Group Relative Policy Optimization

RLVR has substantially improved the reasoning capabilities of LLMs. However, existing methods typically parameterize temporal progression in the Markov Decision Process by token-by-token generation, despite the highly non-uniform information flow along autoregressive trajectories. In this paper, we propose InfoPPO, which reparameterizes temporal progression using information density rather than raw token count. This reparameterization induces a common state-dependent structure for both temporal credit propagation and policy updates. InfoPPO restores the effectiveness of non-trivial discounting in long-horizon reasoning, retaining effective-horizon contraction while avoiding excessive attenuation of terminal supervision over long token sequences. Moreover, the information-time policy-improvement analysis naturally leads to a state-dependent update constraint, which we implement through adaptive clipping. By adapting the clipping threshold at each token position to the information density of its corresponding state, this mechanism enables more targeted policy updates while preserving proximal control. Theoretically, we extend performance-difference and policy-improvement analyses to the information-time MDP, deriving a policy-improvement lower bound when policy changes are regulated by information density. We further connect the general information-time analysis to practical LLM policy optimization by relating state-wise information density to local policy movement, while also providing theoretical grounding for the adaptive update mechanism. Experiments on Qwen3 models demonstrate consistent gains over competitive baselines across five challenging competition-style mathematical reasoning benchmarks. InfoPPO also maintains stable accuracy and response length across non-trivial discount settings under which token-time PPO deteriorates.

Group-relative reinforcement learning compares rollouts of the same prompt, but independent environment noise can obscure these comparisons. We study paired rollouts, which share an event-keyed noise schedule within each group while preserving each rollout's marginal distribution. Pairing removes the between-schedule component of reward-contrast variance, but need not reduce gradient variance. For one-sided grader noise, we derive an exact condition for reduction and give a counterexample in which reward contrasts improve while gradient variance increases. A controlled study trains a 2B tool-use agent under tool faults and grader flips, with three seeds per design. The protocol was registered with a disclosed, previously completed pilot. Under tool faults, pairing improves final noisy-test success by +5.1 percentage points on average, with all three seed differences positive, but misses the registered learning-curve criterion. The criterion is also missed under grader flips: the validation-AUC difference is +0.003 (95% interval [-0.029, +0.033]). A gradient probe on eight distinct checkpoints from two fault-trained trajectories finds lower mean-centered covariance traces under both noise types: 21 to 30% for grader flips and 40 to 63% for tool faults. These finite-sample measurements support the variance mechanism without establishing a general learning-speed benefit. The results distinguish improving reward comparisons, reducing estimator variance, and improving learning.

Battery energy storage system (BESS) dispatch must preserve operational feasibility while declining price spreads reduce the margin available to pay for cycling. We study a proximal policy optimization (PPO) controller whose pre-selection physical action mask and emergency projection are separated from a causal, forecast-informed economic advisory. All forecast-dependent methods receive the same causal 24-step forecast and grid-side settlement. Across five PPO seeds, advice-on net profit is 30.59 and 18.04 USD per 336-hour T1 and T2 window, versus 36.77 and 22.94 USD for proxy-cost MPC; PPO remains below this reference in both periods. Advice raises T2 profit from 16.45 to 18.04 USD while reducing throughput, but is immaterial in T1. On disjoint weekly blocks, PPO is stable under daily, weekly, and blended seasonal forecasts, weakens under persistence, and remains below proxy-cost MPC. Paired diagnostics localize changes to the observed 5-10 USD/MWh regime with mixed SoC-dependent effects. An M0-M6 ablation shows that mask removal sends thousands of infeasible requests to projection, while removing both physical layers exposes ramp violations. The evidence separates economic screening from feasibility enforcement without claiming formal safety, lifecycle-optimal aging, or RL dominance.

Reward-based reinforcement learning for language models, exemplified by Group Relative Policy Optimization (GRPO), collapses an entire stochastic trajectory into a single scalar reward. This is clean and scalable, but it explores and allocates reward inefficiently: a trajectory may contain many causal decisions, recovery attempts, and environment-randomness events, yet every token or action inherits one trajectory-level advantage. We study tree-based rollout construction as a compute-allocation problem for policy-gradient estimation. Our central claim is that branches should be placed not where the policy is merely uncertain, but where an additional branch most reduces uncertainty about the policy gradient per unit of compute. From a law-of-total-variance decomposition of the local policy-gradient random variable, we derive two allocation laws: new branches reduce decision uncertainty, while repeated suffix rollouts reduce continuation uncertainty. The resulting EPIG-Tree score allocates branches using the already computed rollouts. It estimates occupancy- and score-weighted value uncertainty, along with a suffix law $n_e \propto w_e \|\nabla_θ\log π(a_e|h_e)\| σ_e / \sqrt{c_e}$. Empirically, EPIG reduces gradient MSE in cloned-state control, winning in all nine dense continuous-control environments of a 13-environment sweep and recovering the reference gradient direction near-perfectly, and it improves frozen-LLM gradient calibration relative to entropy branching. In online single-turn math, tree-local credit beats flat GRPO, while branch placement is secondary to token-level credit assignment. In online multi-turn Wordle, EPIG attains the highest final win rate (0.850), overtaking flat GRPO, which saturates early at 0.790, and entropy branching as training proceeds, confirming that the gradient-estimation advantage transfers to a stateful, large-action setting.

Actor-critic architecture has been widely used in continuous robot control. However, they rely on learning a value network, introducing additional computational overhead during training. Moreover, policy learning may also be affected by the approximation error of value estimation. Critic-free group relative policy optimization methods provide a simpler training approach by removing the need for a critic. However, they fail to learn long-term action outcomes when directly applying immediate rewards to policy optimization in dense-reward environments. To address these problems, we propose Group Relative Return Policy Optimization (GR2PO), a critic-free reinforcement learning framework for continuous robot control. GR2PO estimates the discounted returns from the parallelly collected trajectories, performs group normalization at each rollout time index, and uses relative advantages and clipped targets to update the policy. To evaluate the effectiveness of the proposed framework, we instantiate it on robot control simulation environments and deploy the model to a real-world edge device. The results show that GR2PO significantly outperforms critic-free baselines that use immediate rewards and performs competitively against state-of-the-art actor-critic methods. Furthermore, GR2PO demonstrates competitive training efficiency. Inference tests on NVIDIA Jetson TX2 demonstrate the feasibility of deploying the learned policies on edge platforms. Further ablation experiments analyze the effects of parallel group size, return estimation methods, and target clipping ratio on learning performance. To support follow-up research, we will make the complete code publicly available after the paper is accepted, including the framework implementation, experimental configuration, and training and evaluation scripts.

Reinforcement learning for LLM agents involves two distinct optimization di- mensions: how environment feedback is exploited within a trajectory, and how complete trajectories are aggregated across a batch. We formulate these dimen- sions as Intra-Trajectory Feedback Attribution and Inter-Trajectory Objec- tive Aggregation, and introduce BATON (Bayesian Attribution and Trajectory Objective Normalization), a dual-axis policy optimization framework. BATON instantiates the first axis with Bayesian Feedback Attribution, which constructs a feedback-conditioned posterior over sampled actions, and the second with Trajec- tory Mass Normalization (TMN), which assigns equal optimization mass to com- plete trajectories. Experiments with GRPO and GiGPO on ALFWorld, WebShop, and SearchQA show that both axes provide independent gains and that their combi- nation consistently achieves the strongest overall performance across model scales.

Training embodied foundation models typically requires massive-scale datasets and extensive computational resources, yet often suffers from three critical limitations: (1) inefficient sample utilization due to low-informative samples; (2) imbalanced gradient contributions across heterogeneous tasks; and (3) severe credit assignment problem in long-horizon planning, where trajectory-level rewards indiscriminately penalize all tokens. To address these issues, we propose an efficient training paradigm that achieves state-of-the-art average performance through strategic data selection and hierarchical policy optimization. Our approach consists of three synergistic stages. First, Rejection Sampling-based Fine-Tuning (RSFT) filters out low-informative samples to establish robust behavioral priors while preventing distributional collapse. Second, Iterative Rejection GRPO (IR-GRPO) employs task-specific queues stratified by difficulty to keep datasets balanced across reinforcement learning iterations, coupled with a hybrid reward mechanism for precise cross-task feedback. Third, to enhance long-horizon task planning, we introduce Trie-GRPO, a novel reinforcement learning algorithm based on action prefix trees, which enables step-level advantage estimation. This resolves the credit assignment problem by isolating intermediate correct decisions from downstream errors, while effectively balancing exploration efficiency and depth compared to conventional search trees. As a result, EmbodiedMind achieves a state-of-the-art average performance of 70.02% across 18 benchmarks, and significantly outperforms other embodied foundation models in long-horizon task planning accuracy. Our project will be released for reproducibility.

