Better Call Group Relative Policy Optimization

Evaluating LLM agents still ends with a human reading trajectories, because automatic judges carry no guarantee on how often they are wrong. We ask the operational question: what fraction of agent evaluation can a judge take over, with a certificate that the error rate among auto-decided trajectories stays below a budget alpha? Agent corpora resist the standard answer: many agents attempt the same tasks, so trajectories arrive in correlated clusters, and the i.i.d. certificates of existing selective-judging methods can overstate what is safe: a naive certificate can claim 98% automation while its realized error exceeds the budget in 17.5% of task resamples. We introduce a task-level bootstrap certificate that is valid in every regime we test while matching the naive certificate's coverage; finite-sample cluster-valid alternatives certify nothing at realistic task counts. Under this certificate, a 4B logprob judge trained with SFT and reject-weighted GRPO certifies 0.30-0.59 of evaluation on tool-use and web corpora at alpha=0.1, the only judge, among strongly elicited frontier models, certifying on both headline corpora. Certified coverage is predictable before training from base rate and discrimination alone (leave-one-corpus-out R^2=0.96). Finally, the certificate doubles as a self-training filter: pseudo-labels harvested inside certified regions have contamination bounded by alpha by construction (realized 0.000-0.041 across six harvests), letting a judge enter an unseen domain at in-domain strength with zero target training labels.

On-policy distillation (OPD) accelerates post-training by providing dense token-level supervision from a frozen teacher on the student's own rollouts. Vanilla OPD applies this supervision uniformly across prompts, without checking whether the teacher is reliable for each prompt. Because reverse KL is mode-seeking, a confidently wrong teacher can induce a strong yet misleading update. Distributional proxies, such as entropy or teacher-student likelihood agreement, measure uncertainty or agreement but do not directly verify outcome correctness. We introduce Teacher-Gated On-Policy Distillation (TGOPD), built on the principle that teacher reliability should be verified at the prompt level before dense supervision is admitted. TGOPD estimates reliability from a small set of verifier-scored teacher probes and routes each prompt exclusively to dense OPD when the reliability check passes or to verifier-grounded GRPO otherwise. Across 4B and 35B students in mathematics, code, and instruction following, TGOPD outperforms Vanilla OPD in all six single-domain settings and achieves higher seven-benchmark averages at both scales under multi-domain training. By using otherwise-idle teacher capacity for reliability estimation, TGOPD also reduces teacher-side compute waste in asynchronous OPD, increasing teacher-node GPU utilization from 9.8% to 78.9% in the measured 4B single-domain run.

Large language models can infer sensitive personal attributes, such as age, location, and occupation, from ordinary text, turning everyday writing into a privacy risk. Adversarial anonymization defends against this by rewriting a text with a capable language model that also plays the attacker, but it needs a powerful model at inference time and thus sends private text to a third party, the very exposure anonymization should prevent. Recent work distills this behavior into a small on-device model using supervised fine-tuning and direct preference optimization (DPO), but DPO only imitates the teacher's offline choices and never directly optimizes the privacy--utility objective we care about. We introduce \textbf{GRASP} (\textbf{G}roup-\textbf{R}elative \textbf{A}nonymization via \textbf{S}elf-refinement \textbf{P}olicy-optimization), which reinforces the local anonymizer online with Group Relative Policy Optimization. A single small model acts as anonymizer, adversary, and utility judge, trained against a self-generated reward that hides attributes while preserving meaning, with a design that guards against reward hacking. Trained on Llama-3.1-8B, \ours{} improves the privacy--utility trade-off over the DPO-distilled baseline, consistently across three independent LLM judges. Against adversarial anonymization driven by frontier models such as Gemini2.5Flash and Claude, it achieves a comparable or better overall trade-off while removing substantially more private information, and it runs entirely on-device at roughly $1\%$ of the GPT-4o teacher's cost.

We tackle the challenging yet underexplored task of Generalized Referring Expression Comprehension (GREC), which requires a model to localize the object described by a textual expression when it exists (positive sample) and to refuse output when it does not (negative sample). Although Multimodal Large Language Models (MLLMs) excel at localizing existing objects, they often fail to reject nonexistent ones due to the absence of negative samples during training, producing hallucinated bounding boxes. Existing post-training approaches such as supervised fine-tuning (SFT) and reinforcement learning (RL) enhance refusal behavior but usually degrade localization accuracy on positive samples, undermining the model's core competence. To address this, we propose Refusal-Calibrated Group Relative Policy Optimization (RC-GRPO), a calibrated RL strategy that strengthens the refusal ability of MLLMs while preserving localization performance. It enforces "None" outputs in rollouts for valid advantage estimation on negative samples and applies a penalty to prevent over-refusal on positives, achieving a balanced trade-off between accuracy and reliability. A second-stage reasoning reinforcement further consolidates causal understanding and interpretability. Experiments on three GREC benchmarks demonstrate that RC-GRPO attains superior localization accuracy while maintaining strong refusal capability.

Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.

LLM-based ASR adapted to regulated domains such as banking is bottlenecked by privacy: real speech is costly and legally constrained to collect, making synthetic text-to-speech (TTS) an attractive substitute. Yet synthetic speech stays acoustically mismatched with real recordings, and work on this gap has stayed within supervised fine-tuning (SFT). We instead turn to reinforcement learning, and show that Group Relative Policy Optimization (GRPO) extracts far more from the same synthetic speech than SFT. Synthetic-only adaptation of the model with GRPO, a critic-free method rewarding low-WER hypotheses, reduces WER by 40% relative to SFT (36.71%$\to$22.09%), and an SFT-then-GRPO combination pushes this further to 45%. We trace the gain to behavior rather than representation: GRPO reduces insertion errors by improving stopping calibration and speech-to-text alignment by better anchoring attention to audio, leaving early-layer representations intact. When synthetic speech is the main resource, reinforcement learning should be preferred over supervised fine-tuning.

Asynchronous reinforcement learning improves the throughput of large language model post-training by decoupling rollout generation from policy optimization, but introduces a mismatch between the behavior and learner policies. How the resulting policy staleness couples with the learning rate to govern training stability and collapse time remains poorly understood. We investigate this coupling in vanilla GRPO through controlled sweeps of the synchronization interval $S$ and constant learning rate $η$ on Llama-3.2-1B/3B, complemented by experiments on Qwen3-8B. We identify two empirical scaling laws: (i) Stability-boundary scaling: the largest stable learning rate scales approximately as $S^{-1}$, yielding a stability boundary characterized by an approximately constant product $Sη$. (ii) Collapse-time scaling: among collapsing runs, estimated collapse times scale approximately as $η^{-1}$, corresponding to a model- and setup-dependent cumulative learning-rate budget that aligns across synchronization intervals in the Llama sweeps. We interpret these laws through a local analysis of the behavior-dependent GRPO surrogate and a complementary mean-field model. Under local regularity conditions, the analysis yields an $O(Sη)$ upper bound on the staleness-induced update bias that resets at synchronization. The mean-field model shows how sufficiently strong positive feedback can sustain directional drift when update directions persist across synchronization cycles. When drift speed saturates under optimizer normalization, this mechanism predicts exit from a local surrogate-validity region after an approximately fixed cumulative learning rate. Together, these findings motivate a practical calibration rule: estimate the stability threshold and collapse budget from a coarse sweep, then jointly select $S$ and $η$ for the intended training horizon.

Vision-Language-Action (VLA) models offer a promising framework for robotic manipulation by connecting language instructions, visual observations, and continuous control. However, most existing policies remain limited by behavior cloning or supervised fine-tuning (SFT) from fixed demonstrations, which provides limited opportunity to improve from the policy's own failures. In this paper, we present Z-1, a reinforcement learning (RL) post-training framework for flow-based VLA models. Built on top of $π_{0.5}$, Z-1 uses only publicly released RoboCasa demonstrations for SFT and then applies a task-wise Group Relative Policy Optimization (GRPO) strategy across $24$ standard RoboCasa tasks. To improve the efficiency and stability of online optimization, Z-1 combines shared-prefix rollout construction, tree-structured trajectory branching, completion-aware reward calibration, and selective joint training of VLM and Action Expert. Across all $24$ RoboCasa tasks, Z-1 achieves an average success rate of $80.6\%$, improving over its SFT initialization by $13.2\%$ points and outperforms the published sota models. These results show that systematic GRPO post-training can substantially improve flow-based VLA policies without additional private demonstrations.

