Group Relative Policy Optimization

Agentic reinforcement learning (RL) for software engineering spends much of its compute on stateful trajectories whose grouped binary rewards are highly skewed and weakly contrastive. We frame this as pass-rate control and show that the binary reward-side signal is strongest near a 50% rollout pass rate under four criteria: reward entropy, group-filtering survival, leave-one-out (RLOO) advantage energy under Group Relative Policy Optimization (GRPO), and success-failure pair count. We propose Prefix Sampling (PS), which replays self-generated trajectory prefixes to steer skewed groups toward this regime: successful prefixes give mostly failing groups a head start, while failing prefixes handicap mostly passing groups. Replayed states are reconstructed through the existing rollout path, and replayed tokens are masked from the loss so optimization applies only to current-policy continuations. On SWE-bench Verified, PS reaches the baseline high-score regime within evaluation variability while delivering 2.01x and 1.55x end-to-end wall-clock speedups on Qwen3-14B and Qwen3-32B; the 14B peak improves from 0.274 to 0.295. AIME 2025 experiments on 4B and 8B show the same pass-rate-control pattern, and 4B ablations attribute gains to replay, bidirectional coverage, and adaptive control.

Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), has advanced LLM reasoning. However, GRPO suffers from three credit assignment failures: uniform token-level granularity that ignores heterogeneous informational value, uniform polarity that penalizes correct steps and rewards incorrect ones, and zero-variance collapse that erases outcome-driven gradients. We systematically quantify these failures, revealing highly non-uniform token informativeness, widespread step-level polarity misalignment, and substantial training waste. To address these limitations, we propose Entropy-Progress Aligned GRPO (EP-GRPO), a framework that mines the model's intrinsic information flow for dense, self-supervised guidance. EP-GRPO integrates entropy-gated modulation to prioritize high entropy decision pivots, implicit process signals from policy divergence anchored to outcome advantages for directional token-level feedback without external reward models, and cumulative entropy mapping that enables progress-aligned advantage normalization, naturally maintaining gradient flow under zero reward variance. Extensive experiments on mathematical reasoning benchmarks demonstrate that EP-GRPO achieves superior accuracy and efficiency compared to GRPO and its variants. The code will be available.

We formalize Rollout Informativeness under a Fixed Budget (RIFB) as the expected non-vanishing policy-gradient mass that a tool-use rollout set injects into Group Relative Policy Optimization (GRPO). We prove that any budget-agnostic independent sampler suffers a collapse rate bounded away from zero for hard prompts regardless of the budget. Motivated by this, we recast intermediate state selection as a monotone submodular maximization problem, where a greedy one-step selector enjoys a 1 minus 1/e approximation guarantee. Our Uncertainty-aware Upper Confidence Bound (UUCB) terms arise as closed-form marginal gains of this objective. This turns the token-level entropy bonus from an empirical trick into an analytic consequence of the formulation. We present InfoTree, a training-time tree-search framework coupling UUCB with a learned Adaptive Budget Allocator (ABA) and an asynchronous Speculative Expansion scheme. ABA rescues prompts whose initial tree is wasted on uniform outcomes, lifting the mixed-outcome ratio from 58.1 percent to 76.3 percent with less than 5 percent budget overhead. Speculative Expansion reduces wall-clock overhead from 14.3 percent to 4.8 percent by tolerating bounded staleness in UUCB scores. Across nine benchmarks spanning math reasoning (AIME 2024 and 2025, MATH-500, OlympiadBench, USAMO), web-search agents (GAIA, HLE-100, BrowseComp-lite), and tool-rich coding and OS agents (APPS-verified, AgentBench-OS), InfoTree outperforms flat GRPO, DeepSearch, Tree-GRPO, AT2PO, CW-GRPO, and RC-GRPO. Head-to-head compositions with Tree-GRPO prefix sharing and CW-GRPO contribution weights deliver further gains, confirming that our selector operates orthogonally to rollout reuse and trajectory re-weighting. A 5 by 5 by 5 robustness grid reveals that over three quarters of the hyperparameter space lies on a performance plateau, confirming UUCB robustness.

Group Relative Policy Optimization (GRPO) has recently shown strong performance in post-training large language models and vision-language models. It raises a question of whether the GRPO also significantly promotes the test-time adaptation (TTA) of vision language models. In this paper, we propose Group Relative Policy Optimization for Test-Time Adaptation (GRPO-TTA), which adapts GRPO to the TTA setting by reformulating class-specific prompt prediction as a group-wise policy optimization problem. Specifically, we construct output groups by sampling top-K class candidates from CLIP similarity distributions, enabling probability-driven optimization without access to ground-truth labels. Moreover, we design reward functions tailored to test-time adaptation, including alignment rewards and dispersion rewards, to guide effective visual encoder tuning. Extensive experiments across diverse benchmarks demonstrate that GRPO-TTA consistently outperforms existing test-time adaptation methods, with notably larger performance gains under natural distribution shifts.

Autonomous 3D indoor scene synthesis breaks down in non-convex rooms with tightly coupled spatial constraints. Data-driven generators lack topological priors for long-horizon planning, while iterative agents fragment semantics and become geometrically brittle. We present ZoneMaestro, a unified framework that shifts the paradigm from object-centric synthesis to Zone-Graph Orchestration. By internalizing a novel zone-based logic, ZoneMaestro translates high-level semantic intent into functional zones and topological constraints, enabling robust adaptation to diverse architectural forms. To support this, we construct Zone-Scene-10K, a large-scale dataset enriched with explicit Zone-Graph annotations. We further introduce an Alternating Alignment Strategy that cycles between reasoning internalization and Zone-Aware Group Relative Policy Optimization (Z-GRPO), effectively reconciling the tension between semantic richness and geometric validity without relying on external physics engines. To rigorously evaluate spatial intelligence beyond convex primitives, we formally define the task of Intricate Spatial Orchestration and release SCALE, a stress-test benchmark for irregular indoor scenarios with complex, dense spatial relations. Extensive experiments demonstrate that ZoneMaestro resolves the density-safety dichotomy, significantly outperforming state-of-the-art baselines in both structural coherence and intent adherence.

