Process reward models (PRMs) have proven effective for test-time scaling of Large Language Models (LLMs) on challenging reasoning tasks. However, reward hacking issues with PRMs limit their successful application in reinforcement fine-tuning. In this paper, we identify the main cause of PRM-induced reward hacking: the canonical summation-form credit assignment in reinforcement learning (RL), which defines the value as cumulative gamma-decayed future rewards, easily induces LLMs to hack steps with high rewards. To address this, we propose PURE: Process sUpervised Reinforcement lEarning. The key innovation of PURE is a min-form credit assignment that formulates the value function as the minimum of future rewards. This method significantly alleviates reward hacking by limiting the value function range and distributing advantages more reasonably. Through extensive experiments on 3 base models, we show that PRM-based approaches enabling min-form credit assignment achieve comparable reasoning performance to verifiable reward-based methods within only 30% steps. In contrast, the canonical sum-form credit assignment collapses training even at the beginning! Additionally, when we supplement PRM-based fine-tuning with just 10% verifiable rewards, we further alleviate reward hacking and produce the best fine-tuned model based on Qwen2.5-Math-7B in our experiments, achieving 82.5% accuracy on AMC23 and 53.3% average accuracy across 5 benchmarks. Moreover, we summarize the observed reward hacking cases and analyze the causes of training collapse. We release our code and model weights at https://github.com/CJReinforce/PURE.

One of the challenges in applying reinforcement learning in a complex real-world environment lies in providing the agent with a sufficiently detailed reward function. Any misalignment between the reward and the desired behavior can result in unwanted outcomes. This may lead to issues like "reward hacking" where the agent maximizes rewards by unintended behavior. In this work, we propose to disentangle the reward into two distinct parts. A simple task-specific reward, outlining the particulars of the task at hand, and an unknown common-sense reward, indicating the expected behavior of the agent within the environment. We then explore how this common-sense reward can be learned from expert demonstrations. We first show that inverse reinforcement learning, even when it succeeds in training an agent, does not learn a useful reward function. That is, training a new agent with the learned reward does not impair the desired behaviors. We then demonstrate that this problem can be solved by training simultaneously on multiple tasks. That is, multi-task inverse reinforcement learning can be applied to learn a useful reward function.

It is commonly believed that optimizing the reverse KL divergence results in "mode seeking", while optimizing forward KL results in "mass covering", with the latter being preferred if the goal is to sample from multiple diverse modes. We show -- mathematically and empirically -- that this intuition does not necessarily transfer well to doing reinforcement learning with reverse/forward KL regularization (e.g. as commonly used with language models). Instead, the choice of reverse/forward KL determines the family of optimal target distributions, parameterized by the regularization coefficient. Mode coverage depends primarily on other factors, such as regularization strength, and relative scales between rewards and reference probabilities. Further, we show commonly used settings such as low regularization strength and equal verifiable rewards tend to specify unimodal target distributions, meaning the optimization objective is, by construction, non-diverse. We leverage these insights to construct a simple, scalable, and theoretically justified algorithm. It makes minimal changes to reward magnitudes, yet optimizes for a target distribution which puts high probability over all high-quality sampling modes. In experiments, this simple modification works to post-train both Large Language Models and Chemical Language Models to have higher solution quality and diversity, without any external signals of diversity, and works with both forward and reverse KL when using either naively fails.

This paper presents GSWorld, a robust, photo-realistic simulator for robotics manipulation that combines 3D Gaussian Splatting with physics engines. Our framework advocates "closing the loop" of developing manipulation policies with reproducible evaluation of policies learned from real-robot data and sim2real policy training without using real robots. To enable photo-realistic rendering of diverse scenes, we propose a new asset format, which we term GSDF (Gaussian Scene Description File), that infuses Gaussian-on-Mesh representation with robot URDF and other objects. With a streamlined reconstruction pipeline, we curate a database of GSDF that contains 3 robot embodiments for single-arm and bimanual manipulation, as well as more than 40 objects. Combining GSDF with physics engines, we demonstrate several immediate interesting applications: (1) learning zero-shot sim2real pixel-to-action manipulation policy with photo-realistic rendering, (2) automated high-quality DAgger data collection for adapting policies to deployment environments, (3) reproducible benchmarking of real-robot manipulation policies in simulation, (4) simulation data collection by virtual teleoperation, and (5) zero-shot sim2real visual reinforcement learning. Website: https://3dgsworld.github.io/.