In reinforcement learning for large language models, Proximal Policy Optimization (PPO) commonly uses a critic to estimate state values and reduce the variance of policy updates. However, we uncover a systematic failure mode in PPO critics, which we call Value Flattening: state values, estimated from multiple Monte Carlo continuations, change sharply across intermediate states while critic predictions remain comparatively flat. We further observe this phenomenon in a controlled FrozenLake environment and find that it becomes more pronounced as the state space grows. Our theoretical and empirical analyses relate Value Flattening to an implicit variance penalty in the critic loss and redundant updates from temporally correlated states with similar gradients. Motivated by these findings, we introduce SParse Proximal Policy Optimization (SP$^3$O), which applies the value loss to only a few well-separated states in each response to mitigate both effects. Experiments on Qwen3-Base show that SP$^3$O with only three states supervised per response can mitigate Value Flattening and consistently improve the learned policy across model sizes and evaluation suites. Together, our results identify Value Flattening as an important yet overlooked failure mode of critic learning in standard PPO and show that a simple sparse supervision strategy can mitigate it.

Streaming automatic speech recognition (ASR) must be judged jointly on what it transcribes and on how quickly it commits each word. Delayed streams modeling (DSM) has become the dominant paradigm for streaming large audio-language models, exposing a structural delay $τ$ that bounds the decoder's lookahead. We show that $τ$ is a poor proxy for user-perceived latency, and that the alignment-based supervision of DSM leaves latency on the table: the same forced-aligned transcript is used at every $τ$, forcing the model to withhold words it could already commit. We introduce AWED, a word-level emission-delay metric defined relative to the acoustic end of each word, and post-train a DSM recognizer with GRPO under a reward that scores transcription accuracy and measured delay jointly. Trained at a single operating point ($τ=6$ frames), our model dominates both its supervised fine-tuning initialization and the Voxtral Realtime backbone across all evaluated lookahead budgets: it cuts WER by 30.8% relative at an 80,ms structural delay, and by 5.7% relative at 480,ms while lowering median AWED from 1.17,s to 1.04,s. Latency-rewarded post-training thus advances the accuracy--latency Pareto frontier of streaming ASR without architectural change.

Limited controlled evidence exists on how training data, adaptation method, and model scale jointly affect tool-calling performance in language-model agents. We evaluate supervised fine-tuning (SFT) with LoRA, reinforcement learning (RL) via Group Relative Policy Optimization (GRPO), and SFT followed by GRPO across six Qwen3 models from 0.6B to 32B parameters, covering both in-distribution performance and cross-dataset transfer. SFT with LoRA is the strongest in-distribution method throughout the 0.6B-32B range and best in 15 out of 18 experimental settings. On cross-dataset transfer, the methods are closer: GRPO wins 29 out of 54 settings where training and test datasets differ, but its margin over SFT averages under one point, and SFT->GRPO is rarely strongest in either comparison. Dataset mixing gives consistently strong transfer while staying close to specialized in-distribution training, regardless of method. Additional analysis further confirms that LoRA outperforms full-parameter fine-tuning, demonstrating that LoRA better preserves pretrained agentic behavior.

Wireless edge caching networks typically consist of many independent Base Stations (BSs), each facing its own request rate and content popularity profile. Training a Reinforcement Learning (RL) caching agent from scratch at every BS forces each agent to relearn, through slow trial and error, a decision problem that is structurally identical across the network. Meta-reinforcement learning removes this redundancy by learning a shared initialization that adapts to any BS in a few local updates; however, meta-training itself becomes the bottleneck at scale: the meta-gradient must be estimated from a small subset of BSs at each meta-iteration, and sampling this subset uniformly at random yields a high-variance estimate, an issue existing meta-RL caching frameworks leave unaddressed. This paper proposes a meta-reinforcement learning framework for caching across independent, non-overlapping BSs that directly targets this bottleneck. Each BS runs a local Proximal Policy Optimization (PPO) agent, formulated as a Semi-Markov Decision Process (SMDP) over content popularity, size, lifetime, and importance, while a shared meta-policy is learned via a Model-Agnostic Meta-Learning (MAML)-style loop. To scale meta-training and accelerate convergence, we introduce gradient-based clustering, which groups BSs by local gradient similarity and draws from every cluster, in proportion to its size, at each meta-iteration. We prove, via an Analysis of Variance (ANOVA)-style decomposition of gradient variance, that this strategy yields a strictly lower-variance meta-gradient estimator than uniform random sampling under BS heterogeneity.

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models (LLMs). We introduce Bellman Policy Optimization (BPO), a critic-free method derived from Policy Mirror Descent (PMD). For autoregressive generation with terminal rewards, BPO uses the Bellman equations to reformulate PMD as a trajectory-level objective. The reformulation avoids estimating state values at intermediate states. We prove that it has the same unique optimal solution as the original PMD objective. We derive the practical BPO loss by approximating this objective. Its mismatch-correction weight is a smoothed ratio of complementary token probabilities. Experiments on mathematical reasoning benchmarks demonstrate the effectiveness of BPO.

Reinforcement learning with verifiable rewards (RLVR) has become a central approach for improving mathematical reasoning in language models, but long-form completions introduce a difficult credit-assignment problem: different parts of a solution trace may contribute unevenly to final correctness. Existing policyoptimization objectives for RLVR commonly apply importance-sampling correction at either the token level (GRPO, DAPO) or the sequence level (GSPO), imposing different granularities for assigning credit across a response. We introduce Hierarchical Importance-Sampling Policy Optimization (HISPO), a segment-level policy-optimization method that constructs rollout-time entropy-derived contiguous segments, assigns soft entropy-based saliency weights, and applies clipped importance-sampling correction at the segment granularity. This provides an intermediate correction unit between token-level GRPO/DAPO and sequence-level GSPO. We evaluate HISPO by fine-tuning Qwen3-1.7B-Base on mathematical reasoning tasks. Across six benchmarks, HISPO improves Pass@8 over the strongest baseline on all benchmarks and matches or exceeds the strongest baseline in Acc@8 on five of them. On AIME25, HISPO improves over GRPO by +3.75 Acc@8 and +3.78 Pass@8, and over GSPO by +2.50 Acc@8 and +1.27 Pass@8. These results suggest that segment-level correction is a promising granularity for RLVR in long-form mathematical reasoning.

Combining aerial thrust with spring-loaded hopping makes monopedal quadcopters promising for locomotion over complex terrain, but heuristic proportional-integral-derivative (PID) tuning limits coordination between active thrust and passive contact dynamics. We present a direct estimated-state-to-motor Proximal Policy Optimization (PPO) policy that commands four motors without an explicit hopping state machine or low-level attitude PID. Its reward combines Energy-Manifold Shaping for mass-normalized vertical-energy tracking and apex-state anchoring with Efficiency Shaping, which uses a history-aware power estimator to penalize general power use, impose an additional airborne-power cost, and penalize airborne near-stationarity. In representative hardware runs, the PPO-based control stack reduced cycle-averaged measured electrical power by 30.7% and mean total normalized thrust by 49.8% relative to the tuned PID-based control stack, while retaining repeatable commanded-height hopping and more concentrated landings. These observations are consistent with improved use of passive dynamics and reduced measured electrical demand.