Mathematical reasoning is a key benchmark for large language models. Reinforcement learning is a standard post-training mechanism for improving the reasoning capabilities of large language models, yet performance remains sensitive to the design of the reward function that drives policy optimization. This paper introduces a search-driven framework that treats the reward specification itself as an object of optimization. The setting of interest is one in which the base model is held fixed and the reward specification is the primary remaining design lever. Candidate reward functions are generated by a frontier language model, validated automatically, screened through 500-step Group Relative Policy Optimization (GRPO) training runs on a Llama-3.2-3B-Instruct base model with Low-Rank Adaptation (LoRA), and ranked by F1 on the GSM8K test set. Ranked summaries from prior rounds are then fed back into the next round of generation. Over five rounds, the search produces 50 candidate rewards. The mean F1 rises from 0.596 in Round 1 to 0.632 in Round 5, and the top individual reward reaches F1 = 0.787. Seven ensemble configurations of top-ranked rewards are evaluated. The best ensemble achieves F1 = 0.795 (95% bootstrap CI [0.756, 0.832]) and accuracy 0.660 [0.635, 0.686], a 0.19 absolute F1 gain over a base-rewards-only GRPO baseline (F1 = 0.609). Pairwise McNemar tests with Bonferroni correction show all five-or-more-reward configurations are statistically indistinguishable at α = 0.05/21. A three-seed re-training of the best ensemble yields F1 of 0.785. A randomly drawn 5-reward control collapses to F1 = 0.047, which shows that the ranked-feedback loop, not the additive signal of having more rewards, drives the gain.

Multi-Hop Fact Verification requires complex reasoning across disparate evidence, posing significant challenges for Large Language Models , which may suffer from hallucinations and fractured logical chains. Existing methods, while improving transparency via Chain-of-Thought , often lack explicit modeling of the structural dependencies between evidence and claims. In this work, we introduce an SCM-inspired framework that grounds reasoning in explicit directed dependency graphs, treating verification as a constructive structural reasoning process rather than full causal inference with interventions or counterfactual semantics. We empirically identify an "inverted U-shaped" correlation between reasoning-chain length and accuracy, revealing that excessive structural complexity can degrade performance. To address this, we propose a rule-based reinforcement learning strategy using Group Relative Policy Optimization. This approach dynamically optimizes the trade-off between structural depth and conciseness. Extensive experiments on HoVer and EX-FEVER demonstrate that our SCM-GRPO framework outperforms strong baselines while producing more traceable reasoning structures for complex fact verification.

We consider the problem of Cost-Aware Learning, where sampling different components of a finite-sum objective incurs different costs. The objective is to reach a target error while minimizing the total cost. We propose Cost-Aware SGD, which uses a distribution based on gradient norms and costs to sample components. We provide a thorough analysis of this algorithm, including cost-improvement bounds over baselines, a characterization of distribution proxy sub-optimality, and a lower bound. We apply our theoretical insights to reinforcement learning with language models, where the computational cost of sequence-level policy gradients varies with length. We find that the advantage magnitude serves as a high-fidelity proxy for gradient norms, and use this to introduce Cost-Aware GRPO. Empirical results on 1.5B, 4B, and 8B LLMs demonstrate that this algorithm significantly reduces the tokens used in policy optimization while matching or exceeding baseline accuracy.

Latent reasoning offers a more efficient alternative to explicit reasoning by compressing intermediate reasoning into continuous representations and substantially shortening reasoning chains. However, existing latent reasoning methods mainly focus on supervised learning, and reinforcement learning in latent space remains highly unstable. We study this problem through the lens of Group Relative Policy Optimization (GRPO), and show that directly adapting GRPO to latent reasoning is fundamentally non-trivial: latent reasoning changes both the probability density and the sampling mechanism, causing three coupled bottlenecks: absence of intrinsic latent manifolds, where unconstrained exploration pushes rollouts off the valid latent manifold; exploration-optimization misalignment, where trajectory-level rewards can induce incorrect token-level updates; and latent mixture non-closure, where jointly reinforcing multiple correct latent paths can produce an invalid averaged state. To address them, we propose \textbf{Latent-GRPO}, which combines invalid-sample advantage masking, one-sided noise sampling, and optimal correct-path first-token selection. Across four low-difficulty benchmarks (e.g., GSM8K-Aug) and four high-difficulty benchmarks (e.g., AIME), Latent-GRPO improves over its latent initialization by 7.86 Pass@1 points on low-difficulty tasks and surpasses explicit GRPO by 4.27 points on high-difficulty tasks while using 3--4$\times$ shorter reasoning chains. It also achieves stronger pass@$k$ performance under Gumbel sampling. These results establish Latent-GRPO as an effective approach for stable and efficient latent reasoning.

We introduce Skills-Coach, a novel automated framework designed to significantly enhance the self-evolution of skills within Large Language Model (LLM)-based agents. Addressing the current fragmentation of the skill ecosystem, Skills-Coach explores the boundaries of skill capabilities, thereby facilitating the comprehensive competency coverage essential for intelligent applications. The framework comprises four core modules: a Diverse Task Generation Module that systematically creates a comprehensive test suite for various skills; a Lightweight Optimization Module dedicated to optimizing skill prompts and their corresponding code; a Comparative Execution Module facilitating the execution and evaluation of both original and optimized skills; and a Traceable Evaluation Module, which rigorously evaluates performance against specified criteria. Skills-Coach offers flexible execution options through its virtual and real modes. To validate its efficacy, we introduce Skill-X, a comprehensive benchmark dataset consisting of 48 diverse skills. Experimental results demonstrate that Skills-Coach achieves significant performance improvements in skill capability across a wide range of categories, highlighting its potential to advance the development of more robust and adaptable LLM-based agents.

We focus on the problem of \emph{Answer-Level Fine-Tuning} (ALFT), where the goal is to optimize a language model based on the correctness or properties of its final answers, rather than the specific reasoning traces used to produce them. Directly optimizing answer-level objectives is computationally intractable due to the need to marginalize over the vast space of latent reasoning paths. To overcome this, we propose a general game-theoretical framework that lifts the problem to a \emph{Distributional Alignment Game}. We formulate ALFT as a two-player game between a Policy (the generator) and a Target (an auxiliary distribution). We prove that the Nash Equilibrium of this game corresponds exactly to the solution of the original answer-level optimization problem. This variational perspective transforms the intractable marginalization problem into a tractable projection problem. We demonstrate that this framework unifies recent approaches to diversity and self-improvement (coherence) and provide efficient algorithms compatible with Group Relative Policy Optimization (GRPO), such as Coherence-GRPO, yielding significant complexity gains in mathematical reasoning tasks.

