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Reinforcement Learning · Policy Search

Zuyuan Zhang, Sizhe Tang, Tian Lan

Non-Markovian dynamics are commonly found in real-world environments due to long-range dependencies, partial observability, and memory effects. The Bellman equation that is the central pillar of Reinforcement learning (RL) becomes only approximately valid under Non-Markovian. Existing work often focus on practical algorithm designs and offer limited theoretical treatment to address key questions, such as what dynamics are indeed capturable by the Bellman framework and how to inspire new algorithm classes with optimal approximations. In this paper, we present a novel topological viewpoint on temporal-difference (TD) based RL. We show that TD errors can be viewed as 1-cochain in the topological space of state transitions, while Markov dynamics are then interpreted as topological integrability. This novel view enables us to obtain a Hodge-type decomposition of TD errors into an integrable component and a topological residual, through a Bellman–de Rham projection. We further propose HodgeFlow Policy Search (HFPS) by fitting a {potential network} to minimize the non-integrable projection residual in RL, achieving stability/sensitivity guarantees. In numerical evaluations, HFPS is shown to significantly improve RL performance under non-Markovian.

Reinforcement Learning · Planning

Benjamin Howard, Keith Frankston

We introduce a recursive AlphaZero style Monte--Carlo tree search algorithm, "RMCTS". It first generates the search tree using prior policies, and then recursively re-estimates action values by using the regularized optimal posterior policies from ``Monte--Carlo tree search as regularized policy optimization'' (Grill et al., 2020) at each node of the search tree, starting from the leaves and working back up to the root. We find that RMCTS matches or exceeds the quality of AlphaZero's MCTS-UCB in a tiny fraction of the time.

Reinforcement Learning · Online

Wenqian Weng, Yi He, Xingyu Zhou

In this paper, we study the private and robust alignment of language models from a theoretical perspective by establishing upper bounds on the suboptimality gap in both offline and online settings. We consider preference labels subject to privacy constraints and/or adversarial corruption, and analyze two distinct interplays between them: privacy-first and corruption-first. For the privacy-only setting, we show that log loss with an MLE-style algorithm achieves near-optimal rates, in contrast to conventional wisdom. For the joint privacy-and-corruption setting, we first demonstrate that existing offline algorithms in fact provide stronger guarantees---simultaneously in terms of corruption level and privacy parameters---than previously known, which further yields improved bounds in the corruption-only regime. In addition, we also present the first set of results for private and robust online alignment. Our results are enabled by new uniform convergence guarantees for log loss and square loss under privacy and corruption, which we believe have broad applicability across learning theory and statistics.

Reinforcement Learning · Online

Jiamin Xu, Kyra Gan

Online reinforcement learning in non-episodic, finite-horizon MDPs remains underexplored and is challenged by the need to estimate returns to a fixed terminal time. Existing infinite-horizon methods, which often rely on discounted contraction, do not naturally account for this fixed-horizon structure. We introduce a modified Q-function: rather than targeting the full-horizon, we learn a K-step lookahead Q-function that truncates planning to the next K steps. To further improve sample efficiency, we introduce a thresholding mechanism: actions are selected only when their estimated K-step lookahead value exceeds a time-varying threshold. We provide an efficient tabular learning algorithm for this novel objective, proving it achieves fast finite-sample convergence: it achieves minimax optimal constant regret for $K=1$ and $\mathcal{O}(\max((K-1),C_{K-1})\sqrt{SAT\log(T)})$ regret for any $K \geq 2$. We numerically evaluate the performance of our algorithm under the objective of maximizing reward. Our implementation adaptively increases K over time, balancing lookahead depth against estimation variance. Empirical results demonstrate superior cumulative rewards over state-of-the-art tabular RL methods across synthetic MDPs and RL environments: JumpRiverswim, FrozenLake and AnyTrading.

