Multi-Objective 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.

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.

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.

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

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.

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.

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.

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.

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.

Reinforcement learning with Verifiable Reward (RLVR) has emerged as a powerful paradigm for training coding agents, where the execution feedback from compilation and tests provides objective verification. However, unlike agent tasks, coding agents face a unique and finer-grained credit assignment challenge: at each step, coding actions simultaneously pack varying changes into different regions of a code version, which makes the contribution of independent change indistinguishable. Existing RLVR methods mostly leverage the outcome reward or step-level reward, which fails to dive into a code diff and makes unique properties of coding actions invisible to training. In this paper, we propose Diff-in-Diff Policy Optimization (DiDPO), a critic-free RL method that constructs fine-grained credit units directly from the structure of code diffs. DiDPO organizes multi-turn coding interactions into multiple thought--action steps and discovers code diffs across sampled trajectories. It then selects anchors by aggregating highly similar sub-diffs split from each whole diff by our ``groupability score'', which provides the splitting schema that optimally balances the semantic scope of anchors and the group mass they may form. Finally these anchors form advantage groups and project the diff-level advantage back to individual response tokens. Experiments on long-horizon coding and reasoning benchmarks show that DiDPO significantly outperforms strong agentic RL baselines. On Qwen2.5-7B-Coder, DiDPO exceeds comparable methods by over 10% and narrows the gap with far larger models, offering a principled framework for fine-grained credit assignment in coding agent training. We also open-source verl-code, an agentic rl codebase that supports various RL methods and coding benchmarks.

This work studies model-free reinforcement learning for co-safe linear temporal logic (sc-LTL) objectives in finite Markov decision processes, which can be reduced to maximal reachability objectives via the standard product construction. For this problem, direct sample-based bootstrap methods (e.g., TD or Q-learning) may fail to converge to optimal policies due to the noncontractive nature and nonuniqueness of solutions to the Bellman equation. We develop a new two-step model-free reinforcement learning method that first uses a discounted surrogate to identify a clamp set that resolves this nonuniqueness, and then applies undiscounted policy evaluation and greedy policy improvement with guarantees of finding an optimal solution. We prove almost-sure convergence of the policy evaluation step and finite termination of the policy iteration algorithm at an optimal policy. These theoretical results are validated through numerical experiments on a stochastic grid world.

Generative Flow Networks (GFlowNets) have emerged as a flexible framework for amortised inference over discrete and mixed discrete-continuous objects, requiring only an unnormalised target density specified through a reward. In this work, we formulate forward-policy training in GFlowNets through the information geometry of the induced trajectory sampler. Treating the forward policy as an induced trajectory sampler, we show that its intrinsic first-order geometry is given by the Fisher-Rao metric of the trajectory family, and that the associated natural gradient provides the canonical local update whenever the corresponding Fisher information is computable or accurately approximable. We derive an exact decomposition of the trajectory Fisher into per-step conditional second moments, which clarifies when temporal score interactions vanish and when dense couplings remain under shared parameterisation. This leads to three computational regimes: settings with tractable exact Fisher information, settings where Monte Carlo estimators of the expected Fisher are sufficient, and structure-exploitable settings in which target locality or factorisation yields accurate approximations of the Fisher expectation. In the latter case, graphical-model tools such as exact marginalisation, separator methods, and belief propagation provide principled surrogates for natural-gradient updates. The resulting framework turns target structure into optimisation geometry and yields a tractable route to structure-aware forward-policy training in GFlowNets. We illustrate the framework empirically through examples comparing convergence and exploration behaviour under Riemannian and Euclidean optimisation.

Reinforcement fine-tuning (RFT) is widely believed to inherently resist catastrophic forgetting in continual post-training of multimodal large language models. Under pronounced task distributional shifts, however, forgetting across representative RFT algorithms escalates sharply. This stems from the implicit reward-variance regularization inherent to RFT, which proves incapable of suppressing uncontrolled optimization risk. We propose Risk-Aware Policy Optimization (RAPO), the first dual-channel framework for explicit risk governance in continual RFT. On the policy channel, Risk-Aware Policy Scaling adaptively calibrates per-sample update magnitude via rollout reliability and Fisher-inspired local predictive sensitivity; on the data channel, Risk-Aware Dynamic Bucket Sampling reorganizes training batches through dynamic risk stratification, steering optimization toward informative yet stable samples. As a plug-and-play strategy requiring no cross-task memory, RAPO generalizes to any RFT algorithm without modification. On the public MLLM-CL benchmark, RAPO reduces final forgetting by 79.8% relative to its RLOO backbone while retaining new-task competitiveness.

Reinforcement learning (RL) has emerged as an effective method for enhancing the reasoning capabilities of large language models (LLMs). However, existing methods suffer from insufficient precision in feedback on generated answer trajectories and exhibit the phenomenon of problem difficulty drift. To address these challenges, we propose CVPO - Curriculum-guided Value-Variance Policy Optimization. At the response trajectory level, we find that token-level value-variance correlates with exploration intensity. Our theoretical analysis shows this variance bounds policy update magnitude. We then use the estimated trajectory value-variance to quantify the intrinsic randomness in generation. Based on this, we design a variance-aware advantage adjustment mechanism for different reward types. At the question level, we introduce a dynamic curriculum weighting method that adapts to question difficulty. This helps the model focus on tasks matched to its current ability during each training stage. Experimental results show our method outperforms strong value-based baselines like VAPO. It achieves better performance and stronger exploration, enabling more accurate and robust reasoning in language models across various math tasks.

Proximal Policy Optimization (PPO) for large language models typically trains its critic by mean-squared-error (MSE) regression on scalar value targets. Although scalar MSE is statistically valid for estimating the conditional expected return, sparse binary rewards in reinforcement learning with verifiable rewards (RLVR) make critic optimization and calibration especially consequential: small value errors directly distort the scalar advantages used by PPO. We study whether a classification-based training objective can improve this critic signal. HL-Gauss PPO replaces the scalar MSE head with a categorical predictor over a discretized value support, trained by cross-entropy against smoothed HL-Gauss targets. Its output is decoded to a scalar expectation for standard GAE and PPO; the actor update is therefore unchanged and is not distributional. Across mathematical reasoning, tool-augmented math, and Search-R1, and on both Qwen2.5 and Qwen3 backbones, HL-Gauss PPO consistently improves over strong PPO and DAPO baselines. Controls with one-hot, two-hot, and Bernoulli two-bin critics show that neither a larger output head nor binary classification alone explains the gains. On a common collection of reasoning prefixes, HL-Gauss improves Brier score and calibration error and yields more symmetric, lower-variance advantages. These results position categorical value learning as an effective optimization surrogate for PPO critics in RLVR.