Multimodal deception detection is critical for identifying fraudulent intentions, yet existing approaches predominantly rely on end to end black--box paradigms. These methods suffer from a severe lack of interpretability failing to provide transparent reasoning trajectories and struggling to explicitly capture the subtle, cross modal inconsistencies inherent in deceptive behaviors. To transcend these limitations, we propose ThinkDeception, a novel and interpretable multimodal deception detection framework. As a pioneering effort, it introduces Multimodal Large Language Models (MLLMs) into this domain, transforming deception detection from a traditional binary classification task into an explicit cognitive reasoning process. Facilitated by the first meticulously annotated step--by--step multimodal Chain of Thought (CoT) dataset, we develop a foundational model, ThinkDeception Base, empirically validating the critical role of modal inconsistency in decoding deception. Building upon this foundation, our core innovation lies in proposing Visual-Audio Consistency Group Relative Policy Optimization(VAC--GRPO) equipped with a progressive training strategy. Distinct from standard GRPO, we stratify the training data into four progressive difficulty tiers, guiding the model through a psychologically grounded easy--to--hard cognitive transition. By innovatively coupling this dynamic curriculum scheduler with a multi dimensional, process aware reward mechanism and a reflective learning paradigm, we significantly elevate the model's overall reasoning quality. Extensive experiments on mainstream benchmarks demonstrate that ThinkDeception establishes a new SOTA, significantly outperforming existing methods in both detection accuracy and rationale quality. Ultimately, this work successfully drives the field of deception detection toward interpretable, multimodal cognitive reasoning.

Long-context reasoning is an essential capability for large language models, particularly when they are deployed as autonomous agents that must reason over lengthy trajectories. Reinforcement learning (RL) has recently emerged as a dominant paradigm for improving this ability, yet existing work largely focuses on reward engineering while diverse training data remains scarce. We revisit this problem from a data-centric perspective and show that a simple yet effective data recipe alone, paired with a minimal outcome-based GRPO setup, suffices to substantially improve long-context reasoning. Our recipe targets three complementary task families -- retrieval, multi-evidence synthesis, and reasoning -- for which we construct and curate eight datasets totaling ~14K examples. Experiments on three models (Qwen3-4B/8B/30B-A3B) yield average gains of +7.2/+3.2/+6.4 points across seven long-context benchmarks, surpassing prior RL training sets. We further demonstrate that these gains transfer to agentic tasks, where continuing RL training on an agent-tuned model with our data recipe improves GAIA by +4.8 and BrowseComp by +7.0 points. We will release our datasets to facilitate future research.

Long-horizon tool-use reinforcement learning learns from outcome verification, but trajectory-level advantages are broadcast over reasoning, API, and answer tokens. Direct self-distillation can supply a denser signal, but in our experiments it can also destroy tool use by rehearsing teacher behavior without identifying which actions the verifier rewards. We introduce Sibling-Guided Credit Distillation (SGCD), which uses distillation for bounded credit weighting rather than as a competing actor loss. Dynamic sampling produces mixed successful and failed sibling rollouts; an external LLM summarizes their contrast into a training-only credit reference; and detached teacher/student divergence reshapes GRPO token advantages. The deployed student receives only the clean task prompt. Across AppWorld and tau^3-airline, SGCD reports higher held-out point estimates than GRPO-family comparators: AppWorld TGC improves from 42.9 to 45.6 on test_normal and from 24.7 to 27.0 on test_challenge, and tau^3-airline held-out evaluator score improves from 0.583 to 0.602. These results support a narrow design rule for long-horizon tool-use agents: use distillation to guide credit assignment while keeping policy gradient in charge of the actor update.

Recent advances in language models have established reinforcement learning as the primary paradigm for eliciting self-correction and long-chain reasoning. While group relative policy optimization (GRPO) offers superior scalability by eliminating the critic network, deploying it on a central infrastructure entails collecting a large volume of data from distributed owners, which poses significant privacy risks. To address these concerns, we introduce federated GRPO (FGRPO), a framework designed to decentralize the fine-tuning of reasoning models across heterogeneous data owners. To effectively mitigate the instability caused by divergent reward scales across heterogeneous tasks, FGRPO incorporates an adaptive aggregation mechanism based on relative performance gain. By characterizing each client's improvement relative to its personalized historical baseline, the framework dynamically prioritizes effective learning trajectories regardless of local task difficulty. FGRPO ensures robust convergence on non-IID data while preserving data privacy.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, its effectiveness is substantially hindered by the prevalence of ineffective training data: many sampled prompts yield response groups that are either entirely correct or entirely incorrect, resulting in zero-variance rewards and limited learning signals. Recent state-of-the-art methods address this issue through extensive LLM rollouts to filter ineffective samples, but at the cost of considerable computational overhead. Alternative approaches, including predictive sampling and trajectory replay, aim to improve data efficiency but often remain insufficient and may introduce additional issues such as systematic bias or suboptimal constraints. To address these limitations, we propose Group Prioritized Off-Policy Optimization (POPO), a simple yet effective framework that fully exploits effective training batches without additional rollout overhead. POPO comprises two key components: prioritized group replay and decoupled off-policy optimization. The former replaces ineffective on-policy groups with effective off-policy groups via a recency-based replay mechanism that jointly considers sample quality and the degree of off-policiness. To further mitigate the off-policy gap, POPO employs decoupled importance sampling to correct off-policy bias while maintaining stable policy updates under consistent trust-region constraints. Empirical evaluations across diverse reasoning tasks, including mathematics, planning, and visual geometry, demonstrate that POPO substantially accelerates RL finetuning and achieves strong reasoning performance with significantly fewer rollouts.