Significant progress has been made in safeguarding deep reinforcement learning (DRL) policies against input perturbations. Developing robust DRL involves three main stages: algorithm design, implementation, and evaluation. In this work, we identify and address a key limitation at each stage. First, we introduce Adversarial Importance Sampling (Advis), a method that uses importance sampling over trajectories from standard training to estimate and optimize verifiable worst-case returns. Advis satisfies three desirable criteria not jointly achieved by prior work: it requires no additional environment interactions, no auxiliary networks, and captures long-term robustness. Second, we introduce advrl, a modular PyTorch library that provides clean, single-file implementations of existing robustness methods and adversarial attacks, facilitating rapid prototyping and enabling reproducible and traceable evaluations. Third, we revisit evaluation under learned adversaries and show that optimal adversarial hyperparameters do not transfer across agents, which can lead to an overestimation of robustness when using a limited set of attacker configurations. Accordingly, we evaluate policies against a large and diverse set of attackers, using 6-14x more configurations than prior work. Finally, we evaluate our approach on continuous control environments, demonstrating its effectiveness relative to existing baselines. The code is available at: https://github.com/AmineAndam04/advrl

Continuous emotion control in text-to-image generation requires a model to improve affective alignment without changing the objects, layout, or scene described by the prompt. Existing supervised emotion-injection methods often optimize feature-space proxies and may therefore exhibit emotion-semantic drift, in which stronger emotional conditioning is accompanied by unintended content changes. We address this problem with a flow-matching image-generation framework that combines continuous valence-arousal (VA) conditioning, Group Relative Policy Optimization (GRPO), and a neutral semantic anchor. The deterministic probability-flow ODE is converted into a marginal-preserving SDE, yielding non-degenerate transition densities for trajectory sampling and policy-ratio estimation. A frozen CLIP-based VA regressor supplies a terminal reward measuring the distance between the predicted and target VA coordinates, while an image generated from the same prompt under zero VA conditioning provides a feature-space reference for semantic preservation. A reduced denoising schedule is used for online RL sampling, whereas the original schedule is retained at inference. Experiments on 3,300 prompt-emotion combinations show substantially lower valence and arousal errors than the VA-conditioned baseline and an improved CLIPScore relative to EmotiCrafter, with a measurable trade-off in reference-free image quality. The results support anchor-regularized Flow-GRPO as a practical approach to balancing emotional alignment and semantic consistency in continuous-affect image synthesis.

Warning: This submission studies stereotypes and biases, and contains toxic and offensive examples, used for illustration purposes only. Fairness benchmarks such as BBQ have become the de facto standard for fairness evaluation across major model families. We argue that these benchmarks are too easy to support their role: training Qwen 2.5 7B Base with Group Relative Policy Optimization (GRPO) on a single BBQ example, or placing that example in context as a one-shot demonstration for in-context learning (ICL), lifts mean BBQ accuracy from 79.9% to 92.9% and 99.0%, respectively, closing 80% of the gap to its large-scale RLHF counterpart (96.1%) with GRPO, and surpassing it with ICL. These effects generalize across model families. A cross-conditioning analysis shows the improvement is carried by the reasoning traces generated by the model, and one example suffices to elicit a category-agnostic ``missing evidence'' reasoning pattern. We argue that BBQ-style multiple-choice abstention benchmarks measure a single structural cue, and a model that solves them does not thereby become fair. We call for evaluation suites that cover a broader spectrum of fairness alignment.

Reinforcement learning over a frozen reasoner has become a common recipe for teaching a policy which external tools to invoke. We show that this recipe becomes structurally mismatched in specialist scientific settings where the complete tool-subset space is enumerable. There, a small set of recurring computational capabilities covers the domain, so the space of tool subsets is combinatorial yet small enough to enumerate, and GRPO still estimates an action expectation from a handful of sampled rollouts. Worse, the approximation degrades as training succeeds: as the policy concentrates on preferred subsets it resamples them, sampled rewards collide, and the group-normalized advantage vanishes. On genomic reasoning the fraction of questions yielding no reward signal rises from 0.2% under a uniform reference policy to 20.8% after GRPO training. As a remedy, we introduce FGPO (Full-Group Policy Optimization), which (1) scores every tool subset and optimizes the exact action expectation, so each update sees the complete action space, and (2) precomputes the reward of each question--subset pair into an exhaustive table, removing frozen-reasoner calls from the training loop entirely. Across five frozen reasoners and three genomic benchmarks, FGPO outperforms GRPO in all 15 settings by 6.75 points on average and up to 14.20, while a standard on-demand GRPO schedule would require 2.4 times as many frozen-reasoner reward evaluations and, on GenomeQA, FGPO cuts invoked tools per question from 2.36 to 1.40.

In reinforcement learning with verifiable rewards (RLVR) trained with group relative policy optimization (GRPO), the KL-free reward-advantage term studied here depends on within-group reward variation. If all rollouts in a group are correct or all are wrong, their group-relative advantages are identically zero; these zero-advantage silent groups provide no reward-advantage gradient, yet uniform sampling spends 39% of a run's rollouts on them. History-based prompt selection must first spend target-policy rollouts to estimate difficulty, creating a cold start with rollout waste; ThinkPrior instead uses an external anchor in one offline pass to construct a zero-rollout difficulty prior before the first target-policy rollout. The verifier-scored anchor pass rate supplies an external-anchor initialization for a Beta posterior; ThinkPrior selects by expected learnability and then updates from training outcomes, changing neither the loss nor the optimizer. On Qwen2.5-Math-7B across sixteen seeds, ThinkPrior more than halves early silent groups and cuts wasted rollouts through step 30 by nearly a fifth, while we detect no difference in final accuracy. On this 250-prompt pool the fixed-budget result is a reallocation rather than a net saving. The measured ThinkPrior+DAPO composition reduces generated rollouts by 10.6% while both arms retain the same 3840-rollout update budget. The prior requires no target-policy rollout before the first selection, but the posterior thereafter uses target-policy outcomes.

Model-based reinforcement learning (MBRL) is a family of RL methods that learn a model of the environment and use it for action selection, making it well suited to robotics due to its sample efficiency. Combining learned models with online planning can further improve action selection, as the planner can exploit the model to find better actions than the learned policy alone. Recent methods combining learned policies with online planning typically learn the value of the policy rather than the stronger planner-guided behavior. We present CAST (Critic with Alternating State-value Target), which uses planner-guided behavior to improve value learning while regularizing the value estimate with the current policy. CAST replaces the action-value critic with a state-value critic, trained using a target that combines a real planner-guided transition and an imagined transition under the current policy. The resulting value function corresponds to an alternating process between planner-guided behavior and the current policy, allowing it to benefit from the stronger planner behavior while being regularised by the policy being learned. We evaluate CAST on the DeepMind Control and HumanoidBench Suites against several state-of-the-art methods, and demonstrate successful transfer to a physical Unitree Go2 quadruped performing a dynamic handstand.

Reinforcement Learning with Verifiable Rewards (RLVR) has been central to the recent success of Large Reasoning Models. However, while RLVR significantly improves single-sample accuracy, it often fails to expand the model's intrinsic reasoning coverage (pass@k) due to limited exploration during training. To address this, we optimize the structural design of train-time rollouts to enhance pass@k. Our analysis identifies three key design principles: (1) difficulty-adaptive rollout can play an important role in expanding pass@k, beyond serving as an efficiency heuristic; (2) tree-based rollout outperforms parallel sampling in discovering correct answers; and (3) sentence-entropy-guided forking overcomes the localization phenomenon of token-level branching to maximize semantic diversity. Building on these insights, we propose DATPO (Difficulty-Adaptive Sentence-entropy-guided Tree-structured Policy Optimization). DATPO integrates difficulty-adaptive tree search with a sibling-diversity advantage term, explicitly promoting semantic diversity to expand reasoning coverage during training. Experiments on mathematical reasoning benchmarks demonstrate that DATPO outperforms baselines especially in pass@k, which directly translates to superior test-time scaling performance.

Multi-agent large language models solve complex tasks by coordinating several policies in a shared environment. However, existing reinforcement learning methods usually optimize each response or trajectory separately, even when several outputs jointly cause one state transition. Consequently, the update unit differs from the action executed by the system. To address this problem, we propose SRPO (Setwise Relative Policy Optimization), which treats the active set the minimal set of outputs consumed by one transition, as one multi-agent action. Specifically, SRPO combines member log-ratios into one cardinality-normalized set ratio, assigns one relative advantage, and clips the set once. This formulation unifies division of labor and joint co-evolution as actions with different set sizes. Experiments on mathematical reasoning and multi-turn search demonstrate one training interface for fixed, mixed, and dynamically routed workflows across four model scales, with the strongest macro-average results among the reported comparisons. Optimization diagnostics further characterize its stability under different event reductions and set sizes.

In electric delivery fleets, mid-shift charging is non-trivial: each vehicle must decide when, where and how much to charge to finish on time with battery above a safety floor. The choices are coupled: queues build where too many vehicles pick the same station. Prior work resolves this coupling with central dispatching, precomputed schedules or reservations, machinery that charging infrastructure rarely supports. Instead, we use a family of learning agents under purely local control: every vehicle runs the same policy, deciding alone from its time budgets and broadcast station occupancies, leading to emergent coordination without central control or messaging. We validate this paradigm in simulation on real OpenStreetMap networks of twenty cities, each with a frozen scenario calibrated by an omniscient Oracle (99.5% of shifts completed on time), whereas a naive greedy rule (nearest station on low battery) completes just 73%. Agents trained with neuroevolution (NEAT) and policy gradients (PPO) on four cities and deployed zero-shot across all twenty, sixteen never seen in training, complete 96.8% and 98.6% of shifts, with the policy-gradient controllers proving more robust when demand or vehicle characteristics drift beyond the trained regime. In contrast, tuned threshold heuristics that read vehicle urgency alone fall short in contended cities (~80%). Through training, these learning agents rediscover partial charging and short opportunistic sessions, and route around busy stations, cutting per-session queue waits from about 45 minutes to under 2. In summary, this coordination paradigm balances local urgency against public occupancy, reaching near-Oracle performance at minimal implementation cost.