Traffic signal control (TSC) plays a central role in reducing congestion and maintaining urban mobility. This dissertation introduces DGLight, a critic-guided reinforcement-learning framework for adapting a pretrained large language model to TSC. DGLight first trains a CoLight-based Deep Q-Network critic to estimate traffic-aware action values from structured intersection states, then uses the frozen critic to score candidate language-model actions and optimize the policy with Group Relative Policy Optimization (GRPO). The resulting controller maps traffic states to interpretable reasoning traces and signal decisions while learning from dense per-state supervision rather than raw cumulative environment rewards. Experiments on TSC benchmarks covering Jinan and Hangzhou show that DGLight is the strongest overall method among the compared LLM-based controllers, remains competitive with strong RL baselines, and transfers well to city datasets not used to fit the critic. Qualitative examples further show that the model's generated reasoning is interpretable and aligned with the chosen signal phase. The project code is available $\href{https://github.com/yyccbb/FYP_LLMTSC}{here}$.

Aligning denoising generative models with human preferences or verifiable rewards remains a key challenge. While policy-gradient online reinforcement learning (RL) offers a principled post-training framework, its direct application is hindered by the intractable likelihoods of these models. Prior work therefore either optimizes an induced Markov decision process (MDP) over sampling trajectories, which is stable but inefficient, or uses likelihood surrogates based on the diffusion evidence lower bound (ELBO), which have so far underperformed on visual generation. Our key insight is that the ELBO-based approach can, in fact, be made both stable and efficient. By reducing surrogate variance and controlling gradient steps, we show that this approach can beat MDP-based methods. To this end, we introduce Variational GRPO (V-GRPO), a method that integrates ELBO-based surrogates with the Group Relative Policy Optimization (GRPO) algorithm, alongside a set of simple yet essential techniques. Our method is easy to implement, aligns with pretraining objectives, and avoids the limitations of MDP-based methods. V-GRPO achieves state-of-the-art performance in text-to-image synthesis, while delivering a $2\times$ speedup over MixGRPO and a $3\times$ speedup over DiffusionNFT.

Group Relative Policy Optimization (GRPO) performs coarse-grained credit assignment in reinforcement learning with verifiable rewards (RLVR) by assigning the same advantage to all tokens in a rollout. Process reward models can provide finer-grained supervision, but they require step-level annotation or additional reward modeling. We show that hidden-state distributions contain a useful signal for local reasoning quality that can be extracted using only outcome-level correctness labels available in RLVR. Specifically, within each GRPO group, the Wasserstein distance between span-level hidden state distributions of correct and incorrect rollouts increases around regions where their local reasoning quality diverges. This association holds both across examples and within individual trajectories, suggesting that hidden-state distributional divergence can serve as a self-supervision signal for fine-grained credit assignment. We formalize this observation with a separation theorem showing that, under mild structural assumptions, post-divergence spans have larger Wasserstein distances than pre-divergence spans whenever the population-level distributional gap exceeds finite-sample noise. Motivated by this result, we propose \textbf{S}pan-level \textbf{H}idden state \textbf{E}nabled \textbf{A}dvantage \textbf{R}eweighting (SHEAR), which modifies GRPO by using span-level Wasserstein distances to scale token-level advantages, amplifying updates on tokens whose hidden states are more separated from the opposing group. The method requires no additional model and only minimal changes to the training pipeline. Experiments on five mathematical reasoning benchmarks and five code generation benchmarks show improvements over standard GRPO and strong performance relative to supervised process reward models, while requiring no additional annotation or reward model training.

Sports videos are a challenging domain for multimodal understanding because they involve complex and dynamic human activities. Despite rapid progress in Multimodal Large Language Models (MLLMs), long-horizon reasoning in sports videos remains difficult, as answering questions requires both locating temporally sparse evidence and integrating it into reasoning. We attribute this limitation to two closely coupled factors: insufficient supervision over temporally dispersed evidence, and the lack of methods that require models to identify, localize, and justify temporal evidence. To address these gaps, we introduce SportsTime, a large-scale benchmark for long-form sports video understanding, comprising 14K+ open-ended QA pairs and 50K+ step-wise temporal evidence annotations. Building on SportsTime, we propose Chain-of-Time Reasoning (CoTR), which treats reasoning as a process of temporally grounded evidence composition. Specifically, during training, CoTR introduces a temporal-reward GRPO to encourage temporally grounded reasoning. During inference, it employs an anchor-observe-infer evidence-seeking loop to iteratively localize, verify, and compose temporal evidence before producing the final answer. Experiments demonstrate the usefulness of SportsTime as a benchmark and the effectiveness of CoTR, which consistently improves temporal compositional reasoning and step-wise grounding quality over strong MLLM baselines.

Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capabilities of Large Language Models (LLMs) by leveraging direct outcome verification instead of learned reward models. Building on this paradigm, Group Relative Policy Optimization (GRPO) eliminates the need for critic models but suffers from indiscriminate credit assignment for intermediate steps, which limits its ability to identify effective reasoning strategies and incurs overthinking. In this work, we introduce a model-free and verifiable process supervision via probing the model's belief in the correct answer throughout its reasoning trajectory. By segmenting the generation into discrete steps and tracking the conditional probability of the correct answer appended at each segment boundary, we efficiently compute interpretable segment-wise progress measurements to refine GRPO's trajectory-level feedback. This approach enables more targeted and sample-efficient policy updates, while avoiding the need for intermediate supervision derived from costly Monte Carlo rollouts or auxiliary models. Experiments on mathematical and general-domain benchmarks show consistent gains over GRPO across diverse models: up to 2.6-point accuracy improvements and 13.7% reasoning-length reductions on math tasks, and up to 2.4 points and 4% on general-domain tasks, demonstrating strong generalization.

Traditional policy learning methods in cooperative pursuit face fundamental challenges in biomimetic underwater robots, where long-horizon decision making, partial observability, and inter-robot coordination require both expressiveness and stability. To address these issues, a novel framework called Mamba-based multi-agent group relative policy optimization (M$^{2}$GRPO) is proposed, which integrates a selective state-space Mamba policy with group-relative policy optimization under the centralized-training and decentralized-execution (CTDE) paradigm. Specifically, the Mamba-based policy leverages observation history to capture long-horizon temporal dependencies and exploits attention-based relational features to encode inter-agent interactions, producing bounded continuous actions through normalized Gaussian sampling. To further improve credit assignment without sacrificing stability, the group-relative advantages are obtained by normalizing rewards across agents within each episode and optimized through a multi-agent extension of GRPO, significantly reducing the demand for training resources while enabling stable and scalable policy updates. Extensive simulations and real-world pool experiments across team scales and evader strategies demonstrate that M$^{2}$GRPO consistently outperforms MAPPO and recurrent baselines in both pursuit success rate and capture efficiency. Overall, the proposed framework provides a practical and scalable solution for cooperative underwater pursuit with biomimetic robot systems.