Reinforcement learning has become a central paradigm for improving the reasoning capabilities of large language models. Existing methods generally aim to reduce the failure probabilities induced across problems. In this paper, we introduce a moment-based perspective on policy optimization for LLM reasoning by treating the failure probability of a randomly sampled problem as a random variable and characterizing optimization objectives through its moments. Under this perspective, many existing methods optimize only a single moment of the failure-probability distribution, leaving its broader distributional structure largely uncharacterized. We propose \textbf{M}ulti-\textbf{M}oment \textbf{P}olicy \textbf{O}ptimization (MMPO), a novel policy optimization framework that jointly minimizes multiple moments of the failure-probability distribution. MMPO admits a direct operational interpretation as minimizing the expected truncated time required to obtain the first successful response. Beyond MMPO, we further develop a general moment-transformation framework that systematically induces different moment profiles and provides a unified view of a broader family of policy optimization objectives. Experiments across five mathematical reasoning benchmarks and models of different scales demonstrate that MMPO consistently outperforms strong baselines. We hope this moment-based perspective offers new insights into the design of policy optimization objectives for LLM reasoning.

Autoregressive rollout generation is a major computational cost in reinforcement learning for large language models. Reusing each rollout batch for additional learner updates amortizes this cost, but later updates become increasingly off-policy as the learner departs from the behavior policy. At a token position, exact off-policy correction must account for both the current action and the probability of reaching its prefix. The cumulative importance ratio provides this correction, but its product form can produce an unwieldy dynamic range. We study Prefix-Normalized Policy Optimization (PNPO), which replaces the cumulative ratio with the geometric mean of likelihood ratios along each causal prefix, preserving causal-prefix dependence at each position while compressing the log-weight scale. In controlled long-context mathematical reasoning experiments, we induce two off-policy regimes by using one or four policy-update epochs per rollout batch. PNPO does not consistently outperform GSPO with one epoch. With four epochs, it attains the highest observed Avg@32 on each benchmark; the unweighted mean of the three independently selected benchmark peaks is 50.24, 3.00 percentage points above GSPO. Under a matched 2,400-update budget, four-epoch PNPO reaches a final macro Avg@32 of 49.66 after 150 rollout batches, comparable to the 49.56 reached after 600 batches with one epoch. These results provide preliminary evidence that PNPO can be advantageous as training moves further off-policy.

This paper studies the policy gradient update for a multi-arm bandit problem in diffusion environment that is described by a stochastic differential equation (SDE) under the continuous-time reinforcement learning framework by Wang et al. (2020), Jia and Zhou (2022b). With the logit parameterization for the stochastic policy, we show that it converges almost surely to the optimal arm under an arbitrary constant learning rate. Furthermore, we derive the non-asymptotic regret upper bound when the constant learning rate is below a time-invariant threshold; and the regret bound has order $O(\log T)$. We improve the analysis in Lattimore (2026a) for the same SDE by constructing a novel Lyapunov function and demonstrate the transparency of analyzing policy gradient using the tools in SDEs. In addition, the same Lyapunov function is also helpful in analyzing the discrete-time policy gradient algorithm.

Predicting the 3D structures of atomic systems is fundamental to advancing material science and drug discovery. While flow-matching models (, FlowDPO) have recently shown promise in this domain, their performance relies heavily on alignment with ground-truth coordinates via supervised preference learning. However, obtaining experimental labels for novel crystal phases or de novo proteins is prohibitively expensive, creating a bottleneck for structural modeling in data-scarce regimes. In this work, we propose (Atomic Policy Optimization), a fully unsupervised alignment framework that eliminates the need for ground-truth reference structures. APO adapts group-relative policy optimization to 3D atomic environments, utilizing a novel dual-reward mechanism: (i) a that reinforces the policy's dominant latent structural modes through eigen-decomposition of sample similarities, and (ii) a that enforces thermodynamic stability. Our framework enables the model to ``self-correct'' by identifying physically plausible configurations within sampled groups. Extensive benchmarks on crystal and antibody structure prediction demonstrate that APO consistently outperforms fully supervised baselines, achieving a new state-of-the-art in match rates and structural fidelity. Furthermore, we show that APO effectively straightens probability paths, significantly improving inference efficiency. Our results suggest that intrinsic physical consistency can serve as a superior guide for alignment compared to noisy, supervised coordinate matching.

This thesis studies policy learning in interactive systems where an agent observes a context, selects an action from a very large set, and receives partial feedback. The main framework is contextual bandits, with two paradigms: on-policy learning, where the agent interacts sequentially with the environment and minimizes regret, and off-policy learning, where it learns from logged data collected by a logging policy. In large action spaces, both settings face major challenges: inefficient exploration, sparse data coverage, high-variance importance weights, extrapolation bias, and difficult optimization landscapes. The first part develops structured Bayesian methods for on-policy learning. We introduce meTS, a mixed-effect extension of Thompson sampling, and dTS, which leverages diffusion-inspired priors to model dependencies between actions. These methods share information across actions and yield regret guarantees depending on an effective number of actions. The second part addresses off-policy learning. We propose sDM, a structured direct method based on latent variables, show that optimization error can dominate estimation error in large action spaces, and introduce concave, efficiently optimizable policy-weighted log-likelihood objectives. Finally, we develop differentiable pessimistic methods based on exponential smoothing and PAC-Bayesian bounds to control the bias-variance trade-off of regularized importance-sampling estimators.

Computer-use agents often fail on transient GUI events because they produce the correct action only after the relevant window has already closed. We identify the main cause as expensive autoregressive decoding on the decision-time critical path. We propose Adaptive Anticipatory Policy Trees (AAPT), which eliminates this delay without modifying the underlying model. During idle screen periods, the same frozen multimodal model constructs a bounded conditional policy tree with observable guards, pre-authorized actions, and branch-specific deadlines. The tree is sized to cover the model's own decoding latency. When an event occurs, a lightweight observer matches change-gated frames to a prepared branch and immediately executes the corresponding action without generating new text. In paired trials with pre-registered endpoints and exact McNemar tests, AAPT improves the success rate from 0.50 to 0.79 within a contested decision window ($p=1.8\times10^{-3}$), while producing no incorrect actions. Both open-loop and predict-and-replan baselines achieve zero success because they still decode during execution. A preparation-time sweep shows that the gain emerges where the latency-based tree-sizing rule predicts, and ablations reveal three key requirements: fast observer decoding, valid tree planning, and accurate branch routing. A pre-registered oracle probe rejects our initial hypothesis and instead points to branch routing as the causal bottleneck. We further reproduce the effect on an independent general-purpose multimodal model over 126 paired trials ($p=4.9\times10^{-13}$). On an external benchmark, AAPT matches the overall performance of a reactive baseline, although the two methods exhibit complementary strengths. Together, these results suggest that AAPT performs best when candidate actions can be enumerated in advance, whereas reactive execution remains stronger when they cannot.