Deep Learning · Theory

Etienne Boursier, Claire Boyer

Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis. We develop a unified, measure-based framework for studying single-layer softmax attention under both finite and infinite prompts. For i.i.d. Gaussian inputs, we lean on the fact that the softmax operator converges in the infinite-prompt limit to a linear operator acting on the underlying input-token measure. Building on this insight, we establish non-asymptotic concentration bounds for the output and gradient of softmax attention, quantifying how rapidly the finite-prompt model approaches its infinite-prompt counterpart, and prove that this concentration remains stable along the entire training trajectory in general in-context learning settings with sub-Gaussian tokens. In the case of in-context linear regression, we use the tractable infinite-prompt dynamics to analyze training at finite prompt length. Our results allow optimization analyses developed for linear attention to transfer directly to softmax attention when prompts are sufficiently long, showing that large-prompt softmax attention inherits the analytical structure of its linear counterpart. This, in turn, provides a principled and broadly applicable toolkit for studying the training dynamics and statistical behavior of softmax attention layers in large prompt regimes.

Reinforcement Learning · Online

Jongchan Park

While the "Scaling Laws" have driven massive success in Computer Vision and NLP through large-scale training with massive batch sizes, Reinforcement Learning (RL) has largely failed to benefit from this paradigm. In RL, increasing batch sizes beyond a modest threshold often leads to diminishing returns or performance degradation due to the inherent non-stationarity of the data distribution. In this paper, we challenge the prevailing static view of batch sizes in RL by observing that the degree of non-stationarity is not constant: early training involves rapid behavioral shifts requiring small batches for plasticity, whereas late training approaches a quasi-stationary regime where large batches are essential for high-precision convergence. To leverage this insight, we propose Adaptive Batch Scaling (ABS), a simple yet effective framework that dynamically adjusts the effective batch size based on the stability of the learning process. We introduce Behavioral Divergence, a novel metric that quantifies non-stationarity by measuring action-level shifts between policy updates, and use it to scale the batch size inversely to the policy's volatility. By integrating ABS with the Parallelised Q-Network (PQN) algorithm, we demonstrate on the ALE benchmark that our method synergizes early-stage model plasticity with late-stage accurate and stable convergence. Our empirical results show that ABS not only yields substantial performance improvements over static baselines but also successfully scales to larger network architectures, offering a foundational step toward bridging the scaling gap between RL and supervised learning.

Reinforcement Learning · Online

Andrew Wagenmaker, Perry Dong, Raymond Tsao, Chelsea Finn, Sergey Levine

Standard practice across domains from robotics to language is to first pretrain a policy on a large-scale demonstration dataset, and then finetune this policy, typically with reinforcement learning (RL), in order to improve performance on deployment domains. This finetuning step has proved critical in achieving human or super-human performance, yet while much attention has been given to developing more effective finetuning algorithms, little attention has been given to ensuring the pretrained policy is an effective initialization for RL finetuning. In this work we seek to understand how the pretrained policy affects finetuning performance, and how to pretrain policies in order to ensure they are effective initializations for finetuning. We first show theoretically that standard behavioral cloning (BC) can fail to ensure coverage over the demonstrator's actions, a minimal condition necessary for effective RL finetuning. We then show that if, instead of exactly fitting the observed demonstrations, we train a policy to model the posterior distribution of the demonstrator's behavior given the demonstration dataset, we do obtain a policy that ensures coverage over the demonstrator's actions, enabling more effective finetuning. Furthermore, this policy achieves this while ensuring pretrained performance is no worse than that of the BC policy. We then show this approach is practically implementable with modern generative models and leads to significantly improved RL finetuning performance on both realistic robotic control benchmarks and real-world robotic manipulation tasks, as compared to standard behavioral cloning.

Reinforcement Learning · Multi-agent

Bin Wu, Haoran Xu, Xiang Zhuang, Zonghao Chen, Zhu Li, Emine Yilmaz, Qiang Zhang

Large language model (LLM)-based multi-agent systems commonly rely on natural-language prompts to specify agent behavior, yet optimizing these prompts remains challenging when agent roles and interaction structures are fixed by design. In such systems, behaviors emerge over long, noisy interaction trajectories, making it difficult to determine which prompt components are responsible for success or failure. As a result, outcome-level feedback alone is insufficient, while existing prompt optimization methods typically rely on final task scores or global prompt rewrites, limiting their ability to exploit trajectory evidence or support the localized updates. We propose Trajectory-based Rule Credit Estimation (TRUCE), a framework for prompt optimization in multi-agent systems that explicitly addresses this credit assignment challenge. TRUCE performs trajectory-aware attribution by linking outcome feedback to informative sub-trajectories and translating the resulting credit signals into unit-level edits over prompt-defined behavioral rules. By preserving agent roles and interaction structures, TRUCE enables prompt refinement through localized updates aggregated across tasks. Experiments on multiple benchmarks demonstrate that TRUCE consistently improves task performance and efficiency over competitive baselines.