Reinforcement learning, particularly Group Relative Policy Optimization (GRPO), has emerged as an effective framework for post-training visual generative models with human preference signals. However, its effectiveness is fundamentally limited by coarse reward credit assignment. In modern visual generation, multiple reward models are often used to capture heterogeneous objectives, such as visual quality, motion consistency, and text alignment. Existing GRPO pipelines typically collapse these rewards into a single static scalar and propagate it uniformly across the entire diffusion trajectory. This design ignores the stage-specific roles of different denoising steps and produces mistimed or incompatible optimization signals. To address this issue, we propose Objective-aware Trajectory Credit Assignment (OTCA), a structured framework for fine-grained GRPO training. OTCA consists of two key components. Trajectory-Level Credit Decomposition estimates the relative importance of different denoising steps. Multi-Objective Credit Allocation adaptively weights and combines multiple reward signals throughout the denoising process. By jointly modeling temporal credit and objective-level credit, OTCA converts coarse reward supervision into a structured, timestep-aware training signal that better matches the iterative nature of diffusion-based generation. Extensive experiments show that OTCA consistently improves both image and video generation quality across evaluation metrics.

Accurate disease classification from radiology reports is essential for many applications. While supervised fine-tuning (SFT) of lightweight LLMs improves accuracy, it can degrade reasoning. We propose a two-stage approach: SFT on disease labels followed by Group Relative Policy Optimization (GRPO) to refine predictions by optimizing accuracy and format without reasoning supervision. Across three radiologist-annotated datasets, SFT outperformed baselines and GRPO further improved classification and enhanced reasoning recall and comprehensiveness.

Uniform Discrete Diffusion Model (UDM) has recently emerged as a promising paradigm for discrete generative modeling; however, its integration with reinforcement learning remains largely unexplored. We observe that naively applying GRPO to UDM leads to training instability and marginal performance gains. To address this, we propose UDM-GRPO, the first framework to integrate UDM with RL. Our method is guided by two key insights: (i) treating the final clean sample as the action provides more accurate and stable optimization signals; and (ii) reconstructing trajectories via the diffusion forward process better aligns probability paths with the pretraining distribution. Additionally, we introduce two strategies, Reduced-Step and CFG-Free, to further improve training efficiency. UDM-GRPO significantly improves base model performance across multiple T2I tasks. Notably, GenEval accuracy improves from $69\%$ to $96\%$ and PickScore increases from $20.46$ to $23.81$, achieving state-of-the-art performance in both continuous and discrete settings. On the OCR benchmark, accuracy rises from $8\%$ to $57\%$, further validating the generalization ability of our method. Code is available at https://github.com/Yovecent/UDM-GRPO.

Search agents achieve strong question-answering performance through multi-turn interactions with search engines, with Group Relative Policy Optimization (GRPO) being a widely used training algorithm. However, GRPO-style algorithms still face several challenges in multi-hop search settings. First, correct intermediate steps are often penalized when the final answer is wrong. Second, training is highly unstable, often causing degradation of natural language ability or even catastrophic training collapse. Our analysis attributes these issues to coarse-grained advantage assignment and an imbalance between positive and negative advantages. To address these problems, we propose CalibAdv, an advantage calibration method specifically designed for search agents that enables more accurate and more stable modeling of penalties and rewards. Specifically, CalibAdv leverages the correctness of intermediate steps to downscale excessive negative advantages at a fine-grained level. It then further rebalances positive and negative advantages to improve training stability. Importantly, CalibAdv adopts a lightweight design that calibrates advantages from standard rollout signals, making it simple and easy to deploy. Extensive experiments across three models and seven benchmarks demonstrate that CalibAdv improves both model performance and training stability. Our code is available at https://github.com/wujwyi/CalibAdv.

Visual-Language-Action (VLA) models represent a paradigm shift in embodied AI, yet existing frameworks often struggle with imprecise spatial perception, suboptimal multimodal fusion, and instability in reinforcement learning. To bridge these gaps, we propose OmniVLA-RL, a novel architecture that leverages a Mix-of-Transformers (MoT) design to synergistically integrate reasoning, spatial, and action experts. Furthermore, we introduce Flow-GSPO, which reformulates flow matching as a Stochastic Differential Equation (SDE) process and integrates it with Group Segmented Policy Optimization (GSPO) to enhance action precision and training robustness. Extensive evaluations on the LIBERO and LIBERO-Plus benchmarks demonstrate that OmniVLA-RL achieves decent overall performance and surpasses mainstream existing methods, effectively overcoming the fundamental limitations of current VLA models.

Agentic search -- the task of training agents that iteratively reason, issue queries, and synthesize retrieved information to answer complex questions -- has achieved remarkable progress through reinforcement learning (RL). However, existing approaches such as Search-R1, treat the retrieval system as a fixed tool, optimizing only the reasoning agent while the retrieval component remains unchanged. A preliminary experiment reveals that the gap between an oracle and a fixed retrieval system reaches up to +26.8% relative F1 improvement across seven QA benchmarks, suggesting that the retrieval system is a key bottleneck in scaling agentic search performance. Motivated by this finding, we propose CoSearch, a framework that jointly trains a multi-step reasoning agent and a generative document ranking model via Group Relative Policy Optimization (GRPO). To enable effective GRPO training for the ranker -- whose inputs vary across reasoning trajectories -- we introduce a semantic grouping strategy that clusters sub-queries by token-level similarity, forming valid optimization groups without additional rollouts. We further design a composite reward combining ranking quality signals with trajectory-level outcome feedback, providing the ranker with both immediate and long-term learning signals. Experiments on seven single-hop and multi-hop QA benchmarks demonstrate consistent improvements over strong baselines, with ablation studies validating each design choice. Our results show that joint training of the reasoning agent and retrieval system is both feasible and strongly performant, pointing to a key ingredient for future search agents.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach to improve the reasoning abilities of Large Language Models (LLMs). Among RLVR algorithms, Group Relative Policy Optimization (GRPO) and its variants have demonstrated strong performance and high training efficiency. However, GRPO-style objectives exhibit two issues on high accuracy prompts including mastered prompts (rollout accuracy =1) and majority-correct prompts (rollout accuracy in (0.5,1)). For mastered prompts, group-relative advantages vanish, yielding no training signal and unconstrained policy drift that can cause forgetting. For majority-correct prompts, the induced query weight shrinks as accuracy increases, weakening consolidation from partial correctness to mastery. To alleviate this, we propose Mastery-Consolidated Policy Optimization (MCPO), which introduces (i) a hinge-KL regularizer applied exclusively to mastered prompts to bound harmful policy drift between successive gradient steps, and (ii) a weighting mechanism that prioritizes majority-correct prompts to better allocate optimization effort. Extensive experiments across three mathematical benchmarks demonstrate that MCPO consistently improves pass@1 performance. Counter-intuitively, rather than restricting exploration, MCPO boosts pass@k metrics, indicating that mastery consolidation further catalyzes solution diversity.