Recently, Reinforcement Learning (RL) has emerged as a crucial paradigm for the post-training of Large Language Model (LLM) agents. However, existing methods predominantly rely on sparse task rewards for policy optimization, failing to fully exploit another class of inherently dense supervisory signals naturally present during online interaction: environmental feedback following action execution. Recent theoretical studies suggest that generalization in multi-step, goal-oriented tasks hinges on predictive knowledge of environmental consequences. Inspired by this, we propose TAPO: Transition-Aware Policy Optimization for LLM Agents, a unified training framework that alternates between policy optimization and transition supervision. Beyond standard RL updates, TAPO repurposes rollout data to apply action-conditioned next-observation prediction supervision on a shared backbone model. This approach enhances the model's sensitivity to environmental transition dynamics and action consequences while concurrently optimizing the policy. It serves as a computationally lightweight, plug-and-play enhancement module for existing agent RL algorithms, requiring no additional expert data, extra sampling costs, or inference-time overhead. We conduct systematic experiments on WebShop and ALFWorld, integrating foundation models of various scales with different policy optimization algorithms. Empirical results demonstrate that TAPO consistently improves task performance over pure policy optimization baselines.

Reinforcement learning from verifiable rewards (RLVR) for mathematical reasoning suffers from a structural blind spot: on "cliff" prompts-those on which every sampled rollout in a group fails-the group-normalized advantage is identically zero, so GRPO produces no gradient on precisely the prompts at the frontier of the model's capability. We introduce LoRA Scaffolded Policy Optimization (LSPO), a sampling-time mechanism that recovers this lost gradient. Each RL step, LSPO detects cliff prompts, fits a small low-rank (LoRA) adapter by a brief supervised step on their ground-truth solutions, re-rolls the cliffs with the base-plus-adapter model, splices the now-successful completions back into the RL batch with an importance-sampling correction, and takes a GRPO step on the base alone; the adapter receives only the supervised gradient and is discarded at checkpoint, yielding a base-only model. On DeepMath-103K with DeepSeek-R1-Distill-Qwen-1.5B, evaluated over n=5 paired seeds per arm at a matched 1000-step reporting horizon, LSPO's 5-seed mean matches or beats a DAPO baseline on all 16 (benchmark, pass@k) cells (15 strict wins and one exact tie), with gains of up to +10.7 points on AIME24/pass@4, +6.7 points on AIME24 and AIME26 at pass@16, and +2.4 points on MATH500/pass@1; averaged over the 16 cells the improvement is +3.8 points.

Agentic systems have rapidly advanced in their ability to interact with real-world environments, leverage external tools, and provide services for users. However, unlike natural-world tasks that assume well-defined instructions, human-centered scenarios are characterized by ambiguous requests that lead to large, open-ended solution spaces. Decoding users' personalized preferences is therefore essential for narrowing the candidate solution space. This introduces a new challenge, personalized agentic reasoning, which requires agents to jointly interact with both users and environments to deliver personalized services. In this paper, we present ODYSSE, a Reinforced Fine-Tuning (RFT) framework for personalized agentic reasoning. At its core, ODYSSE proposes Episode-wise GRPO (ESPO), a novel extension of Group Relative Policy Optimization (GRPO) designed to address long action horizons and strong cross-step dependencies in personalized agentic reasoning. Rather than optimizing individual steps independently, ESPO introduces an episode-level reward mechanism together with episodic advantage estimation, enabling upstream evidence to effectively guide downstream personalized decisions and allowing agents to progressively resolve ambiguous user requests across multiple interaction steps. We further propose an episodic batch sampler that groups actions from the same episode into unified training batches, facilitating coherent optimization under ESPO. We evaluate ODYSSE on realistic long-horizon personalized GUI reasoning tasks. Experimental results demonstrate that ODYSSE consistently outperforms both specialist and general-purpose LVLMs, highlighting its effectiveness for personalized agentic reasoning.

Group Relative Policy Optimization (GRPO) is the dominant reinforcement learning algorithm for training reasoning capabilities in large language models, notably adopted by DeepSeek-R1. The recent improvement Dr. GRPO (COLM 2025) identifies the response-level length bias caused by per-trajectory length normalization in GRPO and proposes removing this normalization, claiming the resulting optimizer is "unbiased." We show that this claim is incomplete. Specifically, we establish an impossibility theorem: under the standard outcome reward + GRPO setting, no length-based weighting scheme can simultaneously achieve the following two properties. (P1) Gradient unbiasedness: the gradient estimator is an unbiased estimate of the true policy gradient. (P2) Length invariance: each trajectory's effective contribution to the gradient is independent of its token length. GRPO approximately satisfies P2 but violates P1; Dr. GRPO satisfies P1 but violates P2. We characterize the complete tradeoff spectrum via the parametric family f_alpha(L) = L^{alpha - 1}, where alpha = 0 recovers GRPO, alpha = 1 recovers Dr. GRPO, and provide quantitative analysis showing that Dr. GRPO's length bias can cause longer trajectories to dominate gradient updates by a factor proportional to the length ratio. Our results reveal that neither algorithm is universally "done right"; they occupy opposite ends of a fundamental and unavoidable tradeoff.

Recent large reasoning models often develop long chain-of-thought responses during reinforcement learning (RL), resulting in high inference latency and deployment cost. Existing methods for response length control typically rely on explicit length penalties or additional control modules, which require careful tuning and may compromise reasoning quality. We propose Quadrant-weighted Sampling for Length-aware Policy Optimization (QLPO), a simple resampling-based variant of GRPO that introduces implicit length control without modifying the reward function. QLPO first over-generates candidate responses and then resamples the training group by preserving the empirical correct/incorrect ratio while favoring short correct responses and long incorrect responses. This reshapes the training distribution and implicitly encourages shorter model outputs. Across models ranging from 1.5B to 32B parameters, including both base models and strong reasoning models, QLPO consistently improves the accuracy-length trade-off. It reduces response length by 30% to 70% while preserving reasoning performance. These results suggest that structured resampling provides an effective and robust approach to efficient reasoning.