Reinforcement Learning · Multi-agent

Pietro Zanotta, Dibakar Sarkar, Honghui Zheng, Somdatta Goswami, Jan Drgona

Controlling partial differential equations (PDEs) with learning-based policies remains fundamentally limited by fixed-dimensional representations: policies trained for a specific sensor, actuator, or agent configuration typically fail when the configuration changes. This limitation is particularly severe in multi-agent PDE control, where policies do not scale across population sizes without retraining. We address this challenge by reformulating PDE control as an operator learning problem that maps state fields to continuous control functions and trains them end-to-end through differentiable PDE solvers, yielding policies that naturally adapt to varying sensor and actuator configurations. Remarkably, policies trained on small swarms exhibit cardinality invariance, allowing for zero-shot transfer to significantly larger populations as well as robustness to partial agent failure. This scalability arises from agents sharing a common policy and coordinating through their physical environment, which produces an emergent self-normalization effect. To explain this phenomenon, we provide a theorem grounded in mean-field theory demonstrating that policy gradients computed from finite-agent systems converge to those of a continuous control limit. Empirically, we validate the framework on tracking, stabilization, and density transport across linear, nonlinear, chaotic, and turbulent PDEs.

Reinforcement Learning · Deep RL

Jeong Woon Lee, Kyoleen Kwak, Daeho Kim, Hyoseok Hwang

Policies learned via continuous actor-critic methods often exhibit erratic, high-frequency oscillations, making them unsuitable for physical deployment. Current approaches attempt to enforce smoothness by directly regularizing the policy's output. We argue that this approach treats the symptom rather than the cause. In this work, we theoretically establish that policy non-smoothness is fundamentally governed by the differential geometry of the critic. By applying implicit differentiation to the actor-critic objective, we prove that the sensitivity of the optimal policy is bounded by the ratio of the Q-function's mixed-partial derivative (noise sensitivity) to its action-space curvature (signal distinctness). To empirically validate this theoretical insight, we introduce PAVE (Policy-Aware Value-field Equalization), a critic-centric regularization framework that treats the critic as a scalar field and stabilizes its induced action-gradient field. PAVE rectifies the learning signal by minimizing the Q-gradient volatility while preserving local curvature. Experimental results demonstrate that PAVE achieves smoothness and robustness comparable to policy-side smoothness regularization methods, while maintaining competitive task performance, without modifying the actor.

General Machine Learning · Evaluation

Nathan Jo, Ashia Wilson

Evaluations of generative models are now ubiquitous, and their outcomes critically shape public and scientific expectations of AI's capabilities. Yet skepticism about their reliability continues to grow. How can we know that a reported accuracy genuinely reflects a model’s underlying performance? Although benchmark results are often presented as direct measurements of capability, in practice they are inferences: treating a score as evidence of capability already presupposes a theory of what it means to be capable at a task. We argue that AI evaluations should instead be framed as inference tasks grounded on an explicit theory of capability. While this perspective is standard in fields like psychometrics, it remains underdeveloped in AI evaluation, where core assumptions are often left *implicit*. As a proof-of-concept, we empirically show that reported performance can depend strongly on the evaluator’s modeling assumptions, underscoring the need for transparent, theory-driven evaluation practices. We conclude by offering practical guidelines for rigorously designing evaluations built on explicit theories of capability.

Applications · Robotics

Yajie Li, Bozhou Zhang, Chun Gu, Zipei Ma, Jiahui Zhang, Jiankang Deng, Xiatian Zhu, Li Zhang

Video generation models offer a promising imagination mechanism for robot manipulation by predicting long-horizon future observations, but effectively exploiting these imagined futures for action execution remains challenging. Existing approaches either condition policies on predicted frames or directly decode generated videos into actions, both suffering from a mismatch between visual realism and control relevance. As a result, predicted observations emphasize perceptual fidelity rather than action-centric causes of state transitions, leading to indirect and unstable control. To address this gap, we propose MoLA (Mixture of Latent Actions), a control-oriented interface that transforms imagined future videos into executable representations. Instead of passing predicted frames directly to the policy, MoLA leverages multiple pretrained inverse dynamics models to infer a mixture of latent actions implied by generated visual transitions. These modality-aware inverse dynamics models capture complementary semantic, depth, and flow cues, providing a structured and physically grounded action representation that bridges video imagination and policy execution. We evaluate our approach on simulated benchmarks (LIBERO, CALVIN, and LIBERO-Plus) and real-world robot manipulation tasks, achieving consistent gains in task success, temporal consistency, and generalization. Code will be released.