Agent reinforcement learning (RL) increasingly runs through full execution harnesses, and a multi-harness recipe mixes two choices: exposing the policy to several harnesses, and comparing their rewards inside one relative-advantage group. We isolate the second choice in repository-level coding. From one Qwen3-8B supervised warm start we replay the same frozen task-harness records from Aider, OpenHands, Qwen Code, and SWE-agent, with the same number of updates, under two rules for group-relative policy optimization (GRPO), Within (one group per task-harness pair) and Cross (harnesses pooled within a task), and score every checkpoint with a sealed SWE-bench Verified oracle on four source harnesses and a minimal harness held out of training. The evaluation harness is the dominant variable: across 24,000 sealed evaluations it moves the mean solve rate from 2.14% to 9.27%, a factor of 4.3, where the training recipe moves it by 1.16. The grouping rule is not. On the held-out harness, Cross minus Within is +0.25 pp, 95% confidence interval [-0.48, +1.02], at eight attempts per task, and +0.16 [-0.41, +0.72] pooled over three training seeds whose individual estimates change sign. Each rule's own seed range, 0.42 to 0.45 pp, exceeds the difference between them. Both rules place their largest gains on the same source harness. The pooled advantage carries the harness: an out-of-fold classifier recovers the generating harness from Cross's advantage +4.48 pp above the shuffled-label baseline and from Within's not at all, and the two rules still reach the same held-out score and action distribution inside each harness. Re-collecting half the training data on-policy does not change this. Cross-harness credit yields configuration adaptation and no more portable capability than within-harness credit. Multi-harness RL reports should state the grouping boundary and test under an unseen harness.

Existing post-training pipelines for coding and terminal agents suffer severe token and control fidelity errors: simplified training environments mismatch production deployments, and offline token reconstruction from agent logs distorts original prompts and conflates policy calls with background model operations. We present a fidelity-aware training coupling framework that retains trainer-side sampling over original prompts, eliminates spurious model calls via a negotiated training protocol, and restricts loss computation to verifiable token spans with closed-failure guarantees. We further propose Certified Divergence Proximal Policy Optimization (C-DPPO), which establishes tight two-sided TV certification bounds, adaptive-K rules, budget-aware sequence guarantees, and error-robust policy masking atop standard DPPO. Evaluated on matched Baize5B and Baize10B models with identical training and test protocols on TMax-100, C-DPPO yields a consistent +3.0-point performance gain over standard DPPO across model scales. Certificate audits validate the reliability and full operational coverage of our certified training pipeline.

Group Relative Policy Optimization (GRPO) is widely studied for reinforcement learning with verifiable rewards, where its advantage estimator assigns each rollout a magnitude from within-group reward statistics. In the common case, this magnitude rewards rollouts that reach the correct answer through reasoning. Yet, an overlooked case shares the same surface: a rollout may land on it by guessing, and the formula still assigns a high magnitude, which we identify as the spurious advantage. This arises in three cases: bounded-answer tasks with a small candidate set; open-answer sets hosting bounded sub-cases; and search agents whose budget opens many paths to the same answer. In all three, this misleads the policy toward guess-like behaviors. We propose SIGNBALANCE, whose magnitude is composition-free: it keeps the verifier sign, uses a global scale, and restores zero-mean balance via a stop-gradient per-class rescaling. Across math and search agent benchmarks at different scales, SIGNBALANCE matches GRPO on open-answer math and improves on bounded-answer math and search agents. Code will be released.

RL-based post-training for reasoning models is increasingly bottlenecked by repeated fresh rollout generation, particularly in agentic settings where environment interaction dominates wall-clock cost. Replay can reduce this burden by reusing past trajectories, but existing methods typically embed it within larger training pipelines involving exploration, experience restructuring, or mixed-policy optimization. This makes replay's own contribution difficult to isolate. We ask a focused question: how far can principled replay selection alone go? We introduce Headroom-Drift Replay, a group-level replay control primitive for GRPO that separates reuse into two decisions. Headroom ranks stored groups by remaining learning value, while Drift gates them by compatibility with the current policy. The fresh on-policy stream remains unchanged, and the method adds no auxiliary generation or training machinery. Across mathematical reasoning, multimodal reasoning, and Agentic Search benchmarks, this single intervention outperforms naive replay and matches or exceeds broader replay methods on Avg Mean@32. In Agentic Search, where environment interaction dominates cost, it delivers comparable quality at materially lower wall-clock time.

We study the allocation of indivisible goods among agents with identical additive valuations, focusing on envy-freeness up to one good (EF1) and Nash social welfare (NSW). Since every maximum-NSW allocation is EF1 under additive valuations, the associated threshold problem inherits the known strong NP-hardness of NSW maximization under identical additive valuations and is strongly NP-complete. We therefore focus on welfare guarantees satisfied by arbitrary EF1 allocations. Although every such allocation is known to achieve an $e^{-1/e}$-approximation to the unrestricted optimal NSW, we identify conditions yielding stronger guarantees. Under uniform valuations, every EF1 allocation is NSW-optimal. Under an $\varepsilon$-small-item condition, every EF1 allocation achieves an explicit approximation ratio $ρ_n(\varepsilon)$ satisfying $ρ_n(\varepsilon) = 1-O(\varepsilon^2)$ as $\varepsilon\to 0$ for fixed $n$. We further consider the stronger sequential requirement that $\operatorname{EF1}$ be maintained after every item assignment. For this setting, we introduce \emph{PriorityNet}, a deep reinforcement learning framework trained with Proximal Policy Optimization (PPO) and equipped with prospective $\operatorname{EF1}$ action masking, which guarantees prefix-wise $\operatorname{EF1}$ by construction. Across 3,000 test instances in each of the offline full-information and random-order online regimes ($n\in[2,20]$, $m\in[5,100]$), PriorityNet achieves mean normalized $\operatorname{NSW}$ values of $0.9911$ and $0.9701$, respectively. Relative to the offline Longest Processing Time (LPT) heuristic and the online least-valued-bundle rule, it attains instance-wise win-minus-loss rates of $+27.10\%$ and $+17.87\%$. Its aggregate welfare matches the offline LPT baseline to four decimal places and modestly improves upon the online baseline, from $0.9694$ to $0.9701$.

Offline reinforcement learning (RL) must reconcile two competing requirements: policy updates should stay near dataset-supported actions to keep value estimates reliable, yet meaningful gains often require moving beyond the behavior distribution. We develop a geometric view of offline actor updates by modeling policies as a probability manifold endowed with a chosen metric geometry. Under this lens, a broad class of offline actor objectives can be interpreted as a single proximal policy improvement step (SPI), i.e., an implicit discretization of a manifold gradient flow induced by a critic-defined energy. Building on this insight, we propose multi-step proximal policy improvement (MPI), a plug-in refinement mechanism that composes sequential re-centered proximal steps. MPI enables controlled policy improvement beyond dataset support while retaining proximal control at each refinement. The framework accommodates multiple policy geometries and admits practical instantiations for deterministic and diagonal-Gaussian policies. Experiments on D4RL benchmarks show that small numbers of MPI refinements improve strong offline baselines, including TD3+BC, ReBRAC, and IQL, on many tasks. Focused diagnostics further distinguish re-centered refinement from fixed-objective update scheduling and characterize limitations under critic error.

With the rapid development of the Internet of Things, computation intensive directed acyclic graph (DAG) tasks have become increasingly common in cloud-edge-end collaborative environments. However, cloud, edge, and end nodes are highly heterogeneous in computing capacity, network bandwidth, and energy consumption, which makes the efficient scheduling of tasks with complex dependencies an NP-hard problem. Traditional heuristic algorithms and conventional reinforcement-learning methods often fail to capture the spatio-temporal dynamics of system resources. This paper proposes PPO-STGNN, a DAG task-scheduling algorithm that integrates proximal policy optimization (PPO) with spatio-temporal graph neural networks (STGNNs). The method uses an STGNN to extract features from both the DAG task topology and the physical cloud-edge-end resource graph, and then optimizes the scheduling policy through PPO to minimize makespan and schedule length ratio (SLR) while improving CPU and memory load balancing. To accelerate convergence, a multi-teacher behavior-cloning mechanism is introduced for pretraining. Experimental results show that PPO-STGNN significantly improves load balancing while maintaining a low completion time, making it suitable for dynamic and heterogeneous cloud-edge- end DAG scheduling scenarios.

