Integral Feedback GRPO (TIF-GRPO)}, a novel framework integrating control-theoretic principles into policy optimization. By formulating clinical reasoning as a pseudo-temporal trajectory for anomaly discovery, TIF-GRPO regulates anatomy-aware rewards via an integral feedback loop that penalizes persistent omissions as cumulative state errors and suppresses hallucinations as excessive control effort. Experiments on 3D CT benchmarks demonstrate that our approach significantly enhances abnormality detection and clinical faithfulness, establishing a new paradigm for fine-grained regulation in medical VLMs. Our project is available at \href{https://github.com/ZJU4HealthCare/TIF-GRPO}{GitHub}.

Competitive multi-agent reinforcement learning in imperfect-information games requires agents to act under partial observability and against adversarial opponents, necessitating stochastic policies. While self-play reinforcement learning with Proximal Policy Optimization (PPO) has achieved strong empirical success, its standard advantage estimator, generalized advantage estimation, suffers from additional variance due to the sampling of stochastic future actions. This variance is amplified in equilibrium self-play because of the stochastic nature of the equilibrium policy and persists even when the critic is exact. We address this bottleneck by introducing $Q$-boosting, a variance-reduced advantage estimator based on a centralized action-value critic, and propose Variance-Reduced Policy Optimization (VRPO), incorporating this new estimator. The algorithm replaces sampled multi-step backups with a multi-step Expected SARSA$(λ)$ trace, computing policy expectations at each step to average out action-sampling noise, while retaining PPO's clipped objective and on-policy actor updates. Empirically, VRPO consistently achieves strong performance from mid-sized to large-scale games including Dou Dizhu and Heads-Up No-Limit Texas Hold'em.

Natural policy gradients improve optimization by accounting for the geometry of distribution space, but their practical use is limited by the cost of estimating and inverting the Fisher matrix. We present Randomized Advantage Transformation (RAT), a method for estimating Tikhonov-regularized natural policy gradients via direct backpropagation. By applying the Woodbury formula, we reformulate the regularized natural policy gradients as vanilla policy gradients with a transformed advantage. RAT computes this transformation efficiently via randomized block Kaczmarz iterations on on-policy mini-batches, avoiding explicit Fisher construction, conjugate-gradient solvers, and architecture-specific approximations. We provide convergence guarantees for RAT and demonstrate empirically that it matches or exceeds established natural-gradient methods across continuous and visual control benchmarks, while remaining simple to implement and compatible with various architectures.

Large language models (LLMs) have increasingly leveraged tool invocation to enhance their reasoning capabilities. However, existing approaches typically tightly couple tool invocation with immediate execution. Such immediate tool interaction may disrupt the reasoning coherence of LLMs and constrain their expressivity, ultimately degrading reasoning performance. To this end, for the first time, we propose and formalize the problem of decoupling tool invocation from execution during reasoning, and introduce delayed execution with explicit control to enhance tool-integrated reasoning (TIR). Furthermore, we propose a hierarchical control framework and theoretically derive a surrogate loss that enables an implicitly hierarchical policy to learn behavior equivalent to that of an explicit hierarchical policy, leading to the proposed IH-GRPO algorithm. Extensive experiments on IH-GRPO achieve absolute improvements of 1.87%, 2.16%, and 2.53% on Qwen3-1.7B, Qwen3-4B, and Qwen3-8B across six out-of-domain mathematical reasoning benchmarks over the strongest baseline method, while also yielding consistent performance gains in other domains. Our code is available at https://github.com/Lumina04/IH-GRPO-01.

Video generation models produce visually compelling results but systematically violate physical commonsense -- on VideoPhy-2, the best model achieves only 32.6% joint accuracy. We identify a specification bottleneck: text prompts are lossy compression of the physical world, omitting the parameters that fully determine dynamics, and no amount of model scaling can recover what was never specified. From this diagnosis we derive three properties that physics conditioning must satisfy -- sufficiency, dynamism, and verifiability -- and show that no existing approach satisfies all three. We present NEWTON, in which video generation is demoted from the system output to one action inside an agent's toolbox: a learned planner orchestrates physics-aware tools (keyframe generation, scientific computation, prompt refinement) to construct rich conditioning, and a verifier closes the loop for iterative re-planning. The planner is the sole trainable component, optimized on-policy via Flow-GRPO inside the live multi-turn loop. On VideoPhy-2, NEWTON improves joint accuracy from 21.4% to 29.7% on LTX-Video and from 30.7% to 37.4% on Veo-3.1, without modifying either generator. Our project page: https://Newton026.github.io/newton