Rubric-based RL has recently shown promise in improving LLMs on open-ended tasks. A widely recognized limitation of rubric-based RL is limited exploration: criteria that no rollout manages to satisfy (Unexplored Criteria, UC) receive no optimization signal. Recent methods address this by incorporating rubric information as external guidance during rollout, yet they introduce a train-inference mismatch: the policy is optimized on rollouts produced under external guidance while this guidance is absent at inference time, causing error accumulation through autoregressive decoding. Moreover, these exploration-focused approaches overlook a fundamentally different failure mode that we term Suppressed Criteria (SC) -- criteria that are satisfied by some rollouts yet whose learning signals are lost during optimization because scalar reward aggregation assigns them non-positive aggregate advantages. Our analysis reveals that SC are remarkably prevalent: over 57% of samples exhibit this failure mode throughout training, with an average of 1.8 SC per sample. To simultaneously address both UC and SC without introducing training-inference mismatch, we propose Criterion-Distilled Policy Optimization (CriPO), which enhances rubric-based RL via on-policy self-distillation. For UC, CriPO constructs a criterion-injection self-teacher and computes a localized forward-KL loss to inject missing behaviors into the policy. For SC, CriPO employs a counterfactual self-teacher to locate criterion-relevant tokens in negative-advantage rollouts and flips their token-level advantages to positive values, preserving useful patterns that would otherwise be suppressed. Experiments on medicine and science benchmarks demonstrate that CriPO consistently outperforms rubric-based RL, achieving stronger final performance with approximately $2\times$ fewer optimization steps.

Multi-task neural solvers aim to handle multiple Vehicle Routing Problem (VRP) variants within a unified model, avoiding separate training for each constraint combination. However, VRP variants differ in optimization difficulty, while existing methods lack stage-wise feedback on their training status, making the model biased to some specific variants. Although meta-learning can support adaptive training, it typically requires bi-level optimization and additional gradient updates, increasing computational cost. To address this limitation, we propose LLM-as-Trainer (LaT), a plug-and-play training paradigm that uses a pretrained large language model as an external trainer. LaT periodically analyzes cross-task validation metrics to generate a stage-wise guidance vector. This vector is combined with the current task's constraint vector and injected into each encoder layer, providing the neural solver with additional training information during subsequent policy optimization. Experiments on 16 VRP variants show that LaT improves the solution quality of several state-of-the-art multi-task neural solvers on both trained and unseen variants, supporting the effectiveness and generality of the proposed training paradigm.

Automated chest X-ray report generation has recently benefited from reinforcement learning (RL) and large language models. However, RL training often suffers from instability or limited exploration due to fixed Kullback-Leibler (KL) regularization and a static reference policy that accumulates KL pressure over time. We propose Response-Weighted and Validation-Anchored Policy Optimization (REVA-PO), a RL framework that stabilizes long-term training via Response-Weighted Regularization (RER) and Validation-Anchored Policy Reset (VAPR). RER dynamically adjusts per-response KL weights based on advantage and reference-policy entropy, relaxing constraints for high-quality responses while tightening them for low-quality ones. Complementarily, VAPR periodically synchronizes the reference and current policies to the best validation checkpoint, resetting accumulated regularization pressure to expand the viable exploration space. To ensure a robust starting point, we employ a three-stage pipeline consisting of warm-up training, classifier-guided supervised fine-tuning, and RL. Extensive evaluations on MIMIC-CXR and IU-Xray demonstrate that REVA-PO sets new state-of-the-art benchmarks in both linguistic quality and clinical accuracy. Notably, BLEU-4 improves by 5.1% on MIMIC-CXR and 3.6% on IU-Xray, while CheXpert F1 and RadGraph F1 scores increase by 4.5% and 12.8%, respectively, over prior leading methods. The code is publicly available at https://github.com/LiGuo12/REVA_PO/.

Reinforcement learning (RL) has become the standard paradigm for enhancing the complex reasoning capabilities of large language models (LLMs). To achieve sample efficiency, modern RL frameworks rely on importance sampling (IS). However, these algorithms suffer from an exploration-stability dilemma. Pure IS often leads to catastrophic training instability, while standard clipping mechanisms used to mitigate this instability strictly constrain the policy update budget. By formalizing the concept of Probability Capacity (Cap), we reveal that conservative clipping structurally stifles exploration by prematurely truncating the update budget for correct but low-confidence reasoning paths. To break free from these constraints, we propose Unbounded Positive Asymmetric Optimization (UP), a universal and plug-and-play objective. UP theoretically restructures the optimization process by anchoring the policy to its current state via the stop-gradient operator. This asymmetric design unleashes unclipped, stable gradients for positive advantages to maximize exploration, while maintaining standard clipping safeguards for negative advantages to prevent training instability. Furthermore, our formulation readily extends across different optimization granularities, including token-level (GRPO, DAPO) and sequence-level (GSPO) frameworks. Extensive experiments demonstrate that UP enhances exploration capacity and achieves superior reasoning accuracy across diverse RL algorithms (DAPO, GSPO, and GRPO), model architectures (Dense, MoE, and vision-language), and training modalities (language and multimodal), validating UP as a truly universal plug-and-play enhancement for RL-based training.

Reinforcement learning has become a promising paradigm for improving large language model (LLM) agents on long-horizon search tasks, where the agent must make a sequence of intermediate decisions before receiving a final outcome. However, existing methods still face a key limitation: the rollout budget is often allocated without explicitly assessing the utility of intermediate states. As a result, substantial computation may be spent on low-value states, even though different branches can vary drastically in their informativeness. In this paper, we propose Information Gain-based Rollout Policy Optimization (IGRPO), a policy optimization framework that treats intermediate-state informativeness as the organizing principle of rollout collection. Specifically, IGRPO performs budget-aware tree-structured rollouts by allocating expansion budget according to node-level informativeness, so that more informative branches are expanded more frequently while unpromising branches are progressively suppressed. We further demonstrate that the information gain-based rollout induces an explicit limiting teacher distribution over trajectories, which naturally yields a clear policy optimization target, thereby unifying adaptive tree-structured exploration with principled policy learning under a single framework. Experiments on seven challenging search-augmented QA benchmarks demonstrate that IGRPO consistently outperforms strong baselines under the same rollout budget constraints, validating the effectiveness of leveraging the induced teacher distribution to guide policy optimization for long-horizon search agents.