Current post-training methodologies for adapting Large Vision-Language Models (LVLMs) generally fall into two paradigms: Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL). Despite their prevalence, both approaches suffer from inefficiencies when applied in isolation. SFT forces the model's generation along a single expert trajectory, often inducing catastrophic forgetting of general multimodal capabilities due to distributional shifts. Conversely, RL explores multiple generated trajectories but frequently encounters optimization collapse - a cold-start problem where an unaligned model fails to spontaneously sample any domain-valid trajectories in sparse-reward visual tasks. In this paper, we propose Supervised Group Relative Policy Optimization (S-GRPO), a unified post-training framework that integrates the guidance of imitation learning into the multi-trajectory exploration of preference optimization. Tailored for direct-generation visual tasks, S-GRPO introduces Conditional Ground-Truth Trajectory Injection (CGI). When a binary verifier detects a complete exploratory failure within a sampled group of trajectories, CGI injects the verified ground-truth trajectory into the candidate pool. By assigning a deterministic maximal reward to this injected anchor, S-GRPO enforces a positive signal within the group-relative advantage estimation. This mechanism reformulates the supervised learning objective as a high-advantage component of the policy gradient, compelling the model to dynamically balance between exploiting the expert trajectory and exploring novel visual concepts. Theoretical analysis and empirical results demonstrate that S-GRPO gracefully bridges the gap between SFT and RL, drastically accelerates convergence, and achieves superior domain adaptation while preserving the base model's general-purpose capabilities.

Large Language Models (LLMs) have shown strong promise in healthcare applications. Yet deploying general-purpose models in real-world settings remains difficult due to data privacy constraints, inference costs, and limited suitability for edge or on-device use. These challenges motivate the development of smaller, more efficient models that require robust post-training strategies to ensure reliable medical reasoning. In this work, we investigate Group Relative Policy Optimization (GRPO) for post-training LLMs on heart-focused medical question answering with rubric-based supervision derived from RaR-Medicine. We propose a Variance-Aware Reward Framework that extends the Explicit Aggregation and Implicit Aggregation strategies of Rubrics as Rewards by replacing weighted binary criterion aggregation and single overall Likert-style scoring with continuous analytical reward functions derived from criterion-level rubric outcomes. This formulation provides richer optimization signals for feedback that is sparse, multi-criteria, and difficult to verify automatically, and enables more stable on-policy reinforcement learning. On a held-out heart-related subset of HealthBench, our best GRPO variant improves accuracy from 0.362 to 0.502 and F1 from 0.532 to 0.668 relative to the Qwen3-14B base model, while remaining competitive with GPT-OSS-120B (0.508 accuracy, 0.674 F1). Our findings show that carefully designed rubric-based rewards provide a practical strategy for improving heart-focused medical question answering in LLMs, with potential to extend to other rubric-based tasks.

High-level autonomous driving requires motion planners capable of modeling multimodal future uncertainties while remaining robust in closed-loop interactions. Although diffusion-based planners are effective at modeling complex trajectory distributions, they often suffer from stochastic instabilities and the lack of corrective negative feedback when trained purely with imitation learning. To address these issues, we propose RAD-2, a unified generator-discriminator framework for closed-loop planning. Specifically, a diffusion-based generator is used to produce diverse trajectory candidates, while an RL-optimized discriminator reranks these candidates according to their long-term driving quality. This decoupled design avoids directly applying sparse scalar rewards to the full high-dimensional trajectory space, thereby improving optimization stability. To further enhance reinforcement learning, we introduce Temporally Consistent Group Relative Policy Optimization, which exploits temporal coherence to alleviate the credit assignment problem. In addition, we propose On-policy Generator Optimization, which converts closed-loop feedback into structured longitudinal optimization signals and progressively shifts the generator toward high-reward trajectory manifolds. To support efficient large-scale training, we introduce BEV-Warp, a high-throughput simulation environment that performs closed-loop evaluation directly in Bird's-Eye View feature space via spatial warping. RAD-2 reduces the collision rate by 56% compared with strong diffusion-based planners. Real-world deployment further demonstrates improved perceived safety and driving smoothness in complex urban traffic.

Recent advances in reinforcement learning (RL) have improved the reasoning capabilities of large language models (LLMs) and vision-language models (VLMs). However, the widely used Group Relative Policy Optimization (GRPO) consistently suffers from entropy collapse, causing the policy to converge prematurely and lose diversity. Existing exploration methods introduce additional bias or variance during exploration, making it difficult to maintain optimization stability. We propose Unified Entropy Control for Reinforcement Learning (UEC-RL), a framework that provides targeted mechanisms for exploration and stabilization. UEC-RL activates more exploration on difficult prompts to search for potential and valuable reasoning trajectories. In parallel, a stabilizer prevents entropy from growing uncontrollably, thereby keeping training stable as the model consolidates reliable behaviors. Together, these components expand the search space when needed while maintaining robust optimization throughout training. Experiments on both LLM and VLM reasoning tasks show consistent gains over RL baselines on both Pass@1 and Pass@$k$. On Geometry3K, UEC-RL achieves a 37.9% relative improvement over GRPO, indicating that it sustains effective exploration without compromising convergence and underscoring UEC-RL as a key for scaling RL-based reasoning in large models. Our code is available at https://github.com/597358816/UEC-RL.