Reinforcement learning has become a cornerstone for aligning and unlocking the reasoning capabilities of large-scale models. At its core, the training loop of GRPO and its variants alternates between rollout sampling and policy update: the policy first samples rollouts from its action space, and then updates its parameters according to the advantages computed over them. Unlike supervised learning, where each gradient step is anchored to an explicit ground-truth target, the optimal gradient direction for updating model parameters in this setting is not known a priori; the high-quality rollouts drawn during the sampling stage therefore act as the implicit "teacher" that guides every parameter update. However, mainstream RL algorithms such as GRPO adopt a simple sampling scheme that conditions all rollouts on the same original prompt. When a task lies beyond the policy model's current capability, this sampling scheme rarely yields a high-quality rollout, leaving the policy model without a meaningful gradient direction when updating its parameters, which causes training to stall. To address this issue, we propose FBOS-RL. Specifically, we let the model perform Feedback-Guided Exploration Enhancement based on the feedback provided by the environment, and on top of this we design two mutually reinforcing training objectives: EPA and ECC. Extensive experiments demonstrate that EPA and ECC can mutually reinforce each other, forming a positive flywheel effect that significantly improves both the training efficiency and the final performance ceiling of reinforcement learning. Specifically, under both an identical number of rollouts and the same number of training steps, FBOS-RL learns substantially faster than GRPO and feedback-based baselines and ultimately attains a higher performance ceiling, while exhibiting higher policy entropy and lower gradient norms throughout training.

In social dilemmas self-interested learning agents face the choice between the societal benefit of cooperation and the immediate reward of defection. Significant evidence exists on the benefits of assortment mechanisms such as partner selection for the emergence of cooperation, but this is largely available through agent-based simulations. In this paper, we provide an analytical solution to the problem, studying the policy-gradient dynamics in a multi-agent environment with partner selection. We show how partner selection changes the opponent distribution and hence the reward landscape, and prove this promotes cooperation under simple rules known from the literature. In particular, we find that population variance is a necessary condition for cooperation to emerge. Using a two-dimensional Wiener process, we extend the dynamics to capture the stochastic effects of partner selection and the resulting opponent distribution. We derive a sufficient condition for the population to be cooperation-promoting and prove the existence of a stationary distribution. Simulations confirm that the stochastic model accurately captures the policy-gradient dynamics and clarifies how the learning rate affects the emergence of cooperation.

Multi-agent policy-gradient methods have been shown to converge locally near stable Nash equilibria. Local convergence, however, does not determine which equilibrium is reached. We study this question through basin-entry probability with respect to a target set of equilibria selected by an external criterion, such as payoff dominance. For finite-unroll Meta-MAPG, we show that the update decomposes into ordinary policy gradient plus own-learning and peer-learning corrections, with controlled sampling noise and finite-unroll bias. We identify the peer-learning correction as the main equilibrium-selection mechanism: under a local alignment condition, the probability of entering the certified attraction region of the target stable-Nash set increases, relative to ordinary policy gradient. Because persistent correction may shift zero-update points of the original game, annealing the correction after entering the basin recovers ordinary policy-gradient dynamics and inherits local stable-Nash convergence guarantees. Experiments in Stag Hunt, iterated Prisoner's Dilemma, and preliminary neural-policy coordination environments support this basin-entry view, showing increased entry into cooperative basins under peer-aware updates.

This paper proposes a Shared Backbone Proximal Policy Optimization (Shared Backbone PPO) algorithm. By sharing the base module between the Actor and Critic networks, the algorithm achieves efficient training and improved performance. The algorithm is implemented in a connectivity-preserving multi-UAV swarm communication coverage task and compared with the standard PPO algorithm. Experimental results demonstrate that the proposed method achieves superior performance. Furthermore, a graph information aggregation module is incorporated into the model architecture to accommodate the communication conditions among agents. With the integration of this module, the algorithm remains effective, and the trained agent swarm exhibits a higher level of cooperation.