Continual post-training is becoming a central paradigm for adapting vision-language models to evolving tasks. Recent work has increasingly favored reinforcement learning over supervised fine-tuning, driven by the belief that reinforcement learning is inherently less prone to forgetting. However, the belief remains insufficiently validated, as existing evidence is largely drawn from outdated or homogeneous benchmarks. We revisit this assumption under recent and diverse multimodal reasoning tasks. To this end, we introduce MRCL, a Multimodal Reasoning Continual Learning benchmark. Experiments on MRCL show that standard reinforcement learning still suffers from severe catastrophic forgetting during continual post-training. We trace this failure to an objective mismatch: the KL regularization used in common policy optimization methods is evaluated on current-task data, whereas forgetting is caused by behavioral drift on prior-task distributions. To address this problem, we propose Continual Policy Optimization (CPO), a replay-free framework grounded in a prior-task behavioral KL objective. CPO relaxes the intractable historical KL constraint into sparse parameter-movement regularization, limiting policy drift without storing old data. Extensive experiments across multiple model scales show that CPO consistently reduces forgetting while preserving, and in some cases improving, pretrained model capabilities. On Qwen3-VL-8B, CPO reduces forgetting by 13.7% and improves pretrained capability by 7.0%. The implementation code is available at https://github.com/MaolinLuo/CPO.

This paper presents a methodology for learning a control policy to intercept an intruder using the 3D direction unit vector to the intruder and the interceptor state. Prior deep reinforcement learning approaches assume either relative position or distance to the intruder is available, but this information is not readily accessible in real-world applications that employ passive, monocular camera sensors. Instead, we propose a solution that leverages an analytical policy gradient method using differentiable quadrotor dynamics to learn agile interception at speeds up to 10 m/s. The proposed approach outperforms baseline methods that utilize simplified point mass dynamics by an average of 30%.

Neural Motion Planners (NMPs) enable fast reactive motion generation, but adapting them to new environments typically requires recollecting large expert datasets, which is computationally prohibitive. We propose ELMP, a framework for data-efficient adaptation via self-supervised fine-tuning. Rather than generating additional expert trajectories with expensive global planners, ELMP directly optimizes the policy through a differentiable kinematic layer using dense collision, target-reaching, and smoothness objectives. This replaces expert data generation with rapid problem sampling, reducing per-sample adaptation cost by roughly two orders of magnitude. To further support robust generalization across changing kinematic chains, we introduce a mechanism to explicitly encode tool geometry via point clouds. Benchmarked against classical and neural baselines, ELMP achieves an 84.8% average success rate with orders-of-magnitude lower cold-start latency than classical methods. In unseen environments, self-supervised fine-tuning improves success rate from 57.3% (zero-shot) to 89.8%, removing the data collection bottleneck. Our approach maintains millisecond-level inference latency and is validated on a physical Franka Emika Panda robot.

Building general-purpose role-playing agents that faithfully portray any character from a natural-language profile remains challenging. The dominant paradigm -- supervised fine-tuning -- encourages behavioral mimicry without deep, human-like internal thought processes, resulting in poor out-of-distribution generalization. Therefore, we propose \textbf{Psy-CoT}, a psychology-grounded chain-of-thought framework that decomposes pre-response reasoning into three role-specific steps -- \emph{Interaction Perception}, \emph{Psychological Empathy}, and \emph{Logical Construction} -- so that the model \emph{thinks dynamically} from the profile rather than merely mimicking surface patterns. While structured reasoning provides a foundation, it alone is insufficient; reinforcement learning is essential to further align the model with character fidelity. However, we observe that under LLM-based reward models, both generic phrases that hack the reward model and genuinely role-specific phrases receive identical gradient signals -- this hacking accumulates over training, misleading the model into treating both as equally optimal choices. To address this, we propose \textbf{Role-Aware Policy Optimization (RAPO)}, which uses profile--token mutual information to weight gradients asymmetrically -- amplifying role-specific tokens under positive advantage while attenuating them under negative advantage. Experiments on CoSER, CharacterBench, and CharacterEval demonstrate that Psy-CoT outperforms existing role-playing CoT methods, and RAPO consistently surpasses GRPO across multiple model scales.

Achieving strong optimization generalization across diverse optimization problems while requiring limited training resources remains a challenging problem for optimization-oriented large language models (LLMs). Existing approaches typically rely on large-scale supervised datasets, costly reasoning annotations, and expensive intermediate step verification, resulting in substantial training overhead. To address these challenges, we propose MiniOpt, a reinforcement learning framework that learns to solve optimization problems through an "reasoning-to-model-and-solve" paradigm. MiniOpt decomposes optimization reasoning into structured optimization modeling and executable solver generation. Building upon this paradigm, we introduce OptReward, a reward function with hierarchical score structure that jointly evaluates formulation and solution, enabling effective policy learning without expert demonstrations. We further develop an optimization-oriented policy optimization strategy that improves exploration efficiency and stabilizes reinforcement learning for compact models. Extensive experiments show that MiniOpt-3B exhibits strong optimization generalization across various optimization types, problem scenarios, and task domains. For models with fewer than 10B parameters, MiniOpt series achieves the highest average solving accuracy (SA). For models with more than 10B parameters, MiniOpt still shows competitive performance. These results suggest that optimization-oriented reward design and reinforcement learning provide an effective pathway for developing compact optimization-specialized language models with strong optimization generalization capabilities. The code is available at https://github.com/Hsiang-1/MiniOpt.

Distilling reasoning capabilities from strong to weak language models typically involves imitating specific solution trajectories, effectively transferring what to answer rather than how to reason. This trajectory-level imitation encourages memorization of instance-specific steps rather than acquisition of transferable problem-solving skills, limiting generalization to novel problems. We propose Strategy-Guided Policy Optimization (SGPO), which replaces instance-level trajectory imitation with reusable strategy distillation. SGPO extracts structured strategy descriptions from strong-model responses and, for each problem, constructs both autonomous and strategy-guided trajectories to enable direct comparison of the model's behavior with and without strategic guidance. The framework then addresses two key questions. For how to distill, a token-level forward-KL objective selectively transfers the distributional shift induced by strategy conditioning into the unguided policy, with proximal constraints ensuring stability. For when to distill, adaptive instance-level weighting strengthens guidance when autonomous exploration falls short and reduces it as the model's own competence grows. Experiments on four mathematical benchmarks across two model families show that SGPO consistently outperforms SFT, on-policy RL, and hybrid-policy baselines, improving the average score by 2.2 points over the strongest baseline on Qwen2.5-7B-Instruct. Analysis reveals that the forward-KL objective provides an inherently selective distillation signal that outperforms direct trajectory imitation, and that strategy distillation exhibits complementary scaling with base model capability.