Reinforcement learning with verifiable rewards (RLVR), especially Group Relative Policy Optimization (GRPO), has been widely used to improve reasoning in large language models. However, outcome-level rewards provide only sparse supervision, and group-relative advantages vanish when all sampled trajectories for a prompt are either correct or incorrect. On-Policy Self-Distillation (OPSD) offers dense token-level guidance, but its token preferences are not necessarily aligned with trajectory correctness; empirical diagnostics show that OPSD signals behave differently on correct and incorrect rollouts, with teacher-positive and teacher-negative gap signals exhibiting different noise profiles. These diagnostics are conducted under an OPSD-style privileged teacher context for analysis only, whereas CAST training uses answer-free self-teacher scoring.Motivated by these observations, this work proposes CAST, an answer-free self-distillation method for GRPO-style RLVR. CAST keeps the verifier-grounded GRPO objective, but uses a stop-gradient self-teacher to shape token-level advantages according to trajectory correctness. Unlike prior self-distilled RLVR methods, CAST does not require reference-solution-conditioned teacher scoring, keeps the self-teacher log-probability gap active throughout training, and applies bidirectional local advantage sign reversal: teacher-negative tokens in correct trajectories can receive negative token-level advantages, while teacher-positive tokens in incorrect trajectories can receive bounded positive local advantages. For zero-variance all-correct and all-wrong groups, CAST assigns bounded sign-constrained base advantages, so these otherwise zero-gradient groups can contribute verifier-signed token feedback. Experiments on mathematical reasoning show that CAST improves RLVR training while retaining a lightweight, verifier-grounded trajectory-level objective.

While rule-based reinforcement learning has recently catalyzed explicit reasoning in multimodal models, tactile reasoning remains largely underexplored. Existing tactile-language models primarily rely on supervised or contrastive objectives, which limits their capacity to ground predictions in physical evidence or rectify misleading visual priors. Tactile reasoning introduces two modality-specific challenges: the ordinal nature of physical attributes (e.g., hardness, roughness) and the cross-sensor distribution shifts inherent in optical tactile hardware. In this work, we introduce TouchReason-1M, a large-scale multimodal dataset comprising over 1M synchronized tactile pairs across four distinct sensors, and TouchReason-Bench, a rigorous framework for evaluating tactile perception and visual-tactile conflict resolution. Building upon these, we propose Touch-R1, a tactile reasoning MLLM based on Qwen2.5-VL-7B. Touch-R1 is trained via a tactile-grounded GRPO objective that combines ordinal-aware accuracy, cross-sensor physical consistency, structured-format control, and an input-side tactile grounding objective. Specifically, the tactile-use reward assigns credit only when authentic tactile inputs yield superior correctness relative to counterfactual controls where the tactile stream is removed, shuffled, or noise-masked. On TouchReason-Bench, Touch-R1-7B outperforms Octopi-13B by 18.4% and GPT-4o by 24.7% on average. Its structured reasoning traces reveal emergent behaviors of probing, comparison, and revision, demonstrating that R1-style reasoning can be effectively grounded in physical contact.

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.