A significant hurdle for current LLMs is the execution of complex, multi-stage tasks. Group Relative Policy Optimization (GRPO) has been emerging as a leading choice, but its reliance on sparse outcome rewards severely limits credit assignment across intermediate steps. Existing remedies such as running full rollouts to assign step-level advantages, calling external LLM judges at each step, or computing intrinsic rewards that require ground-truth answers at every evaluation introduce significant costs or practical constraints. We hypothesize that internal correctness probing over LLM hidden states can be repurposed as a step-level reward signal, potentially addressing all of these limitations at once. However, existing probing research assumes clean inputs, and we first show that this assumption breaks down in multi-step settings: hidden-state probes degrade severely under prefix contamination tracking coherence with the (possibly corrupted) prefix rather than grounded correctness, while attention-based features remain robust to contamination but underperform on clean prefixes. Building on this complementary relationship, we propose the Prefix-Aware Internal Reward (PAIR), a two-stage model with a frozen hidden-state probe estimating belief-consistency and a lightweight attention-based head correcting it toward grounded correctness. Experimental results show that PAIR achieves the highest AUROC on contaminated trajectories while operating at negligible inference cost, enabling dense step-level reward signals for GRPO training without external model calls, ground-truth dependencies, or full-trajectory rollouts.

Recently, vision-language model (VLM) agents have shown promising progress in open-world tasks, where successful task completion often requires multiple turns of visual perception and action execution. However, existing methods still rely primarily on Supervised Fine-Tuning (SFT) with expert demonstrations, while the advanced reinforcement learning (RL) algorithm, specifically Group Relative Policy Optimization (GRPO), has not been effectively employed for multi-turn RL in these tasks because standard GRPO requires full trajectories as training samples which leads to excessively long context and noise. To address this issue, we propose GROW, a RL framework for open-world VLM agents that decomposes collected trajectories into state-action samples, and computes advantages between these samples rather than treating a full trajectory as a single entity. We further provide a surrogate analysis indicating that, even though the grouped samples are conditioned on different local states rather than an identical prompt context, the objective can preserve the core relative policy optimization signal of GRPO under simplifying assumptions. Experiments on more than 800 Minecraft tasks show that our method achieves state-of-the-art (SOTA) performance, demonstrating the effectiveness of our proposed RL framework for open-world VLM agents.

Text-to-Image (T2I) generation has achieved remarkable progress in recent years. Meanwhile, reinforcement learning methods, particularly those based on Group Relative Policy Optimization (GRPO), have attracted widespread attention and been successfully applied to T2I tasks. However, the uniform sampling strategy commonly used during training often ignores the match between sample difficulty and the model's current learning capability, leading to low training efficiency. We argue that improving training efficiency requires continuously prioritizing prompts that match the model's evolving capability and remain actively learnable. To this end, we propose Curriculum Group Policy Optimization (CGPO), an adaptive curriculum training framework. During training, each prompt produces a group of images scored by a reward model. We use the variance of group rewards as an online proxy for prompt inconsistency. A higher variance suggests that the model has partially captured the prompt requirements but has not yet achieved stable mastery. Such prompts are more likely to provide useful learning signals, so we increase their sampling probabilities accordingly. Additionally, to address data imbalance in multi-category datasets, we design a category calibration method based on proportional fairness optimization, which balances training difficulty across categories. Experiments on GenEval, T2I-CompBench++, and DPG Bench demonstrate that our framework effectively improves generation performance.

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

GRPO-style RLVR trains reasoning models from multiple on-policy attempts per prompt, but typically uses these attempts only through terminal rewards. We show that a mixed group contains a richer process signal: a correct completion is a self-generated witness of how the current policy can solve the problem, while a wrong completion provides on-policy prefixes where the policy needs correction. We introduce \emph{Self-Supervised On-Policy Distillation} (SSOPD), which distills a teacher distribution conditioned on the shortest correct completion into prefixes of the longest wrong completion. This converts intra-group correct--wrong contrast into dense process supervision without external solution traces. A stopping-time view motivates the shortest-correct / longest-wrong rule as a finite-group approximation to editing persistent failures toward fast-success actions, and a prompt-level frontier weight concentrates the auxiliary loss where correct and wrong branches coexist. Across AIME 2024, AIME 2025, and HMMT 2025, SSOPD improves over GRPO in all nine model-benchmark settings. On Qwen3-8B, it reaches a macro Avg@12 of 65.6, outperforming GRPO by 1.6 points and the solution-conditioned OPSD baseline by 0.8 points. Code will be released at https://github.com/tzq1999/SSOPD.