Graph-based policy optimization improves credit assignment for long-horizon LLM agents by organizing rollout trajectories into state-transition graphs. However, existing methods construct graphs independently within each policy update, discarding transitions discovered by earlier policies and limiting advantage estimation to small, batch-local rollout groups. We propose \emph{Temporal Instance-Graph Policy Optimization} (TIGPO), which extends graph-based credit assignment across policy updates. TIGPO maintains a persistent transition graph for each task, allowing valid transitions discovered by different policy versions to jointly determine credit for current rollouts. To actively reconnect current exploration with historical experience, TIGPO allocates a fixed rollout budget between Exploration slots for ordinary task sampling and Revisit slots for delayed reattempts of previously explored tasks. For each revisit, TIGPO pairs the current rollout group with its corresponding earlier Exploration group to construct a cross-temporal reference. The enlarged reference is designed to stabilize relative advantage estimation under small rollout groups, while comparison on the same task directly captures policy improvement across training stages. Historical transitions and scores serve only as structural and detached statistical references and are never replayed in the policy loss. Experiments on ALFWorld and WebShop demonstrate that TIGPO consistently outperforms prior group-based and graph-based policy optimization methods.

End-to-end autonomous driving has increasingly adopted world model-based reinforcement learning frameworks to improve learning efficiency through \textit{imagined rollouts}. However, existing world models suffer from three key limitations: temporal inconsistency in long-horizon imagined rollouts, inadequate modeling of ego-environment interactions, and limited adaptability to diverse driving styles. To address these challenges, we propose \textit{StyleDrive}, a world-model-based learning framework that jointly enforces long-horizon consistency, explicitly disentangles interactive traffic states, and supports multi-style policy optimization within a unified learning paradigm. First, we introduce a temporal consistency regularization that integrates historical latent states through gated cross-attention, stabilizing long-horizon imagined rollouts and mitigating error accumulation. Second, we design an explicit state disentanglement module that separates ego-relevant from ego-irrelevant interactive states, enabling more interpretable and efficient decision-making in complex traffic scenarios. Third, we enable multi-style driving behaviors through Group Relative Policy Optimization, which replaces per-step reward optimization with trajectory-wise relative advantages, reducing reward variance and supporting diverse driving styles without retraining. We evaluate StyleDrive on the Bench2Drive closed-loop driving benchmark, achieving a driving score of 88.44 (+17.08 over the previous best world model-based method) and a success rate of 66.82 (+16.58). Furthermore, we deploy StyleDrive on a real automated guided vehicle platform and demonstrate promising sim-to-real transfer capability in dynamic driving scenarios.

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.

Compact instruction-following rerankers are attractive for deployment, but conventional distillation pipelines typically train students by offline imitation of teacher outputs on a fixed set of examples, constraining supervision to the teacher's observed ranking space. We revisit reranker distillation through the lens of reinforcement learning. We propose a two-stage framework combining off-policy teacher optimization with on-policy student distillation. In Stage 1, a 4B teacher reranker is strengthened with off-policy GRPO using LLM-judge feedback on 88K instruction-following examples. In Stage 2, a compact 1B student samples rankings from its own policy and receives soft teacher-derived rewards on those rankings, coupling student exploration with knowledge transfer. Our strongest gains appear under distribution shift. On MAIR-11, the original 11-subset, 869-query evaluation, the proposed student reaches 0.7670 nDCG@6, outperforming offline listwise KD by +4.6 points. Controlled comparisons against offline pairwise RankNet KD and on-policy GKD show that neither changing the offline distillation objective nor moving teacher-distribution matching on-policy reproduces the performance of reward-based on-policy distillation over student-sampled rankings. The advantage persists on MAIR-Full: across all 126 tasks and 9,356 queries, the proposed method obtains the highest task-macro point estimates among the evaluated distillation variants, reaching 0.6808 nDCG@6 and 0.7865 MRR@6. It also exceeds two released 7B RL-trained rerankers on the comparable MAIR-11 evaluation, while the same Stage 2 training procedure consistently improves three architecturally distinct alternative student backbones. On the 9,861-query validation benchmark, the resulting 1B reranker achieves 0.7624 nDCG@6 while providing a favorable quality-efficiency tradeoff relative to larger alternatives.

Combining learned policies with model predictive control can leverage learned task priors while retaining online adaptation to new objectives and constraints, but performance degrades when the policy is out of distribution. In policy-guided model predictive path integral (MPPI) control, a policy-centered warm-start approach centers the sampling distribution on the policy output. When the prior is mismatched, centering the sampling distribution on the policy output restricts exploration around an unsuitable solution and prevents recovery toward the task optimum. We propose Proximal Prior Injection (ProxPI), which retains nominal-centered MPPI sampling and incorporates the policy through a soft proximity cost. This matches the in-distribution performance of existing prior-injection schemes while enabling the optimizer to escape an inaccurate policy and recover vanilla MPPI-level performance. We theoretically show that re-centering on the prior discards the optimizer's correction at every update, whereas nominal-centered sampling retains it and converges to a solution set by both the task cost and the prior, and that this failure is not removed by a larger rollout budget. Simulations and real-robot experiments demonstrate robust performance under both in-distribution and out-of-distribution tasks.

Language models can ignore prompt evidence when it conflicts with memorized knowledge. Post-training can make models follow such evidence more reliably, but it is unclear whether these gains require new machinery or strengthen machinery already present. We compare nine post-training arms spanning GRPO, SFT, and DPO from one starting checkpoint, with key comparisons extended across scales and families. We estimate a grounding direction from that checkpoint before training. Across five tested GRPO variants, grounding gains are small. For the two variants replicated across seeds, equivalence tests bound their effects below the conflict-SFT gain even as the rewarded metric improves. Conflict-SFT improves grounding moderately, while DPO drives grounding near ceiling on its matched distribution. Conflict-SFT and DPO largely use the same causal attention-head set as the starting model. Subtracting the starting-model direction suppresses both gains, while adding it to the starting model recovers 35% of DPO's gain at a dose passing all stated side-effect checks. After a supervised warm start makes the context answer appear in more rollouts, the same GRPO recipe adds essentially no further grounding gain. In our setting, grounding gains largely depend on machinery already present in the starting model.

Many automobile and mobility companies deploy learned driving policies on embedded computers with limited memory and power. Pruning, knowledge distillation, and quantization are the standard methods to reduce the size and the inference cost of these policies. However, these methods are commonly assessed by aggregate numerical scores, and such scores may not reflect the ability of the policy to drive safely when interacting with other road users. In this study, we propose a stage-wise closed-loop evaluation approach to follow a driving policy through a compression pipeline. We formulate the driving task as a partially observable Markov decision process (POMDP) and train a belief-state policy with proximal policy optimization (PPO) in Gym-Duckietown. We then extract the actor, compress it one stage at a time, and evaluate it on five driving curricula. We show that structured pruning is the stage at which the driving capability is first lost. Meanwhile, distillation improves the pruned actor, but the improvement is limited by its rehearsal data. Integer quantization of the improved actor loses some of the curricula that require the vehicle to stop and then resume. Interestingly, the same procedure on the unpruned actor preserves all five curricula. Our study thus provides an empirical analysis aiming to answer the currently active discussions on how to accept a compressed driving policy, so as to achieve a safe and statistically reliable deployment of automated driving functions.

An image may be worth a thousand words, but most captioning models describe it in only a few. Modern vision-language models produce fluent high-level captions, yet routinely miss the attributes, counts, textures, materials, and spatial relations that make an image visually specific. Recent multi-stage systems recover some of these details through generation, decomposition, verification, and rewriting, but they do so at the expense of substantially higher inference latency. We propose SimLoss, a reference-free embedding-space objective for single-pass fine-grained image captioning. SimLoss trains a vision-language model to align its projected hidden-state representation with a frozen image embedding through an InfoNCE contrastive loss, supplying a dense visual supervision signal before any text is decoded, and requiring neither human-written fine-grained captions nor pseudo-captions from a multi-stage pipeline. We instantiate it as SimLoss FFT, which backpropagates through a locally available embedding model, and SimLoss GRPO, which treats that model as a black-box reward. Compared with single-pass, multi-stage verification, reward-optimized, and perception-aware baselines, the fully differentiable fine-tuning variant, SimLoss FFT, achieves the highest precision while nearly matching the F1 score of the multi-stage method, all while retaining single-pass inference and running roughly 20 times faster than the multi-stage pipeline. The reward-based variant SimLoss GRPO attains the strongest recall. Together, these results show that embedding-space supervision can recover the quality of multi-stage verification at the latency of a single-pass captioner.