Visual reasoning, often interleaved with intermediate visual states, has emerged as a promising direction in the field. A straightforward approach is to directly generate images via unified models during reasoning, but this is computationally expensive and architecturally non-trivial. Recent alternatives include agentic reasoning through code or tool calls, and latent reasoning with learnable hidden embeddings. However, agentic methods incur context-switching latency from external execution, while latent methods lack task generalization and are difficult to train with autoregressive parallelization. To combine their strengths while mitigating their limitations, we propose ATLAS, a framework in which a single discrete 'word', termed as a functional token, serves both as an agentic operation and a latent visual reasoning unit. Each functional token is associated with an internalized visual operation, yet requires no visual supervision and remains a standard token in the tokenizer vocabulary, which can be generated via next-token prediction. This design avoids verbose intermediate visual content generation, while preserving compatibility with the vanilla scalable SFT and RL training, without architectural or methodological modifications. To further address the sparsity of functional tokens during RL, we introduce Latent-Anchored GRPO (LA-GRPO), which stabilizes the training by anchoring functional tokens with a statically weighted auxiliary objective, providing stronger gradient updates. Extensive experiments and analyses demonstrate that ATLAS achieves superior performance on challenging benchmarks while maintaining clear interpretability. We hope ATLAS offers a new paradigm inspiring future visual reasoning research.

Aligning streaming autoregressive (AR) video generators with human preferences is challenging. Existing reinforcement learning methods predominantly rely on noise-based exploration and SDE-based surrogate policies that are mismatched to the deterministic ODE dynamics of distilled AR models, and tend to perturb low-level appearance rather than the high-level semantic storyline progression critical for long-horizon coherence. To address these limitations, we present KVPO, an ODE-native online Group Relative Policy Optimization (GRPO) framework for aligning streaming video generators. For diversity exploration, KVPO introduces a causal-semantic exploration paradigm that relocates the source of variation from stochastic noise to the historical KV cache. By stochastically routing historical KV entries, it constructs semantically diverse generation branches that remain strictly on the data manifold. For policy modeling, KVPO introduces a velocity-field surrogate policy based on Trajectory Velocity Energy (TVE), which quantifies branch likelihood in flow-matching velocity space and yields a reward-weighted contrastive objective fully consistent with the native ODE formulation. Experiments on multiple distilled AR video generators demonstrate consistent gains in visual quality, motion quality, and text-video alignment across both single-prompt short-video and multi-prompt long-video settings.

Reinforcement learning with verifiers (RLVR) has become a central paradigm for improving LLM reasoning, yet popular group-based optimization algorithms like GRPO often suffer from exploration collapse, where the models prematurely converge on a narrow set of high-scoring patterns, lacking the ability to explore new solutions. Recent efforts attempt to alleviate this by adding entropy regularization or diversity bonus. However, these approaches do not change the \textit{winner-takes-all} nature, where rollouts still compete for individual advantage rather than cooperating for maximizing global diversity. In this work, we propose Group Cooperative Policy Optimization (GCPO), which shifts the training paradigm from rollout competition to team cooperation. Specifically, GCPO replaces independent rollout scoring with team-level credit assignment: a rollout is rewarded by how much it contributes to the team's valid solution coverage, rather than its individual accuracy. This coverage is described as a determinant volume over reward-weighted semantic embeddings, where only correct and non-redundant rollouts contribute to this volume. During advantage estimation, GCPO redistributes the collective team reward to each single rollout according to its average marginal contribution to the team. This cooperative training paradigm routes optimization toward non-redundant correct reasoning paths. Experiments across multiple reasoning benchmarks demonstrate that GCPO significantly improves both reasoning accuracy and solution diversity over existing approaches. Code will be released at https://github.com/bradybuddiemarch/gcpo.

We introduce Mutual Reinforcement Learning, a framework for concurrent RL post-training in which heterogeneous LLM policies exchange typed experience while keeping separate parameters, objectives, and tokenizers. The framework combines a Shared Experience Exchange (SEE), Multi-Worker Resource Allocation (MWRA), and a Tokenizer Heterogeneity Layer (THL) that retokenizes text and aligns token-level traces across incompatible vocabularies. This substrate makes the experience-sharing design question operational across model families. We instantiate three controlled probes on top of GRPO: data-level rollout sharing via Peer Rollout Pooling (PRP), value-level advantage sharing via Cross-Policy GRPO Advantage Sharing (XGRPO), and outcome-level success transfer via Success-Gated Transfer (SGT). A contextual-bandit analysis characterizes their structural positions on a stability-support trade-off: PRP pays density-ratio variance and THL residual costs, XGRPO preserves on-policy actor support while changing scalar baselines, and SGT supplies a rescue-set score direction toward verified peer successes. In the evaluated regime, outcome-level sharing occupies the favorable point of this trade-off.

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.

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.

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.