Matrix reordering in large sparse solvers seeks a permutation that minimizes factorization fill-in to reduce memory and computation. Because the minimum fill-in ordering problem is NP-complete and fill-in is implicit in the sparsity pattern, graph-theoretic heuristics are used. Existing reinforcement learning methods either ignore sparsity patterns--missing the global fill-in--or lack local exact fill-in feedback. We propose a graph policy optimization method, modeling fill-ins from global and local views: both the policy and value networks use a multi-hop graph neural backbone to embed global fill-in; the policy further interacts with symbolic factorization over graphs to extract local, step-level fill-ins, and the resulting feedback is aligned with the value network via an adaptive saturation function to improve convergence. On the SuiteSparse Matrix Collection, our method achieves mean reductions of 29.3 in fill-ins and 31.3 in peak memory usage over state-of-the-art baselines.

Reinforcement Learning from Verifiable Rewards (RLVR) typically samples multiple responses per prompt and assigns binary rewards based on individual correctness, yet the collective structure of the group output, specifically the distribution of errors, is largely discarded. We identify this as a missed opportunity: empirical analysis reveals that error diversity within a group is a strong predictor of training success, with problems eliciting diverse wrong answers benefiting substantially more from RLVR than those producing homogeneous failures. Motivated by this observation, we propose Error Diversity Advantage Shaping (EDAS), a lightweight, algorithm-agnostic technique that modulates the advantage signal for incorrect rollouts based on intra-group error diversity. EDAS amplifies penalties for dominant, repeated errors and attenuates penalties for rare, exploratory ones, thereby encouraging the model to maintain diverse reasoning paths and discouraging error perseveration. Crucially, EDAS operates as a simple post-hoc adjustment that can be seamlessly integrated into any RLVR algorithm. We validate EDAS on top of several mainstream RLVR methods across a series of models and seven challenging math benchmarks, demonstrating consistent improvements. Notably, EDAS yields an average improvement of 6.29 points over DAPO on Qwen3-8B across seven benchmarks, confirming that exploiting the latent information in group rollouts is a broadly effective strategy for strengthening RLVR.

Modern reasoning agents are increasingly evaluated on their ability to generate multiple valid solution paths, plans, or tool-use traces for a given input. Standard reward-maximizing RL tends to collapse onto the most easily reinforced high-reward mode, whereas distribution-matching RL aims to allocate probability mass across the entire reward-shaped solution set. Achieving this objective requires computing a prompt-dependent partition function over the trajectory space. Because existing distribution-matching methods learn this partition function online alongside the policy, calibration errors in the partition function directly distort policy updates and remain impossible to diagnose independently. We introduce DISA, short for Decoupled Importance-Sampled Anchoring, which moves this calibration problem outside the RL loop. DISA draws proposal trajectories offline, estimates the partition function via importance sampling, and freezes the resulting partition-function estimate before policy optimization begins. This decoupling preserves the distribution-matching objective while strictly separating partition-function estimation from policy learning in data, gradients, loss, and diagnostics. Empirically, on two open-weight backbones across six math and three code benchmarks, DISA matches or exceeds the online-coupled distribution-matching baseline FlowRL, outperforms rewardmaximization baselines GRPO and GSPO on math averages, and exceeds LoRASFT distillation by up to 13.8 Mean@8 points on the same offline trajectories. An LLM-as-judge evaluation further shows that DISA retains substantially more strategy-level diversity than reward-maximization baselines, and sensitivity studies on the proposal strength and inverse temperature follow the bias-variance pattern predicted by the analysis.