Neural Combinatorial Optimization (NCO) achieves strong performance, yet its black-box nature remains a key roadblock to deployment and scientific diagnosis. Standard interpretability tools, such as Concept Bottleneck Models (CBMs), are ill-equipped for NCO, whose decisions are dynamic, state-dependent, and lack proper concept vocabulary definition. To close this gap, we introduce Evolving Programmatic Bottlenecks (EPB), to our knowledge, the first framework for interpreting NCO policies by distilling black-box NCO models into human-readable program portfolios. EPB employs an LLM to autonomously evolve a bank of programs, where each program's per-step action distribution serves as the bottleneck. EPB works through an iterative framework: Block I fixes program bank capacity and introduces a hybrid textual-numerical gradient descent scheme that couples numerical gradients for student router updates and textual gradients for LLM-based program revision; Block II dynamically adapts bank capacity via fault-targeted expansion and redundancy pruning. Extensive experiments demonstrate EPB's effectiveness and broad applicability, where the distilled program portfolios largely match original performance. EPB also reveals that NCO behavior shifts across optimization stages and can be approximated as a composition of classic heuristic variants. Our work advances interpretable NCO and establishes EPB as a promising tool for interpreting sequential decision-making models.

Sequential decision problems often exhibit an asymmetric evolution of information and decision flexibility: as a decision cycle unfolds, the agent receives richer information while feasible actions expire due to operational cutoffs, commitments, or resource constraints. Standard MDP formulations typically flatten this structure into stage-dependent state descriptions and action masks, thereby obscuring the nested information--action asymmetry that determines which decisions are urgent and which can be deferred. We introduce Maturing Markov Decision Processes (MMDPs), a formulation built around this information--action asymmetry. We characterize one of its key consequences through an expiring-action priority principle, which identifies the actions that must be resolved before the next stage. Motivated by this structure, we develop a structure-aware reinforcement learning framework with stage-aware policy design, expiring-action abstraction, and search-augmented learning with distillation. Experiments on a controlled multi-supplier replenishment problem, simplified cash-management environments of increasing complexity, and a production-scale simulator show that explicitly modeling this asymmetry improves learning efficiency and becomes increasingly valuable as decision problems scale.

Web navigation requires agents to follow natural language goals, interact with web pages, and produce accurate answers. While recent advances leverage vision-language models and reinforcement learning, existing methods still suffer from single-step fragility due to reward misalignment and error propagation. To tackle the reward entanglement, we design Dynamic Dual-Policy Optimization (DDPO), which dynamically switches between a navigation-first mode for exploration and an answer-first mode for question-answering to mitigate reward conflict. To calibrate the single-step error, we propose Confidence-Guided Adaptive Navigation Reflection (CANR), a mechanism that estimates per-step confidence, triggers reflection only when necessary, and uses contrastive rewards to encourage self-correction to calibrate the single-step inaccuracy. With the above as the main components, we finally develop our StepGuard, a new framework of Guarding Web Navigation via Single-Step Calibration. Experiments demonstrate that our approach significantly improves navigation and answer accuracy, setting new state-of-the-art performance on standard web navigation benchmarks.

Laser-induced breakdown spectroscopy (LIBS) quantitative analysis faces critical challenges in wavelength selection due to high-dimensional spectral data and the fundamental trade-off between prediction accuracy and feature efficiency. This paper presents a novel Multi-Adapter PPO framework that transforms wavelength selection into a reinforcement learning problem, leveraging cross-attention mechanisms and multiple specialized adapters to capture complex spectral relationships. Our approach outperforms traditional Particle Swarm Optimization (PSO) by an average of 28.4% in comprehensive score and 45.2% in prediction accuracy across steel and coal datasets. The proposed method demonstrates superior performance in balancing prediction accuracy with feature efficiency, achieving state-of-the-art results in LIBS quantitative analysis while maintaining interpretability and computational efficiency. We released our code and dataset here: https://github.com/Hflying/MAPPO

Policy-oriented agent-based models are increasingly used to study regulatory interventions in complex adaptive socio-technical systems. Recent adaptive ABM frameworks distinguish between static and adaptive agents, fixed and adaptive policies, and alternative controller designs. However, most diagnostic workflows remain ex post: trajectories are analysed after simulation, but the resulting evidence is not systematically fed back into the policy controller. This paper proposes a lightweight machine-coached policy-revision layer for adaptive agent-based regulation. The layer represents policy decisions as defeasible rules with explicit conflicts and priorities, generates explanations for controller actions, and allows diagnostic failures to be translated into rule additions, removals, or priority changes. The contribution is not a new optimal controller and does not claim formal guarantees for unrestricted machine coaching. Instead, it provides a simulation-compatible operationalization of controller-level contestability: policy decisions can be explained, challenged, revised, and re-evaluated in held-out simulation runs. A stylized emissions-regulation ABM is used as the experimental component. A controlled simulation experiment focuses on an over-conservatism failure in the VPVA regime. The predefined coaching template adds a relaxation rule to the symbolic controller, reducing over-conservatism recurrence under held-out seeds while preserving violation, overshoot, and volatility guardrails. The paper argues that machine coaching is best understood as a controller-level extension of explainable adaptive ABM, complementary to causal, information-theoretic, and trajectory-based diagnostics.

Long-horizon agents rely on memory mechanisms to compress interaction history, but optimizing memory writing faces a distinct credit assignment challenge: a memory update may be rewarded or penalized due to downstream tool failures, noisy observations, or reasoning errors rather than its own contribution. We propose HiMPO, a Hindsight-Informed Memory Policy Optimization framework for assigning less-entangled credit to memory-writing actions in long-horizon agents. HiMPO first estimates the local utility of a memory update by comparing the task-relevant information recoverable from the previous and updated memories under the same pre-write state. It then uses hindsight relevance as a bounded retrospective filter that attenuates memory credit when local utility is not supported by the target outcome. The resulting memory-specific advantage is applied only to memory tokens, while trajectory-level rewards optimize the rest of the agent's behavior. Across judge-based open-domain tasks and objective compressive-memory QA, HiMPO improves over strong memory-based and RL-based baselines while preserving compressed-context efficiency. Controlled interventions and live replay studies further show that HiMPO reduces blame leakage from tool-induced errors, assigns memory credit that aligns with the functional impact of memory writes, and remains robust to noisy training targets.

Conformal prediction (CP) has been used to obtain probabilistic bounds on the error between a learned dynamics model and the true but unknown system. Such CP bounds can then be embedded into robust control Lyapunov function (CLF) and control barrier function (CBF) frameworks. However, such an approach does not retain stability/safety guarantees because of the distribution shift between the closed-loop trajectory distribution under the deployed CLF/CBF policy and the trajectory distribution from which the CP bound and its guarantees were derived. To address this issue, we propose an episodic framework that iteratively updates the robust conformal CLF/CBF policy while maintaining stability/safety guarantees across episodes. We achieve this by (1) using adversarially robust conformal prediction, and (2) quantifying a distribution shift budget that allows us to control how much the model error can increase across policy updates. This distribution shift budget is derived via a closed-loop trajectory sensitivity analysis, yielding an implicit and an explicit update rule for the CP bound. We analyze convergence of our algorithm, which we demonstrate on three case studies. To the best of our knowledge, these are the first results that provide stability/safety guarantees for robust conformal CBF/CLF policies.