The next generation of mobile networks is envisioned as fully AI-native, with AI-RAN architectures embedding small language models (SLMs) to perform reasoning over real-time telemetry. The state-of-the-art training paradigms for telecom LLMs, exemplified by RANSTRUCT-style supervised fine-tuning (SFT) on curated instruction data, are limited to post hoc rationalization. Here, the explanations, when produced at all, are generated after or independently of the decision, leaving the decision process unauditable. Pre-hoc reasoning, where a causal reasoning trace is produced before the output label, is preferable, and the broader LLM reasoning literature has made real progress toward it via RL methods such as Group Relative Policy Optimization (GRPO). Here we observe that transplanting this recipe into the telecom setting runs into a cold-start barrier: SLMs either learn to output the desired format or learn to predict the label, but rarely both. We identify this barrier and propose CRAFT, which stands for Cold-start Reasoning Alignment via Fine-Tuning, a data-centric method to autonomously generate a verified dataset of (input, trace, label) triplets. CRAFT fine-tunes SLMs on this verified data using low-rank adaptation (LoRA), requiring substantially less compute and wall-clock time than GRPO-based methods. On the TRACTOR and IC xApp telecom datasets, CRAFT achieves up to 86.5% and 94.6% for accuracy and F1 with no parse failures, while direct GRPO and SFT+GRPO fail to exceed 28% and 53.5% F1 with multiple parse failures. We further show that CRAFT-initialized policies serve as a robust foundation for subsequent GRPO fine-tuning, as under diverse reward functions the performance remains consistent with no parse failures. Finally, we demonstrate that CRAFT consumes 59% less energy than GRPO-based baselines, making it a sustainable path to deployable, auditable AI in 6G RAN.

Group relative policy optimization for reinforcement learning with verifiable rewards (RLVR) typically uses a fixed importance-sampling (IS) ratio clipping boundary across all rollouts. We identify a key limitation: rare correct rollouts on harder problems and abundant correct rollouts on easier problems are clipped at comparable rates, despite contributing very different learning signals. Rollouts with low group success exhibit larger IS ratios and carry stronger gradient signal for exploration and solving new problems, yet are disproportionately suppressed by fixed clipping. To address this, we propose Group Adaptive Clipping Policy Optimization (GAPO), a plug-in modification to GRPO methods that adapts the clipping boundary to the rollout advantage. GAPO is motivated by a reverse-KL trust-region perspective, which suggests that rollouts with larger learning signal should receive proportionally greater update headroom. GAPO requires no reward shaping and preserves the standard PPO/GSPO surrogate while adapting only the clipping threshold. Across Qwen and Llama models, GAPO consistently improves both Pass@1 and Pass@k over fixed clipping and advantage-shaping baselines on math reasoning and coding benchmarks where the pass rates by the base model are relatively low.

Codec-based text-to-speech (TTS) models make language-model post-training applicable to speech generation, but it remains unclear when learned perceptual predictors can serve as reinforcement learning rewards without losing alignment with human listeners. We study this question with Group Relative Policy Optimization (GRPO) using learned rewards for anime-like speaking style, naturalness, likability, and arousal. To prevent perceptual rewards from being optimized through transcript drift, we introduce a character error rate (CER) zone constraint and compare policy optimization with Best-of-$N$ reranking under the same reward gate. Across single-reward runs, each reward primarily improves its own target metric, showing that subjective predictors are not interchangeable quality surrogates. Multi-rater A/B tests further show uneven human transfer, while a reward-gap analysis separates average transfer from within-axis calibration: signed reward gaps significantly predict listener choices in the pooled analysis, whereas residual CER gaps do not, but per-axis calibration remains heterogeneous. Best-of-8 is a strong human-level baseline and is not clearly worse than GRPO perceptually, suggesting that GRPO should be viewed as amortizing reward-selected behavior into the policy rather than uniformly outperforming reranking. These results support analyzing subjective speech rewards as predictor-axis-base tuples and provide practical diagnostics for selecting rewards before multi-reward speech post-training.

Existing approaches for synthesizing Partial Differential Equation (PDE) solvers predominantly rely on autoregressive models, yet their global left-to-right decoding incurs substantial redundancy when addressing inherently localized bugs. In this work, we challenge this inefficient paradigm and propose DiffPDE, a framework leveraging discrete diffusion language models for targeted code repair. By introducing a localized re-masking and infilling strategy, DiffPDE regenerates only erroneous regions while preserving correct context, naturally aligning generation with the sparse nature of PDE errors. Furthermore, to handle coupled bugs requiring sequential interventions, we present Iterative Debugging GRPO (ID-GRPO), a reinforcement learning scheme that enables multi-round debugging within single trajectories via intermediate rewards. Experiments on PDEBench show that DiffPDE achieves competitive accuracy, outperforms same-scale AR models, and significantly accelerates repair.

Expected-cost constraints can still permit rare, high-cost events. Monte Carlo conditional value at risk (CVaR) gradients can be noisy at high confidence, whereas critics that model an outcome distribution add complexity. We propose BCPPO (Bachelier-Inspired Constrained Proximal Policy Optimization), a proximal policy optimization (PPO) method. Separately initialized cost-prediction networks (critics), trained with random sample masks, produce disagreement that marks predictions sensitive to which state-action regions occur in the training data and to critic training. A Bachelier formula for the expected amount above a reference level converts this disagreement into a smooth policy-update penalty. Gradients from this penalty do not alter the critics, so temporal-difference (TD) critic learning is unchanged. A saturation-aware controller adjusts the mean-cost penalty and stops accumulated error from growing while that penalty is clipped. Deployment retains only the policy network. The disagreement penalty is neither a tail-event probability nor a guaranteed error bound, and it provides no safety guarantee. Across 175 runs with shared tasks, costs, budgets, training steps, and evaluation seeds, no comparator attains both higher mean return and lower mean CVaR than BCPPO in any task. On Push1, BCPPO has no lower return and no higher CVaR than every comparator, with at least one strict gain. These results support a practical balance among reward, caution around cost predictions that vary across trained critics, and policy-only deployment.

Vision-language-action (VLA) driving methods increasingly combine multi-trajectory imitation learning with group-relative policy optimization (GRPO), making trajectory selection critical to final performance. However, some high-scoring trajectories that improve imitation can degrade subsequent GRPO by inducing advantage estimates misaligned with the current policy's feasible behavior distribution, driving updates away from safe and compliant behaviors. To address this, we propose a novel framework that aligns multi-trajectory supervision with policy optimization. To address the policy gradient bias induced by infeasible noisy trajectories outside the feasible region, augmented trajectories are constrained to a neighboring manifold of the ground-truth feasible region, and a Pareto-optimality criterion is adopted in place of the conventional aggregate score, retaining only non-dominated candidates and thereby filtering out conflicting samples at the source. To ensure that expanded trajectory supervision is effectively absorbed during policy optimization, we introduce two complementary mechanisms: feasibility-first advantage assignment and dynamic distillation. The former adapts Pareto credit to the feasibility composition of each rollout group and guides fully infeasible groups toward safe references. The latter updates teacher trajectories across refinement rounds to continually transfer useful supervision. Together, they progressively translate the benefits of expanded supervision into policy improvement. On NAVSIM v1 and v2, our method achieves 91.4 PDMS and 89.1 EPDMS, respectively, under single-trajectory inference, and recovers 440 of 658 initially failed scenes, 11.1% higher than the original GRPO baseline.

Training multi-turn agentic workflows with reinforcement learning (RL) enables large language models to perform complex reasoning, use external tools, and conduct iterative search beyond single-turn settings. Yet multi-turn RL training remains highly unstable, often causing severe performance degradation as the number of turns increases. Through theoretical analysis, we identify three tightly coupled sources of instability: rollout-training context mismatch, weak turn-level credit assignment under sparse terminal rewards, and asynchronous policy drift when short and long trajectories are optimized under different policy versions. We show that these issues share a common structural origin in flattened trajectory optimization and address them through a unified reverse-turn formulation. We propose Reverse-Turn Policy Optimization (RTPO), which organizes multi-turn rollouts as sparse reverse trees and performs turn-level policy updates in temporal reverse order, aligning each decision with its downstream continuation. RTPO enables causally consistent turn-level credit assignment and on-policy continuation to control asynchronous drift. We provide theoretical guarantees showing that RTPO eliminates context mismatch and asynchronous drift under the proposed turn-level formulation, reduces credit bias, and converges to recursive optimality. Experiments on multi-turn agentic RL benchmarks show that RTPO improves upon trajectory- and turn-level baselines by 21.50% and 10.76%, respectively, highlighting its potential to support more stable training for tool-using agents.