Bi-causal optimal transport (OT) is a natural framework for comparing and coupling stochastic processes under nonanticipative information constraints, with important applications in robust finance, sequential uncertainty quantification, and multistage stochastic optimization. In particular, a learned bi-causal coupling naturally serves as a simulator for generating joint sample paths that respect both prescribed marginal laws and the underlying information flow. Its practical use, however, is limited by the computational difficulty of enforcing bi-causal coupling constraints over path space, especially for continuous distributions and long horizons. We develop a scalable stochastic-optimization framework for computing bi-causal OT couplings under general marginals. Our approach introduces a Kullback--Leibler (KL)-penalized relaxation that replaces hard marginal constraints with tractable divergence penalties while preserving the recursive structure of the problem. We establish dynamic programming principles for both the original and relaxed formulations, prove that the relaxed problem converges to the original bi-causal OT problem as the penalty grows, and derive explicit policy-gradient representations for the relaxed objective. Building on these results, we propose a practical policy-gradient algorithm with unbiased mini-batch estimators, variance reduction, and nonasymptotic regret guarantees. Numerical experiments show that the method accurately captures marginal laws and temporal dependence, and performs well in applications including robust subhedging and time series statistical downscaling. These results provide a scalable computational approach to bi-causal OT and broaden its applicability in settings where nonanticipative information constraints are essential.

Unified multimodal models can encode visual understanding and image generation within a shared backbone, yet understanding does not automatically translate into control: models may infer objects, relations, or knowledge cues but fail to instantiate them in the generated image. We propose Latent Action Control (LAC), which makes reasoning actionable by representing it as hidden continuous actions inside a unified generator. Given a prompt, LAC rolls out a role-structured latent trajectory for planning, internal visual drafting, diagnosis, and refinement, and injects these actions into the hidden stream that conditions flow-based generation, without producing reasoning tokens or intermediate images. Since such action trajectories are unobserved, LAC learns them through prior-guided variational latent action alignment from training-only rendered semantic priors, draft image features, and supervised halting signals, followed by Latent-Flow GRPO to align the latent-to-image rollout with terminal visual feedback. This provides a control path from inferred relations, bindings, and knowledge cues to the generation process. Instantiated on BAGEL-7B-MoT, LAC consistently improves compositional and knowledge-grounded generation across GenEval, WISE, and T2I-CompBench, with the largest gains on spatial relations, attribute binding, and world-knowledge-sensitive prompts. Ablations and latent interventions show that the learned action trajectory is consumed by the generator, suggesting that unified generation benefits when understanding is not only encoded, but made actionable during generation.

Trajectory-controlled video generation has become essential for controllable video generation. While current methods perform well under small-view camera motions, they degrade significantly with large-view motions. Existing solutions for extreme-view synthesis typically require dedicated video pairs, demanding substantial annotation effort. To address these limitations, we propose Dynamic Extreme VIew Synthesis-GRPO (DEVIS-GRPO), a GRPO-based framework for trajectory-controlled video generation, the first online policy gradient method for extreme view video generation. Central to our approach is a novel sampling strategy: Accumulative Dynamic Extreme VIew Synthesis (ADEVIS), which achieves large-view camera motions by progressively accumulating small-view increments. This method delivers two key advantages: 1) enhanced training efficiency, as it eliminates the need to warm-start the policy model by collecting expensive paired large-view videos, and 2) increased sampling diversity, achieved by flexibly varying trajectory configurations. Finally, we designed a multi-level consistency-quality reward function to select high-quality samples for model optimization. Experiments on the Kubric-4D, iPhone, and DL3DV datasets demonstrate our method's superiority. On Kubric-4D, we achieve relative improvements of 21.57% in PSNR and 7.31% in SSIM over the second-best method in non-occlusion areas. On iPhone, LPIPS is reduced by 18.56%.

Diffusion Multi-Modal Large Language Models (dMLLMs) are powerful for image generation, but optimizing them through reinforcement learning (RL) remains a major challenge. One primary difficulty is that a single image can be generated through many different unmasking sequences, which makes calculating importance ratios often intractable. Additionally, existing methods tend to ignore the hierarchical generation process of dMLLMs, where early tokens define the global layout and later tokens focus on local details. By assigning uniform rewards to all tokens, these current methods fail to reflect the actual contribution of each token to the final image. To address these issues, we propose Hierarchical Token GRPO (HT-GRPO), which integrates this hierarchy directly into the policy optimization process. Our approach features a Sketch-Then-Paint training scheme that organizes updates into three distinct stages: global, structure, and refinement. We also use a prompt-conditioned estimator to calculate importance ratios starting from a fully masked state. Furthermore, we introduce a Hierarchical Credit Assignment mechanism that prioritizes key structural tokens to ensure accurate reward propagation. Experiments using two popular dMLLM backbones, MMaDA and Lumina-DiMOO, demonstrate that HT-GRPO achieves substantial gains on the GenEval and DPG benchmarks. Evaluations across six additional metrics confirm significant improvements in image quality, aesthetics, and human preference.