Contextualized assessment offers high ecological validity for evaluating creativity but introduces a critical challenge: observed performance may be confounded with cognitive proficiency (domain knowledge) and agency (willingness to engage). Meanwhile, in the age of generative AI, creative problem solving increasingly occurs in tool-mediated and human--AI interactive environments, making fully static assessment less aligned with contemporary creative practice. To address these issues, this paper proposes IntElicit, a framework for eliciting and assessing contextualized creativity via dialogue policy optimization. IntElicit functions as a constrained adaptive AI Interviewer: it provides non-directive knowledge and agency scaffolds in multi-turn interaction to reduce non-creative confounders, while preserving participants' responsibility for generating the creative content being evaluated. Specifically, to tackle sparse rewards and potential reward hacking (e.g., answer dictation) in open-ended educational dialogue, IntElicit introduces a decomposed process reward mechanism. This mechanism aligns the policy with pedagogical elicitation, rewarding prompts that draw out participant reasoning rather than producing optimal answers on their behalf. Extensive experiments, including participant simulation and a human subject study (N=64), show that IntElicit improves elicited creative outcomes over expert-designed baselines. Together, the results suggest that interactive elicitation can reveal creative potential that static FPSP-style assessment may miss, providing a formative and diagnostic lens for contextualized creativity assessment in AI-mediated learning contexts.

Reinforcement learning promises to optimize sequential decisions in large-scale systems. Semiconductor manufacturing systems are stochastic and highly constrained environments where heterogeneous wafers traverse hundreds of processing steps across extensive equipment networks. These characteristics yield complex, high-dimensional decision problems with delayed feedback and long-horizon requirements, complicating production planning and control. We propose a deep reinforcement learning framework for multi-objective policy optimization at this scale. Specifically, we formulate control as a centralized-agent problem, where a core policy coordinates system-wide decisions, while system evolution is represented as an interconnected temporal process driven by discrete events. Accordingly, we develop a tailored event-driven temporal-difference formulation that remains general and can be integrated with various policy optimization methods under relevant training settings. We investigate several core model-free algorithms incorporated into this framework and evaluate their effectiveness using high-fidelity simulations of diverse, industry-real operating scenarios. Across extensive validation experiments, agents trained in both offline and online settings show significant and consistent gains in throughput and utilization. We further evaluate performance and generalization across training phases, clarifying the relative strengths of alternative reinforcement learning formulations and algorithms. Overall, the results support the scalability, generality, and transferability of the proposed framework for controlling event-driven complex adaptive systems.

Neural combinatorial optimization (NCO) trains autoregressive policies to solve routing problems. The standard training algorithm, REINFORCE with a rollout baseline, requires maintaining and periodically updating a frozen copy of the policy for variance reduction. This baseline introduces a structural vulnerability: on harder instances, a poor baseline produces noisy gradient estimates that can destabilize training. We evaluate Group Relative Policy Optimization (GRPO), an algorithm from large language model alignment that eliminates the baseline entirely by normalizing advantages within groups of sampled trajectories. In a controlled comparison of five RL algorithms on TSP and CVRP benchmarks within the RL4CO framework, we find that: (i) GRPO avoids the training collapse observed with REINFORCE on TSP-100, where performance degrades from cost 9.8 to 52.1 immediately after the warmup phase and does not recover under extended training; (ii) at matched gradient updates, GRPO achieves solution quality within 2% of POMO, a strong AM-based multi-start baseline, while requiring no external baseline; and (iii) P3O, a pairwise preference algorithm also from the alignment literature, is competitive on TSP but shows higher variability on CVRP. These results identify GRPO as a promising baseline-free alternative for NCO, particularly in settings where baseline-dependent training becomes fragile.

Safe exploration is a prerequisite for deploying reinforcement learning (RL) agents in safety-critical domains. In this paper, we approach safe exploration through the lens of epistemic uncertainty, where the actor's sensitivity to parameter perturbations serves as a practical proxy for regions of high uncertainty. We propose Sharpness-Aware Policy Optimization (SHAPO), a sharpness-aware policy update rule that evaluates gradients at perturbed parameters, making policy updates pessimistic with respect to the actor's epistemic uncertainty. Analytically we show that this adjustment implicitly reweighs policy gradients, amplifying the influence of rare unsafe actions while tempering contributions from already safe ones, thereby biasing learning toward conservative behavior in under-explored regions. Across several continuous-control tasks, our method consistently improves both safety and task performance over existing baselines, significantly expanding their Pareto frontiers.

Hard-constraint decision systems usually veto infeasible candidates. This is too rigid when the system can act: if a known affordable repair would make an infeasible candidate feasible and valuable, rejection is a false veto rather than a ranking error. We introduce Q-RACL (Quantum Repair-Augmented Constraint Learning), a repair-before-veto framework that first defines RACL decision semantics and then identifies the single inference link where quantum feature access can be load-bearing. RACL accepts a candidate when a sequential repair plan restores feasibility and preference; otherwise it returns structured rejection credit. The hard link is repair-feasibility inference: which repair class restores feasibility from an observed candidate and context. We construct a discrete-logarithm-hidden RACL family where the repair class is a shifted interval rule in the latent exponent a = log_g(x), while the learner observes only x = g^a mod p. Under standard DLP-based learning separation, this coordinate is inaccessible to efficient raw-input classical policies but accessible to a quantum agent through Shor/Fourier structure. Across six primes and ten seeds, bounded raw-input classical policies and a wrong raw-Fourier encoding remain near chance, whereas the Q-DLP policy keeps false-veto rate below 1.1%, wins all paired seeds, and yields QNI_cond = 0.9777 to 0.9972. A classical DLog oracle matches it, isolating feature access rather than classifier capacity. Thus quantum AI is not added as a generic model upgrade; for this DLP-hidden repair family, it supplies the missing feature that closes the repair-before-veto loop.

RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question difficulty and the model's current competence. Motivated by this, we propose Confidence and Difficulty-adaptive Policy Optimization (CoDaPO), which assigns each question a bounded value from rollout confidence and empirical difficulty. CoDaPO then uses this value to reweight policy updates and resample high-value learnable questions within mini-batches, thereby increasing discovery within the learnable band under a fixed compute budget. Across twelve benchmarks, CoDaPO consistently improves accuracy over existing RL methods. Our code is publicly available at https://github.com/tmlr-group/CoDaPO.