In evolutionary search, a weak child can be a valuable ancestor that makes high-fitness regions reachable. Immediate-return control is blind to this delayed utility, penalizing mutations through their immediate offspring even when they open productive future lineages. We formalize this hidden dynamic as the time value of evolution within a finite-horizon Markov decision process. To exploit it, we introduce Lineage-Value Policy Gradients (LVPG), a long-horizon actor-critic framework for automated trading policy discovery. Our architecture decouples search control into specialized policy heads over a shared generative backbone: a bootstrapped critic head estimates the value of finite-horizon lineage potential from multi-step mutation trees, while an actor head dynamically modulates mutation intensity over the remaining search budget. We isolate the impact of long-horizon credit assignment against immediate-return optimization across 90 paired runs under matched operators, lineage supervision, folds, seeds, and budgets. Path-based credit assignment substantially accelerates finite-budget search, increasing validation best-so-far AUC by 0.394 Sharpe units. LVPG also produces fewer temporary regressions than immediate-return optimization and recovers from them more often. Finite-horizon lineage value yields more selective non-monotonic search and stronger policies within identical resource constraints.

Outcome-driven reinforcement learning offers a scalable way to post-train vision-language-action (VLA) policies from sparse task-success feedback. In common GRPO-based VLA post-training, one rollout-level advantage is applied to every action in the trajectory. A rollout that completes several valid stages but fails later can therefore penalize the actions that produced its earlier progress. We call this trajectory-level credit aliasing. Temporal GRPO addresses this problem by constructing detectable task stages, aligning each rollout with stage-specific action intervals, and comparing only rollouts that have entered the same stage. The resulting stage advantages are applied to their corresponding intervals in a single policy update. On RoboTwin 2.0, Temporal GRPO improves task success and sample efficiency, with consistent gains across task horizons. Controlled updates on LIBERO-Long preserve shared prerequisite stages and concentrate improvement at the first stage where rollout outcomes diverge.

Group Relative Policy Optimization (GRPO) learns from reward differences within a rollout group, but receives no useful relative signal when every sampled response is incorrect. Privileged self-distillation can fill this gap with dense token supervision, yet applying it throughout training creates a different failure mode: the teacher is a biased, low-variance surrogate for the reward objective, so persistent imitation can oppose reward-improving updates after the policy becomes capable of producing successful trajectories. We introduce I-SDPO (Instance-Level Adaptive Self-Distillation Policy Optimization), which treats teacher reliance as capability-dependent. I-SDPO makes one routing decision per input instance and shares it across that instance's rollout group: all-incorrect groups use a privileged self-distillation objective, whereas any-success groups remain intact for GRPO. This design uses imitation only where group-relative rewards are uninformative. A local analysis characterizes when teacher and reward directions align and shows that a non-vanishing biased distillation weight induces an optimization bias floor. The routing rule automatically reduces the expected distillation rate as success probability rises, withdrawing teacher influence without a hand-designed schedule. On SciKnowEval, I-SDPO obtains the best result in all four scientific domains and improves average mean@16 accuracy from 56.67% with GRPO to 70.31%, with a maximum domain gain of 18.24 points.

Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory, which is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5 percent overhead per step from a single additional forward pass.

Autonomous agent teams deployed in settings such as marine and extraterrestrial outposts must coordinate actions to achieve optimal outcomes across multiple competing objectives. Multi-objective evolutionary algorithms such as NSGA-II optimize for diversity in the objective space, but neglect diversity in the behavior space, possibly leading to premature convergence and a collapse in behaviors that may differentiate policies in different external conditions. To address this, we introduce an entropy-augmented policy evaluation strategy that incorporates an entropy bonus into agent fitness scores, discouraging behavioral homogeneity across the evolving population. By augmenting policy evaluation with a behavior-space diversity signal while preserving the underlying Pareto optimization framework, our method is designed to encourage exploration of behaviorally distinct policies in multiagent domains. We evaluate our approach across rover-domain experiments with qualitatively distinct reward structures and observe hypervolume improvements of up to 48% relative to the NSGA-II baseline, suggesting that behavioral diversity is a promising and underexplored direction for improving multi-objective multiagent evolutionary optimization.

Generating actionable financial advice from business records demands that models integrate numerical reasoning, domain knowledge, and sound judgment, while avoiding recommendations that could harm the business. Direct supervision is difficult: historical decisions are not necessarily optimal, and high-quality free-form labels are expensive to obtain. We formulate financial advice generation as a reinforcement learning problem and fine-tune an open-weight language model using Group Relative Policy Optimization (GRPO). Our reward is an LLM-as-a-judge rubric that scores each recommendation across multiple binary dimensions of advice quality, augmented with a safety gate for harm prevention. Since LLM-based evaluation alone cannot confirm whether improvements reflect genuine business value rather than adaptation to the judge, we complement it with a judge-independent audit based on a standard doubly-robust Conditional Average Treatment Effect (CATE) estimator. Under this observational off-policy audit, our trained LLM achieves approximately twice the estimated gross-profit lift of the strongest evaluated commercial baseline ($0.0228$ vs.\ $0.0104$), together with the lowest downside rate and the least negative tail risk of any policy evaluated. Notably, the two evaluations do not rank the baselines identically: the untrained base model places last on the judge rubric but second on the causal audit, indicating that the audit captures a signal the judge does not. Our results demonstrate that GRPO with a finance-grounded reward signal can produce substantially more useful business recommendations than commercial LLMs, and that a judge-independent causal audit is a valuable complement to, rather than a confirmation of, LLM-as-a-judge assessment in financial NLP.

On-policy rollout methods such as GRPO are central to post-training of large language models, yet they frequently suffer from training instabilities, cross-task capability degradation, and response-length inflation. Although prior work has characterized the subspace geometry of aggregate updates, the stepwise variation of this geometry and its relationship to model performance remain unclear. We introduce Principal-Subspace Overlap, a dimension-corrected measure of individual rollout updates relative to the dominant singular subspaces of pretrained weights. Despite low average overlap, transient spikes often precede performance degradation. To address this, we propose GCPO (Geometrically Constrained Policy Optimization), which applies hard bilateral orthogonal projections to constrain updates to the complementary subspaces, preventing such excursions by construction. Across mathematical reasoning, code generation, and tool-use tasks on Qwen3-8B and GLM4-9B, GCPO consistently outperforms GRPO and recent variants, including DAPO and GSPO, improving over the base models and the strongest baseline by up to 27.69 and 2.37 points, respectively. Furthermore, GCPO preserves general capabilities, eliminates response-length inflation, and stabilizes policy entropy. Our findings provide a new diagnostic lens and a principled design perspective for stable reinforcement learning post-training.

Reinforcement learning against rubrics, lists of criteria graded by an LLM judge, has become a standard way to post-train language models on tasks with no deterministic answer. The rubric, however, is a fixed proxy for quality, never a complete description of it, and a policy trained against it long enough will learn to exploit the difference. We measure this directly. Training Qwen3-8B with Group Relative Policy Optimization (GRPO) on medical and science rubrics and grading out-of-distribution (OOD) benchmarks with both the training judge and a stronger gold judge, we find that the two scores diverge during training. The training judge's score keeps climbing while the gold judge's score peaks and then falls, by 3 points on HealthBench-Hard and by 22 points on ResearchQA. A judge with a fixed bias would shift the gold curve by a constant, not send it down while the training score rises, so the divergence is reward hacking, not judge noise. We propose Rubric Dropout, a one-line fix borrowed from neuron dropout. At every step, we randomly drop a subset of the rubric's criteria before computing the reward, so the policy never optimizes the same rubric twice. The dropped subset is shared across each rollout group, so GRPO's group-relative advantages stay comparable, and evaluation always uses the full rubric. Comparing no dropout against dropout at 30% and 50% on both benchmark pairs, dropout raises the OOD gold score at every matched checkpoint (+1 to +2 points on HealthBench-Hard, +6 to +7 points on ResearchQA), lowers the two hacking measures we track, and costs nothing in domain. Sweeping the dropout fraction shows a broad 30-50% sweet spot, while the natural alternative, reweighting criteria by how useful they are to training, performs worse than no intervention at all in our setting.