Instruction-guided image editing requires balancing target modification with non-target preservation. Recently, flow-based models have emerged as a strong and increasingly adopted backbone for instruction-guided image editing, thanks to their high fidelity and efficient deterministic ODE sampling. Building on this foundation, GRPO-based reward-driven post-training has been explored to directly optimize editing-specific rewards, improving instruction following and editing consistency. However, existing methods often suffer from noisy credit assignment: global exploration also perturbs non-target regions, inflating within-group reward variance and yielding noisy GRPO advantages. To address this, we propose RC-GRPO-Editing, a region-constrained GRPO post-training framework for flow-based image editing under deterministic ODE sampling. It suppresses background-induced nuisance variance to enable cleaner localized credit assignment, improving editing region instruction adherence while preserving non-target content. Concretely, we localize exploration via region-decoupled initial noise perturbations to reduce background-induced reward variance and stabilize GRPO advantages, and introduce an attention concentration reward that aligns cross-attention with the intended editing region throughout the rollout, reducing unintended changes in non-target regions. Experiments on CompBench show consistent improvements in editing region instruction adherence and non-target preservation.

Despite the success of Vision-Language Models (VLMs), misleading charts remain a significant challenge due to their deceptive visual structures and distorted data representations. We present ChartCynics, an agentic dual-path framework designed to unmask visual deception via a "skeptical" reasoning paradigm. Unlike holistic models, ChartCynics decouples perception from verification: a Diagnostic Vision Path captures structural anomalies (e.g., inverted axes) through strategic ROI cropping, while an OCR-Driven Data Path ensures numerical grounding. To resolve cross-modal conflicts, we introduce an Agentic Summarizer optimized via a two-stage protocol: Oracle-Informed SFT for reasoning distillation and Deception-Aware GRPO for adversarial alignment. This pipeline effectively penalizes visual traps and enforces logical consistency. Evaluations on two benchmarks show that ChartCynics achieves 74.43% and 64.55% accuracy, providing an absolute performance boost of ~29% over the Qwen3-VL-8B backbone, outperforming state-of-the-art proprietary models. Our results demonstrate that specialized agentic workflows can grant smaller open-source models superior robustness, establishing a new foundation for trustworthy chart interpretation.

Despite their sophisticated general-purpose capabilities, Large Language Models (LLMs) often fail to align with diverse individual preferences because standard post-training methods, like Reinforcement Learning with Human Feedback (RLHF), optimize for a single, global objective. While Group Relative Policy Optimization (GRPO) is a widely adopted on-policy reinforcement learning framework, its group-based normalization implicitly assumes that all samples are exchangeable, inheriting this limitation in personalized settings. This assumption conflates distinct user reward distributions and systematically biases learning toward dominant preferences while suppressing minority signals. To address this, we introduce Personalized GRPO (P-GRPO), a novel alignment framework that decouples advantage estimation from immediate batch statistics. By normalizing advantages against preference-group-specific reward histories rather than the concurrent generation group, P-GRPO preserves the contrastive signal necessary for learning distinct preferences. We evaluate P-GRPO across diverse tasks and find that it consistently achieves faster convergence and higher rewards than standard GRPO, thereby enhancing its ability to recover and align with heterogeneous preference signals. Our results demonstrate that accounting for reward heterogeneity at the optimization level is essential for building models that faithfully align with diverse human preferences without sacrificing general capabilities.

While Group Relative Policy Optimization (GRPO) offers a powerful framework for LLM post-training, its effectiveness in open-ended domains like Machine Translation hinges on accurate intra-group ranking. We identify that standard Pointwise Quality Metrics (PQM) fall short in this context: candidates are evaluated in isolation, so the comparative context is missing for distinguishing fine-grained linguistic nuances. To address this, we introduce the Group Quality Metric (GQM) paradigm and its instantiation, the Group Relative Reward Model (GRRM). Unlike traditional independent scorers, GRRM jointly processes the entire candidate group, leveraging comparative analysis to rigorously resolve relative quality and adaptive granularity. Empirical evaluations confirm that GRRM achieves competitive ranking accuracy among all baselines; integrating GRRM into the GRPO training not only improves general translation quality but also unlocks reasoning capabilities comparable to state-of-the-art reasoning models. We release codes, datasets, and model checkpoints at https://github.com/NJUNLP/GRRM.

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, computational limits often rule out very large groups, so training proceeds with finite rollout sets that can reinforce only the correct behavior they expose. At practical group sizes, updates can miss rare-correct trajectories while still containing mixed rewards, concentrating probability on more common sampled solutions. We derive the probability of such prompt-local tail-miss events as a function of group size, showing non-monotonic behavior, and in the categorical abstraction characterize how unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware scaling coefficient, inspired by Focal loss, that down-weights updates on high-success sampled groups. Empirically, categorical simulation illustrates the same effect in the categorical setting, Maze provides a single-solution test, and LLM experiments include a representative GRPO group-size sweep together with fixed-$N$ transfer across GRPO, DAPO, and CISPO. On Qwen2.5-7B at $N{=}8$, our method improves average math pass@256 from 64.1 $\rightarrow$ 70.3 (GRPO), 69.3 $\rightarrow$ 72.5 (DAPO), and 73.2 $\rightarrow$ 76.8 (CISPO); OOD pass@256 also improves in all three cases, without increasing group size or computational cost.

Deploying GRPO on Flow Matching models has proven effective for text-to-image generation. However, existing paradigms typically propagate an outcome-based reward to all preceding denoising steps without distinguishing the local effect of each step. Moreover, current group-wise ranking mainly compares trajectories at matched timesteps and ignores within-trajectory dependencies, where certain early denoising actions can affect later states via delayed, implicit interactions. We propose TurningPoint-GRPO (TP-GRPO), a GRPO framework that alleviates step-wise reward sparsity and explicitly models long-term effects within the denoising trajectory. TP-GRPO makes two key innovations: (i) it replaces outcome-based rewards with step-level incremental rewards, providing a dense, step-aware learning signal that better isolates each denoising action's "pure" effect, and (ii) it identifies turning points-steps that flip the local reward trend and make subsequent reward evolution consistent with the overall trajectory trend-and assigns these actions an aggregated long-term reward to capture their delayed impact. Turning points are detected solely via sign changes in incremental rewards, making TP-GRPO efficient and hyperparameter-free. Extensive experiments also demonstrate that TP-GRPO exploits reward signals more effectively and consistently improves generation. Demo code is available at https://github.com/YunzeTong/TurningPoint-GRPO.