Reinforcement learning (RL) allows vision-language-action (VLA) policies to generalize beyond their training distribution by optimizing directly for task success, but post-training is computationally expensive. A natural response has been to speed rollout collection through faster simulators and world models. In GRPO-based VLA RL, we find that the dominant cost lies elsewhere: gradient computation accounts for approximately 78% of wall-clock time per step in our runs, while rollout collection accounts for only 21%. Gradient cost dominates because much of this computation is spent on phases that contribute little to learning. GRPO's learning signal is driven by advantage variance: only phases where successful and failed rollouts diverge produce learning signal. However, GRPO assigns the same advantage to every chunk in a rollout. As a result, actor-update compute is spent uniformly across the trajectory, including phases the policy already handles after pre-training and supervised fine-tuning. This paper presents Probabilistic Chunk Masking (PCM), a drop-in modification to GRPO that allocates gradient computation to a small, probabilistically selected subset of chunks per trajectory. PCM scores semantic phases using success-failure action variance, a rollout-derived proxy for per-phase gradient variance, and samples a fixed chunk budget with online-updated phase-level keep probabilities. We formalize per-phase gradient variance as the quantity determines where gradient computation is useful and show that success-failure action variance provides a measurable proxy for it. PCM requires no reward model or learned critic. On three LIBERO benchmarks, PCM matches the final success rate of standard GRPO while achieving 2.38 times wall-clock speedup, 4.8 times faster gradient updates, and 60% lower peak activation memory, while backpropagating through fewer than 20% of trajectory chunks.

Group Relative Policy Optimization has emerged as essential for aligning video diffusion models with human preferences, but faces a critical computational bottleneck: training a 14B parametered model typically demands hundreds of GPU days per experiment. Existing efficiency methods reduce costs through sliding window subsampling training timesteps, but fundamentally compromise optimization, exhibiting severe instability and failing to reach full trajectory performance. We present Flash-GRPO, a single-step training framework that outperforms full trajectory training in alignment quality under low computational budgets while substantially improving training efficiency. Flash-GRPO addresses two critical challenges: iso-temporal grouping eliminates timestep-confounded variance by enforcing prompt-wise temporal consistency, decoupling policy performance from timestep difficulty; temporal gradient rectification neutralizes the time-dependent scaling factor that causes vastly inconsistent gradient magnitudes across timesteps. Experiments on 1.3B to 14B parameter models validate Flash-GRPO's effectiveness, demonstrating substantial training acceleration with consistent stability and state-of-the-art alignment quality.

While reinforcement learning (RL) enables robots to acquire skills autonomously, its real-world deployment is severely limited by inefficient and unsafe exploration. Human-in-the-loop interventions offer a practical solution, yet existing methods typically exploit these interventions as auxiliary training signals, without fully capturing the richer information they provide about when and how autonomy should be guided. Human interventions often encode relative preferences over behavior under safety and task constraints, rather than prescribing exact actions to imitate. Motivated by this perspective, we propose Online Human Preference as Guidance in Reinforcement Learning (OHP-RL), a framework that leverages human interventions as preference information to guide policy learning. OHP-RL introduces a state-dependent preference gate that adaptively regulates when and to what extent human interventions should shape policy learning. This design enables the agent to benefit from intermittent and imperfect human feedback while preserving autonomous exploration and stable policy optimization. We evaluate OHP-RL on three challenging real-world contact-rich manipulation tasks on a Franka robot. Across all tasks, OHP-RL consistently achieves strong success rates, faster convergence, and substantially lower human intervention effort than prior approaches. Moreover, the learned policies exhibit more stable and human-aligned behavior throughout training.

Recent advancements have established Reinforcement Learning (RL) as a pivotal paradigm for aligning generative models with human intent. However, group-based optimization frameworks (e.g., GRPO) face a critical limitation: the rapid decay of intra-group variance. As the distinctiveness among samples within a group diminishes, the variance approaches zero. This eliminates the very learning signal required for optimization, rendering the process unstable and forcing the policy into premature stagnation or reward hacking. Existing strategies, such as varying the initial noise or increasing group sizes, often fail to address this fundamental issue, resulting in training instability or diminishing returns. To overcome these challenges, we propose $\textbf{Embedding-perturbed Exploration Preference Optimization (}E^2\textbf{PO)}$, a novel framework that sustains optimization through embedding-level perturbation. Our method introduces structured, embedding-level perturbations within sample groups, guaranteeing a robust variance that preserves the discriminative signal throughout the training process. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art baselines, achieving a more faithful alignment with human preference.