We identify and formally characterize credit misassignment as a systematic failure mode of GRPO in tool-augmented multimodal search agents: its uniform broadcast of trajectory-level advantages to all tokens causes valuable tool-use steps in failing trajectories to be penalized no differently from valueless ones. We further empirically quantify the scale of this phenomenon. Over half of failing trajectories and failing tool-use actions exhibit correctable credit misassignment, demonstrating that the wasted training signal is both substantial and structurally exploitable. Building on this insight, we propose Tool-Aware Policy Optimization (TAPO), which exploits the parameter-determinism property of information-acquisition tools: similar call parameters define equivalent information-acquisition actions and should therefore share comparable action credit. TAPO constructs counterfactual witnesses within the current training batch and compensates misassigned negative credit via confidence-gated conservative advantage correction. It requires no additional annotation, models, or sampling, and introduces negligible computational overhead. Across multiple multimodal search benchmarks, TAPO delivers consistent, plug-and-play improvements over strong baselines for three mainstream RL algorithms (GRPO, GSPO, and SAPO). Our code and models will be publicly released upon acceptance.

Verifiable reward training has improved mathematical and coding reasoning, but these domains capture only part of step-by-step decision making. Many real-world tasks require finding a high-value feasible plan among many valid alternatives. We introduce OPT*, a scalable family of optimization-style tasks for training and evaluating LLM step-by-step optimization-like reasoning along a complexity axis: each task provides a feasibility checker and evaluator, while a complexity parameter expands the search space without requiring new human labels. This motivates studying these tasks in two regimes: (i) solver-guided online policy optimization, which uses a solver as a value oracle for partial states and applies rank-based reward shaping to reinforce better next steps, and (ii) search-based offline RL when such solvers are unavailable. Theoretically, we relate success in large search spaces to the information a reasoner extracts per unit of search budget. Empirically, we ablate the ingredients that make search efficient on OPT* and show that training on OPT* improves step-by-step optimization-like reasoning.

Self-distilled policy optimization (SDPO) has become a popular paradigm for LLM post-training, where a model learns from its own predictions conditioned on privileged information. SDPO, however, is sensitive to how much each update step should be trusted: corrections from a self-teacher can be highly informative on some batches and misleading on others, and applying them uniformly with a fixed step size can destabilize training. Drawing inspiration from viscous-fluid dynamics and formalizing the analogy at the SDE level, we propose Physics-Guided Policy Optimization (PGPO), which introduces an information-modulated step-size multiplier derived from a mutual-information estimate between the student's predictions and the feedback-conditioned teacher. We show that this modulation preserves the order-1 weak-approximation guarantees of vanilla SGD, and incurs negligible overhead per iteration. We evaluate PGPO on the Science-QA dataset, where it outperforms SDPO on 3 of the 4 domains with gains of up to +4.5 points, while remaining stable in a setting where SDPO collapses late in training.

While Proximal Policy Optimization (PPO) demonstrates strong performance in stationary settings, we show that its standard optimization paradigm struggles in continual and non-stationary environments. The failure does not stem from insufficient model capacity or overly restrictive clipping. Instead, PPO performs persistent, directionally inefficient local updates, which indicates a lack of geometry-aware guidance for accumulating meaningful behavioral change and ultimately hindering transitions toward new behavior patterns. Although divergence-based regularization introduces partial geometric awareness, its monotonically increasing penalties implicitly discourage large policy deviations, even when such shifts are necessary for effective adaptation. To address this limitation, we propose Gaussian Trust Region Policy Optimization (GTR), which reshapes the trust region using a Gaussian kernel. The resulting constraint is bounded and non-monotonic, providing strong local stability while progressively relaxing under sustained high-advantage updates. To further improve robustness, we introduce a Mixture Gaussian Anchor that adapts to recent policy trajectories, reducing variance induced by stale references. GTR is architecture-agnostic and achieves strong performance across games, simulated robotic control, open-world exploration, and language model post-training. These results demonstrate that geometry-aware trust-region design can be a promising direction for robust reinforcement learning in complex non-stationary environments. Our code is available at https://anonymous.4open.science/r/GTR_demo/README.md.

Large scale GPU-parallel reinforcement learning has changed what can be trained in robot simulation, yet most systems still optimize one specialist policy per task. We propose a construction methodology for turning structured manipulation task families into GPU-parallel multi-task RL benchmarks, and instantiate it as MT-Libero using LIBERO assets and task predicates in Isaac Lab. The resulting benchmark supports simultaneous reinforcement learning over heterogeneous task suites with parallel rendering, physics randomization, and state-input or visual-input policies. To make such training practical under sparse success signals and limited prior data, we further propose DGPO, an on-policy demonstration guided method that combines importance weighted PPO with adaptive behavior cloning on matched demonstration actions. DGPO enables a tunable preference toward demonstrated task distributions, outperforming both prior-free RL and existing demonstration-based methods while preserving the stability and online improvement benefits of on-policy PPO.

Recent developments in Large Language Models (LLMs) have showcased impressive reasoning capabilities, with Reinforcement Learning with Verifiable Rewards (RLVR) being a promising enhancement strategy. However, existing reward mechanisms are constrained to the outcome-level correctness and lack explicit signals to guide the model to consider diverse solutions. In contrast, human problem solving typically involves evaluating multiple potential approaches and selecting the most reliable solution, a cognitive process that current RLVR frameworks do not explicitly incentivize. Inspired by this, we propose Hint-Guided Diversified Policy Optimization (HDPO), allowing the model to first list all potential candidate solution outlines as hints and then select the most reliable one for further reasoning. HDPO comprises two stages of Cold Start for Structured Reasoning and Hint-Guided Diversified Reinforcement Learning to incentivize the model to generate diverse and reliable solutions following the ``propose-select-think'' trajectory. Experimental results show that HDPO effectively boosts LLM reasoning and enhances the diversity of candidate solutions as well as the LLM's ability to identify reliable solutions.

Inductive generalization is a framework for reinforcement learning (RL) generalization in which inductively related task instances admit inductively related policies. Prior work captures this structure via a higher-order policy-evolution function learned directly with RL, but suffers from poor training scalability: as training tasks grow, aggregated reward feedback becomes noisy and conflicting, destabilizing training and weakening generalization. We propose DIBS, a decoupled behavioral cloning approach that separates learning task-specific policies from learning the evolution function. We first learn individual teacher policies per task via standard RL, then fit the evolution function via behavioral cloning on teacher-labeled state-action pairs. This replaces noisy reward aggregation with dense, stable supervision. DIBS achieves significant improvements in both training stability and zero-shot generalization against existing RL and meta-RL algorithms.