Reinforcement Learning (RL) for Large Language Models (LLMs) often suffers from training collapse in long-horizon tasks due to exploding gradient variance. To mitigate this, a baseline is commonly introduced for advantage computation; however, traditional value models remain difficult to optimize, and standard group-based baselines overlook sequence heterogeneity. Although classic optimal baseline theory can achieve global variance reduction, it neglects token heterogeneity and requires prohibitive gradient-based computation. In this work, we derive the Optimal Token Baseline (OTB) from first principles, proving that gradient updates should be weighted inversely to their cumulative gradient norm. To ensure efficiency, we propose the Logit-Gradient Proxy that approximates the gradient norm using only forward-pass probabilities. Our method achieves training stability and matches the performance of large group sizes ($N=32$) with only $N=4$, reducing token consumption by over 65% across single-turn and tool-integrated reasoning tasks.

Group Relative Policy Optimization (GRPO) remains the dominant critic-free approach for fine-tuning LLMs and VLMs, but its compatibility with constrained policy optimization (e.g. for safety-critical domains) has not been carefully examined. In this work, we introduce Constrained GRPO, a Lagrangian-based extension of GRPO for constrained policy optimization. We show that the standard practice of scalarizing rewards before normalization introduces a critical Lagrangian-specific failure mode: GRPO's within-group normalization makes constrained optimization highly sensitive to how multi-component learning signals are aggregated. We show that scalarizing rewards before normalization introduces shared-denominator coupling, so that changing one multiplier alters not only the emphasis on its corresponding constraint, but also the relative weighting of the reward and other constraints. We address this with a simple but crucial modification: scalarizing standardized advantages rather than rewards. This yields a better-conditioned update by addressing the coupling induced by reward scalarization, resulting in better-behaved multiplier dynamics and more stable constraint enforcement in practice. Empirically, across a controlled gridworld, a real-world autonomous driving benchmark, and a mathematical reasoning task, Constrained GRPO consistently achieves better adherence to specified constraints while maintaining or improving task performance.

Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.

Large language models (LLMs) struggle with complex, long-horizon reasoning due to instability caused by their frozen policy assumption. Current test-time scaling methods treat execution feedback merely as an external signal for filtering or rewriting trajectories, without internalizing it to improve the underlying reasoning strategy. Inspired by Popper's epistemology of "conjectures and refutations," we argue that intelligence requires real-time evolution of the model's policy through learning from failed attempts. We introduce Policy of Thoughts (PoT), a framework that recasts reasoning as a within-instance online optimization process. PoT first generates diverse candidate solutions via an efficient exploration mechanism, then uses Group Relative Policy Optimization (GRPO) to update a transient LoRA adapter based on execution feedback. This closed-loop design enables dynamic, instance-specific refinement of the model's reasoning priors. Experiments show that PoT dramatically boosts performance: a 4B model achieves 49.71% accuracy on LiveCodeBench, outperforming GPT-4o and DeepSeek-V3 despite being over 50 smaller.

Knowledge Base Question Answering (KBQA) challenges models to bridge the gap between natural language and strict knowledge graph schemas by generating executable logical forms. While Large Language Models (LLMs) have advanced this field, current approaches often struggle with a dichotomy of failure: they either generate hallucinated queries without verifying schema existence or exhibit rigid, template-based reasoning that mimics synthesized traces without true comprehension of the environment. To address these limitations, we present \textbf{KBQA-R1}, a framework that shifts the paradigm from text imitation to interaction optimization via Reinforcement Learning. Treating KBQA as a multi-turn decision process, our model learns to navigate the knowledge base using a list of actions, leveraging Group Relative Policy Optimization (GRPO) to refine its strategies based on concrete execution feedback rather than static supervision. Furthermore, we introduce \textbf{Referenced Rejection Sampling (RRS)}, a data synthesis method that resolves cold-start challenges by strictly aligning reasoning traces with ground-truth action sequences. Extensive experiments on WebQSP, GrailQA, and GraphQuestions demonstrate that KBQA-R1 achieves state-of-the-art performance, effectively grounding LLM reasoning in verifiable execution.

Practical LLM agents often operate over multi-turn conversations where success is determined only after the full interaction ends. Most multi-turn RL methods train via on-policy rollouts, but unlike in single-turn RLHF, the policy cannot produce a trajectory alone, since an external environment must respond after each agent turn. For conversational agents, this environment is a user, but real users are generally unavailable inside the training loop and simulated users are difficult to build faithfully. Separately, real-world deployment is rarely fully online or fully offline. The common production pattern is called "batch online," where the current policy is deployed to collect a batch of interaction data, then retrained on that batch and redeployed. We show that this batch-online setting creates an opportunity for applying the classical approximate policy iteration algorithm. Our central observation is that running standard token-level, single-turn GRPO with a learned turn-level $Q$-function as the reward model is a policy improvement step for the multi-turn problem. Building on this, we present Iterative GRPO, which alternates between fitting $Q^π$ from logged Monte Carlo returns via standard reward modeling (policy evaluation) and running single-turn GRPO against $Q^π$ (policy improvement). During policy improvement, the learned $Q^π$ scores candidate responses by their expected downstream return, avoiding the need for simulator rollouts of the remaining conversation. Overall, this allows us to do principled multi-turn RL using only single-turn RLHF methods without an interactive environment or user simulator inside the training loop. We demonstrate the effectiveness of Iterative GRPO on six multi-turn negotiation environments.

Group Relative Policy Optimization (GRPO) enables stable and preference-oriented updates via group-wise comparisons for post-training video generation. However, GRPO directly optimizes reward-induced advantages. Under sustained optimization, the reward score can lose fidelity as a proxy for true video quality, consistent with the phenomenon described by Goodhart's Law. This leads to two recurring issues: (i) shortcut-driven optimization under composite objectives and (ii) reward saturation within prompt groups. To address these issues, we introduce TaRoS, a Target-Robust Reward Signaling framework for Video generation GRPO. TaRoS leverages component level performance assessment together with intra-group sparsity to organize multi-aspect rewards towards optimization objectives. In addition, it adaptively downweights components that exhibit saturation, thereby preserving effective optimization directions and mitigating redundancy. This maintains meaningful optimization directions and preserves within-group ranking separation, thereby preventing reward hacking and leading to more reliable policy updates. Extensive experiments show consistent improvements in visual fidelity, motion coherence, and text-video alignment over strong baselines.