Safe reinforcement learning maximizes reward subject to safety constraints. For Constrained Markov Decision Processes, the linear-programming view over occupancy measures implies that whenever the constraint is active at optimality, the optimal policy lies exactly on the constraint boundary, yet standard gradient-based methods do not exploit this structure and often settle in the feasible interior. We introduce Boundary-Seeking Policy Gradient (BSPG), a first-order method whose update combines a tangential component that improves reward while preserving cost to first order with a signed, residual-driven normal component that regulates the policy toward the active boundary from either side; the combined direction admits an algebraic Lagrangian form with an induced coefficient and no learned dual variable. Under exact gradients and stated regularity conditions, the constraint residual converges to zero from either side with a finite-horizon $O(1/\sqrt{T})$ bound, the tangential component is a reward-ascent direction on the boundary, and any convergent parameter sequence is stationary on the active constraint set, satisfying the KKT conditions when the limit is also a local maximizer over the feasible set. This complements existing analyses, which certify feasibility but do not characterize the constraint value at convergence. On a standard Safety-Gymnasium navigation task, BSPG attains higher reward while tracking the boundary more tightly than the compared baselines.

Collision avoidance systems are commonly used to avoid fragmentation events occurring in Low-Earth Orbit (LEO) and Geosynchronous Equatorial Orbit (GEO). However, these events have been growing in frequency as orbital congestion worsens with the launch of megaconstellations. Consequently, conjunction alerts and collision risks are becoming increasingly common. Current practices, which are commonly manual or rule-based, have difficulty scaling to these worsening dynamic environments. To address this intensifying situation, we propose a reinforcement-learning policy for autonomous collision avoidance, trained via Proximal Policy Optimization (PPO) along with an open-source, high-fidelity astrodynamics simulator for training and evaluation. In 1,000 deterministic GEO episodes, our agent achieves a 97.5% collision avoidance success rate, outperforming traditional controllers such as a rule-based baseline (20.7% success) and an impulsive delta-v planner baseline (27.5% success). To achieve these results, we designed a simulator to train and evaluate our agent, using real-world and simulated debris. We simulate Newtonian two-body dynamics using Sun/Moon third-body perturbations, fuel-dependent thrust, and configurable debris fields. The agent is trained with curriculum learning and shaped rewards oriented toward encouraging survival, adequate projected miss distance, and delta-v conservation. Finally, our evaluation consisted of a fully deterministic pipeline, including shared seeds, per-episode logs, and telemetry exports. Our work is a publicly available framework at https://purl.org/sat-trajectory-avoidance

User simulators are widely used as scalable environments for training and evaluating interactive assistants. Generating the next user turn is inherently one-to-many: the same profile and dialogue context may support multiple plausible continuations with different local interaction intents. A fluent response may therefore advance the dialogue through an inappropriate intent, such as acceptance rather than repair. Our key insight is that controllable user simulation should separate which local interaction intent the next user turn should realize from how that intent is expressed in language. We introduce UserIDA (User Intent-Directive Alignment), which exposes interaction intent as an explicit per-turn directive. UserIDA defines a six-way intent interface, learns directive-conditioned generation through supervised fine-tuning, and uses intent-calibrated policy optimization during group-based reinforcement learning. The reward preserves composite response quality while ensuring that intent-violating candidates rank below compliant alternatives in mixed groups. On LMSYS-USP, UserIDA achieves 86.6% intent accuracy, outperforming the strongest dedicated user-simulator baseline by 24.3 percentage points while improving semantic and stylistic similarity. In within-context interventions, it realizes at least four of the six target intents in 91.7% of evaluated dialogue states, compared with 22.9% for the strongest external baseline. These results establish per-turn intent control as a complementary dimension to response fidelity in user simulation.

Group-based reinforcement learning objectives such as GRPO can allocate learning signal poorly across prompt difficulty: under binary rewards, group normalization induces a divergent weighting on easy prompts. We introduce Softmax Advantage Group Estimation (SoftmaxGRPO), a drop-in alternative that replaces z-score-normalized group advantages with temperature-scaled softmax advantages, keeping weights bounded regardless of prompt difficulty. For binary rewards, we derive the exact finite-group population objective and identify MaxRL as its low-temperature limit. For bounded scalar rewards, we show that the large-group update exactly optimizes a log-moment-generating-function objective, while a universal finite-group scalar objective cannot exist without additional assumptions on the reward distribution. Empirically, SoftmaxGRPO reallocates measured gradient budget away from near-solved prompts and consistently improves over GRPO under identical rewards. It reaches 51.8% on DeepMath with verifiable rewards and improves a 1.5B instruction-tuned model from 35.0% to 68.0% on Poetry using only lightweight text-similarity rewards.

Large language model-based multi-agent systems have recently shown strong potential for complex, long-horizon tasks. However, existing methods mainly rely on coarse prompt-level differentiation without parameter adaptation for diverse subtasks, resulting in insufficient inter-agent heterogeneity and limited specialized capability that bottleneck performance on tasks with complex requirements. To address this, we introduce a Task-Oriented Multi-Agent System with Mixture of Role-Subtask Experts (MoRSE) that distinguishes agents with (role, subtask)-conditional specialization at both the task structure and parameter levels. To make agents' responsibility explicit at the task structure level, we formulate a task-oriented multi-agent system that decomposes each task into a dependency-aware Directed Acyclic Graph of subtasks and assigns each agent a specific (role, subtask), introducing task-level specialization across collaborating agents. Additionally, to address the diverse role and subtask parameter adaptation demands, we propose a dynamic Mixture of (role, subtask) LoRA Experts module with a prototype-based semantic router for subtasks, augmenting agents with parameter-level specialization on a shared LLM substrate cost-effectively. Then, to co-optimize experts and router stably under sparse task rewards, we further propose a hierarchical group-relative policy optimization with two-layer credit assignment that isolates expert updates from the cross-route variance introduced by routing decisions, disentangling expert quality from routing quality. Experiments on code-generation benchmarks across three backbones demonstrate the effectiveness of our approach, with improvements in both whole-task and step-wise performance, and the gains from trained specialization generalize across held-out task categories and domains.

An LLM judge deployed inside a reasoning pipeline does not merely measure quality, it decides which answer ships. We show that the cost of that decision depends less on judge accuracy than on the decision rule the judge is embedded in. On frozen candidate pools from four GRPO policies, an unconstrained scalar DeepSeek-R1-7B judge buys almost nothing over answer-level majority vote (+1.0 pp on 500 GSM8K questions, +0.34 EM on 300 HotpotQA questions), and on a frozen-rule 30-question confirmation split it is 10 points worse than majority, a judge that destroys accuracy while scoring candidates confidently. We then subordinate the same judge to Evidence-Locked Derive-Gate-Repair (EL-DGR), a task-adaptive non-compensatory rule under which a judge preference may override evidence-supported consensus only with an extractive evidence certificate, and a repair only when neither alternative is certified and the repair is. With no change to the judge, the candidates, or the budget, EL-DGR reaches 58.2% on GSM8K (vs. 56.8% judge, 55.8% majority, 55.4% first candidate) and 17.33 EM / 25.46 F1 on HotpotQA (vs. 15.67/23.49, 15.33/23.19, 15.33/22.97), improving on first-candidate GRPO by +2.8 pp (exact McNemar p=0.0026) and +2.00 EM (p=0.070, borderline). A decision audit shows why: EL-DGR overturns consensus on only 8 of 30 pilot questions and never converts a correct consensus into an incorrect answer. We also report what did not work: the same seven-channel decomposition used as a step-level gated training reward is null, and corrected channel-drop ablations show no channel is individually necessary (p=1.0 throughout). The practitioner-facing finding is negative about judges and positive about admissibility, bound the judge's blast radius rather than trying to make it accurate.

Wasserstein policy gradient (WPG) updates state-conditional action laws by transport in the action space. We study entropy-regularized discounted linear-quadratic (LQ) control. A Bellman verification argument shows that the unrestricted problem has a linear-Gaussian optimal policy, and the discounted-occupancy-weighted statewise Wasserstein gradient is tangent to this policy class. WPG therefore reduces exactly to a finite-dimensional ODE for the feedback gain and action covariance. We prove that this ODE is globally well posed and converges exponentially from every admissible initialization. For each fixed LQ problem, the exponent has a positive limit as the entropy temperature tends to zero and contains no perturbative factor of the form $\exp(-c/τ)$, while retaining the usual dependence on the conditioning of the control problem.