Influence functions approximate how removing a training example changes a quantity of interest, called the target function, such as a held-out loss. To estimate the influence of a group of examples, the standard practice is to sum the individual influences of its members. However, this sum does not capture how examples jointly affect the target: a pair of examples may be redundant or complementary, but the sum cannot distinguish these cases. We propose an interaction-aware influence function that characterizes how interactions between examples influence the target. By expanding the target to second order around the trained parameters, we obtain an estimator that augments the standard sum with a pairwise interaction term that captures the alignment between two examples' effects on the target. We empirically evaluate our estimator in two settings. First, on six dataset-model pairs spanning logistic regression, MLPs, and ResNet-9, our estimator tracks leave-group-out retraining substantially better than first-order influence across all settings. Second, when used as a greedy selection rule for instruction-tuning data on Llama-3.1-8B, it beats prior influence-based and representation-similarity baselines on five of seven downstream tasks, in a regime where standard influence-based selection underperforms random selection.

Modern language models often need to optimize a primary accuracy objective while also accommodating secondary behavioral preferences, such as verbosity, agreeableness, or the level of technical expertise in its response. In practice, a base model may exhibit a desired behavior very rarely or not at all. Thus, endowing the model with a target behavior creates a sparse behavioral reward bottleneck. To address such multi-objective problems, we introduce Vector-Steered Policy Optimization (VSPO) which employs a steering vector associated with the target behavior to control the behavior intensity of the generated rollouts. VSPO is obtained by modifying GRPO to sample rollouts with varying steering intensities. This process can be interpreted as an on-policy latent self-distillation procedure where the model internalizes its steering vector. By varying steering intensities, VSPO upsamples rare behaviors and enriches rollout diversity, which alleviates the sparse reward issue and provably accelerates the policy optimization. Through comprehensive theory and experiments, we establish that VSPO has favorable properties compared to vanilla reward shaping and other alternative approaches. Specifically, under a bandit abstraction, VSPO provably achieves better iteration complexity than reward-shaped GRPO when the steering-induced distributions are sufficiently aligned with the target behavior. We evaluate VSPO across multiple reasoning benchmarks, including MATH and MMLU-Pro, for four target behaviors: explanation expertise, confidence expression, robustness to misleading context, and response verbosity. Our results show that VSPO consistently improves the control along target behavior while maintaining or improving task accuracy compared with reward shaping, teacher-trace distillation, and guidance-based baselines.

Modern quantitative trading increasingly relies on systematic models to extract predictive signals from large-scale financial data, where alpha factor discovery plays a central role in transforming market observations into tradable signals. Recent LLM-based methods have shown promise in automating factor generation, but most of them still rely on prompt-level generation--evaluation--feedback loops for iterative optimization. As the loop becomes longer, repeatedly appended historical candidates and feedback can cause context explosion, increase inference cost, dilute useful information, and introduce feedback drift. Moreover, these methods often depend on very large LLMs whose stable generation preferences may lead to structurally similar expressions, redundant candidates, and search stagnation. To address these limitations, we propose \textsc{QuantEvolver}, a self-evolving alpha factor discovery framework based on reinforcement fine-tuning. Instead of accumulating feedback in the prompt, \textsc{QuantEvolver} converts executable quantitative evaluation into policy updates, enabling a Miner LLM to internalize historical optimization experience through parameter learning. Specifically, \textsc{QuantEvolver} constructs high-quality seed factors, builds diverse seed--time-window training tasks, generates executable Factor DSL expressions, evaluates them through Regime Backtest, and optimizes the Miner LLM with Diversity-Complementarity Reward. During training, high-quality factors are continuously accumulated in a Mined Factor Database, which serves as the final discovered factor library. Extensive experiments on three realistic market benchmarks demonstrate the effectiveness of \textsc{QuantEvolver}, which consistently improves the primary evaluation metric of each task over existing LLM-based alpha factor discovery baselines, produces higher-quality and more complementary factor pools.