Reinforcement Learning · Deep RL

Yudong Luo, Erick Delage

Optimizing Conditional Value-at-risk (CVaR) using policy gradient (a.k.a CVaR-PG) faces significant challenges of sample inefficiency. This inefficiency stems from the fact that it focuses on tail-end performance and overlooks many sampled trajectories. We address this problem by augmenting CVaR with an expected quantile term. Quantile optimization admits a dynamic programming formulation that leverages all sampled data, thus improves sample efficiency. This does not alter the CVaR objective since CVaR corresponds to the expectation of quantile over the tail. Empirical results in domains with verifiable risk-averse behavior show that our algorithm within the Markovian policy class substantially improves upon CVaR-PG and consistently outperforms other existing methods.

Reinforcement Learning · Batch/Offline

Zhiqi Zhuang, di wu, Benoit Boulet

Safe offline reinforcement learning (RL) requires optimizing policies within the support of static datasets while satisfying strict safety constraints. Although recent latent generative policies achieve strong empirical performance, they rely heavily on implicit regularization and lack systematic control over distributional shift during policy improvement. In this work, we propose a geometric control framework that leverages the bijective structure of conditional normalizing flows to provide a tractable mechanism to regulate distributional deviation of the policy. By constraining divergence in the latent base space, we derive tractable upper bounds on the induced Wasserstein distance and total variation of the policy distribution, establishing an analyzable connection between latent geometry and downstream behaviors. This insight motivates a decoupled architecture: a flow prior shapes a feasibility-weighted latent manifold using Hamilton--Jacobi reachability signals, while a latent refiner performs geometrically constrained optimization directly in the base space. Across multiple safe RL benchmarks, our method achieves robustly low violation rates with competitive returns, highlighting the benefits of structured geometric regularization.

Reinforcement Learning · Batch/Offline

Yuan Lu, Dongqi Han, Yansen Wang, Dongsheng Li

Diffusion planners are a strong approach for offline reinforcement learning, but they can fail when value-guided selection favours trajectories that score well yet are locally inconsistent with the environment dynamics, resulting in brittle execution. We propose Self-supervised Action Gating with Energies (SAGE), an inference-time re-ranking method that penalises dynamically inconsistent plans using a latent consistency signal. SAGE trains a Joint-Embedding Predictive Architecture (JEPA) encoder on offline state sequences and an action-conditioned latent predictor for short horizon transitions. At test time, SAGE assigns each sampled candidate an energy given by its latent prediction error and combines this feasibility score with value estimates to select actions. SAGE can integrates into existing diffusion planning pipelines that can sample trajectories and select actions via value scoring; it requires no environment rollouts and no policy re-training. Across locomotion, navigation, and manipulation benchmarks, SAGE improves the performance and robustness of diffusion planners.

Bo-Wen Yin, Qize Yang, Boyuan Sun, Xihan Wei, Qibin Hou

The “thinking with images” paradigm has led multimodal large language models to generate intermediate visual steps—such as cropping, annotation, spatial localization, and sketches—to enhance high-resolution perception and complex reasoning. However, existing multimodal Process Reward Models (PRMs) evaluate only textual reasoning and cannot judge the correctness of these visual steps, creating a key gap when visual reasoning is essential for solving tasks. We propose Discriminative Visual Process Reward Model (DiscPRM), a multimodal PRM that jointly evaluates textual and visual intermediate steps by modeling visual reasoning trajectories, image operations, and text-image consistency. To support this, we build VTReward-100K, a dataset of step-by-step visual reasoning sequences with supervision. Experiments show that using DiscPRM for Best-of-N process supervision substantially improves multimodal reasoning performance on tasks requiring visual intermediate steps, achieving over 5% gains across benchmarks. We further introduce VABench, the first benchmark for evaluating PRMs on visual reasoning error detection. We hope this work can provide foundational support for advancing the emerging direction of visual–textual process reward.