Tabular prediction has long been dominated by gradient-boosted decision trees and specialized deep tabular models, while large language models (LLMs) remain difficult to make competitive despite their cross-task adaptability and transparent reasoning traces. We address this gap by incorporating tabular structural priors into LLM post-training. Specifically, we propose Permutation Relative Policy Optimization (PRPO), which operationalizes column-permutation invariance through label-preserving column permutations and two-level advantage estimation. This design converts sparse outcome rewards into denser and more stable optimization signals. Extensive experiments on 139 OpenML datasets show that our 8B model reaches a genuinely competitive regime against strong specialized tabular baselines. It achieves strong fully supervised performance, dominates zero-shot settings, and performs on par with 32-shot strong baselines. Moreover, it substantially outperforms much larger general-purpose and reasoning LLMs, including up to a 53.17% improvement over DeepSeek-R1 (685B). These results show that structural-prior RL post-training is an effective route for making LLMs competitive in tabular prediction.

Unlike Business-to-Consumer e-commerce platforms (e.g., Amazon), inexperienced individual sellers on Consumer-to-Consumer platforms (e.g., eBay) often face significant challenges in setting prices for their second-hand products efficiently. Therefore, numerous studies have been proposed for automating price prediction. However, most of them are based on static regression models, which suffer from poor generalization performance and fail to capture market dynamics (e.g., the price of a used iPhone decreases over time). Inspired by recent breakthroughs in Large Language Models (LLMs), we introduce LLP, the first LLM-based generative framework for second-hand product pricing. LLP first retrieves similar products to better align with the dynamic market change. Afterwards, it leverages the LLMs' nuanced understanding of key pricing information in free-form text to generate accurate price suggestions. To strengthen the LLMs' domain reasoning over retrieved products, we apply a two-stage optimization, supervised fine-tuning (SFT) followed by group relative policy optimization (GRPO), on a dataset built via bidirectional reasoning. Moreover, LLP employs a confidence-based filtering mechanism to reject unreliable price suggestions. Extensive experiments demonstrate that LLP substantially surpasses existing methods while generalizing well to unseen categories. We have successfully deployed LLP on Xianyu\footnote{Xianyu is China's largest second-hand e-commerce platform.}, significantly outperforming the previous pricing method. Under the same 30% product coverage, it raises the static adoption rate (SAR) from 40% to 72%, and maintains a strong SAR of 47% even at 90% recall.

While Multimodal Large Language Models (MLLMs) demonstrate remarkable capabilities across diverse domains, their application to specialized anomaly detection (AD) remains constrained by domain adaptation challenges. Existing Group Relative Policy Optimization (GRPO) based approaches suffer from two critical limitations: inadequate training data utilization when models produce uniform responses, and insufficient supervision over reasoning processes that encourage immediate binary decisions without deliberative analysis. We propose a comprehensive framework addressing these limitations through two synergistic innovations. First, we introduce a multi-stage deliberative reasoning process that guides models from region identification to focused examination, generating diverse response patterns essential for GRPO optimization while enabling structured supervision over analytical workflows. Second, we develop a fine-grained reward mechanism incorporating classification accuracy and localization supervision, transforming binary feedback into continuous signals that distinguish genuine analytical insight from spurious correctness. Comprehensive evaluation across multiple industrial datasets demonstrates substantial performance improvements in adapting general vision-language models to specialized anomaly detection. Our method achieves superior accuracy with efficient adaptation of existing annotations, effectively bridging the gap between general-purpose MLLM capabilities and the fine-grained visual discrimination required for detecting subtle manufacturing defects and structural irregularities.

Although GRPO substantially enhances flow matching models in human preference alignment of image generation, methods such as FlowGRPO and DanceGRPO still exhibit inefficiency due to the necessity of sampling and optimizing over all denoising steps specified by the Markov Decision Process (MDP). In this paper, we propose $\textbf{MixGRPO}$, a novel framework that leverages the flexibility of mixed sampling strategies through the integration of stochastic differential equations (SDE) and ordinary differential equations (ODE). This streamlines the optimization process within the MDP to improve efficiency and boost performance. Specifically, MixGRPO introduces a sliding window mechanism, using SDE sampling and GRPO-guided optimization only within the window, while applying ODE sampling outside. This design confines sampling randomness to the time-steps within the window, thereby reducing the optimization overhead, and allowing for more focused gradient updates to accelerate convergence. Additionally, as time-steps beyond the sliding window are not involved in optimization, higher-order solvers are supported for faster sampling. So we present a faster variant, termed $\textbf{MixGRPO-Flash}$, which further improves training efficiency while achieving comparable performance. MixGRPO exhibits substantial gains across multiple dimensions of human preference alignment, outperforming DanceGRPO in both effectiveness and efficiency, with nearly 50% lower training time. Notably, MixGRPO-Flash further reduces training time by 71%.

We introduce a novel method that averages the logits of a frozen reference policy (e.g., SFT) and a trainable policy, and incorporate the method into Group Relative Policy Optimization (GRPO). In contrast to Reinforcement Learning with Verifiable Rewards (RLVR) methods, our proposal does not involve a Kullback Leibler (KL) regularization or critic; the trainable policy and the reference anchor are coupled through the logit averaging structure to leverage the reasoning expertise of the trainable policy while maintaining the formatting advantage of SFT. Our method is evaluated on MATH, cn-k12, and MMLU, and the results show a higher accuracy or at least comparable accuracy relative to the canonical KL-regularized GRPO.

Text-to-SQL parsing has achieved remarkable progress under the Full Schema Assumption. However, this premise fails in real-world enterprise environments where databases contain hundreds of tables with massive noisy metadata. Rather than injecting the full schema upfront, an agent must actively identify and verify only the relevant subset, giving rise to the Unknown Schema scenario we study in this work. To address this, we propose TRUST-SQL (Truthful Reasoning with Unknown Schema via Tools). We formulate the task as a Partially Observable Markov Decision Process where our autonomous agent employs a structured four-phase protocol to ground reasoning in verified metadata. Crucially, this protocol provides a structural boundary for our novel Dual-Track GRPO strategy. By applying token-level masked advantages, this strategy isolates exploration rewards from execution outcomes to resolve credit assignment, yielding a 9.9% relative improvement over standard GRPO. Extensive experiments across five benchmarks demonstrate that TRUST-SQL achieves an average absolute improvement of 30.6% and 16.6% for the 4B and 8B variants respectively over their base models. Remarkably, despite operating entirely without pre-loaded metadata, our framework consistently matches or surpasses strong baselines that rely on schema prefilling. Data, code, and checkpoints are available at https://huggingface.co/collections/AIJian/trustsql.