Mengjingcheng Mo, Jiaxu Leng, Xinbo Gao

Video anomaly understanding (VAU) relies on sparse, context-dependent cues. However, existing passive paradigms suffer from observational aliasing, where static sampling fails to disambiguate semantically distinct events. To overcome this, we propose $Anom\text{-}\pi$, a closed-loop framework that reconceptualizes video understanding as an active sequential decision-making process within a dynamic environment. Inspired by human video-reviewing behavior, this framework unifies internal cognitive reasoning and strategic evidence acquisition into an interleaved policy, utilizing temporal atomic operators such as local backtracking, temporal expansion, and fine-grained sampling to endow the model with perceptual proactivity. To learn such complex interaction strategies under video-level weak supervision, we design Interactive Direct Preference Optimization (iDPO) to achieve trajectory-level policy alignment, guided by an Active Evidence Inquiry (AEI) utility that balances task success, informative evidence acquisition, and interaction cost. This approach enables the agent to learn to actively disambiguate hypotheses while suppressing redundant exploration. Extensive experiments demonstrate that our framework, with only 2B parameters, achieves highly competitive performance, significantly outperforming state-of-the-art large-scale VAU models in complex scenarios.

General Machine Learning · Online Learning, Active Learning and Bandits

Ruizhe Deng, Bibhas Chakraborty, Ran Chen, Yan Shuo Tan

We propose Bayesian Forest Thompson Sampling (BFTS), which performs Thompson sampling using arm-wise Bayesian Additive Regression Trees (BART) to model each action's mean reward and generate MCMC-based posterior draws for decision-making. We derive an information-theoretic Bayesian regret bound of order $\widetilde{\mathcal O}(K\sigma\sqrt{T})$ for ideal posterior sampling under a correctly specified Bayesian design. Empirically, BFTS achieves competitive regret on nonlinear synthetic benchmarks with near-nominal uncertainty calibration, attains the best average rank across nine OpenML contextual bandit benchmarks, and yields higher estimated policy values than linear, neural, and tree-ensemble baselines in a Drink Less micro-randomized trial case study. Across OpenML benchmarks, BFTS is robust to hyperparameter choices.

Reinforcement Learning · Batch/Offline

Franki Nguimatsia-Tiofack, Fabian Schramm, Théotime Le Hellard, Justin Carpentier

Standard approaches to goal-conditioned reinforcement learning (GCRL) that rely on temporal-difference learning can be unstable and sample-inefficient due to bootstrapping. While recent work has explored contrastive and supervised formulations to improve stability, we present a probabilistic alternative, called survival value learning (SVL), that reframes GCRL as a survival learning problem by modeling the time‑to‑goal from each state as a probability distribution. This perspective yields a closed‑form identity that expresses the goal‑conditioned value function as a discounted sum of survival probabilities, enabling value estimation via a hazard model trained via maximum likelihood on both event and right‑censored trajectories. We introduce three practical value estimators, including finite-horizon truncation and two binned infinite-horizon approximations to capture long-horizon objectives. Experiments on standard offline GCRL benchmarks show that SVL combined with hierarchical actors matches or surpasses strong hierarchical TD baselines, particularly excelling on complex, long‑horizon tasks.

Reinforcement Learning · Batch/Offline

Sungyoung Lee, Dohyeong Kim, Eshan Balachandar, Zelal Mustafaoglu, Keshav Pingali

We propose Flow-Anchored Noise-conditioned Q-Learning (FAN), a highly efficient and high-performing offline reinforcement learning (RL) algorithm. Recent work has shown that expressive flow policies and distributional critics improve offline RL performance, but at a high computational cost. Specifically, flow policies require iterative sampling to produce a single action, and distributional critics require computation over multiple samples (e.g., quantiles) to estimate value. To address these inefficiencies while maintaining high performance, we introduce FAN. Our method employs a behavior regularization technique that utilizes only a single flow policy iteration and requires only a single Gaussian noise sample for distributional critics. Our theoretical analysis of convergence and performance bounds demonstrates that these simplifications not only improve efficiency but also lead to superior task performance. Experiments on robotic manipulation and locomotion tasks demonstrate that FAN achieves state-of-the-art performance while significantly reducing both training and inference runtimes. We release our code at https://anonymous.4open.science/r/FAN.