This paper demonstrates how reinforcement learning can explain two puzzling empirical patterns in household consumption behavior during economic downturns. I develop a model where agents use Q-learning with neural network approximation to make consumption-savings decisions under income uncertainty, departing from standard rational expectations assumptions. The model replicates two key findings from recent literature: (1) unemployed households with previously low liquid assets exhibit substantially higher marginal propensities to consume (MPCs) out of stimulus transfers compared to high-asset households (0.50 vs 0.34), even when neither group faces borrowing constraints, consistent with Ganong et al. (2024); and (2) households with more past unemployment experiences maintain persistently lower consumption levels after controlling for current economic conditions, a "scarring" effect documented by Malmendier and Shen (2024). Unlike existing explanations based on belief updating about income risk or ex-ante heterogeneity, the reinforcement learning mechanism generates both higher MPCs and lower consumption levels simultaneously through value function approximation errors that evolve with experience. Simulation results closely match the empirical estimates, suggesting that adaptive learning through reinforcement learning provides a unifying framework for understanding how past experiences shape current consumption behavior beyond what current economic conditions would predict.

Thompson sampling (TS) is a powerful and widely used strategy for sequential decision-making, with applications ranging from Bayesian optimization to reinforcement learning (RL). Despite its success, the theoretical foundations of TS remain limited, particularly in settings with complex temporal structure such as RL. We address this gap by establishing no-regret guarantees for TS using models with Gaussian marginal distributions. Specifically, we consider TS in episodic RL with joint Gaussian process (GP) priors over rewards and transitions. We prove a regret bound of $\mathcal{\tilde{O}}(\sqrt{KHΓ(KH)})$ over $K$ episodes of horizon $H$, where $Γ(\cdot)$ captures the complexity of the GP model. Our analysis addresses several challenges, including the non-Gaussian nature of value functions and the recursive structure of Bellman updates, and extends classical tools such as the elliptical potential lemma to multi-output settings. This work advances the understanding of TS in RL and highlights how structural assumptions and model uncertainty shape its performance in finite-horizon Markov Decision Processes.

Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are dominated by graph-based proxies that quantify structural connectivity but do not clarify what constitutes high-quality reasoning; such abstractions can be overly simplistic for inherently complex processes. We introduce a topological data analysis (TDA)-based evaluation framework that captures the geometry of reasoning traces and enables label-efficient, automated assessment. In our empirical study, topological features yield substantially higher predictive power for assessing reasoning quality than standard graph metrics, suggesting that effective reasoning is better captured by higher-dimensional geometric structures rather than purely relational graphs. We further show that a compact, stable set of topological features reliably indicates trace quality, offering a practical signal for future reinforcement learning algorithms.

Existing defence mechanisms have demonstrated significant effectiveness in mitigating rule-based Denial-of-Service (DoS) attacks, leveraging predefined signatures and static heuristics to identify and block malicious traffic. However, the emergence of AI-driven techniques presents new challenges to SDN security, potentially compromising the efficacy of existing defence mechanisms. In this paper, we introduce~AdaDoS, an adaptive attack model that disrupt network operations while evading detection by existing DoS-based detectors through adversarial reinforcement learning (RL). Specifically, AdaDoS models the problem as a competitive game between an attacker, whose goal is to obstruct network traffic without being detected, and a detector, which aims to identify malicious traffic. AdaDoS can solve this game by dynamically adjusting its attack strategy based on feedback from the SDN and the detector. Additionally, recognising that attackers typically have less information than defenders, AdaDoS formulates the DoS-like attack as a partially observed Markov decision process (POMDP), with the attacker having access only to delay information between attacker and victim nodes. We address this challenge with a novel reciprocal learning module, where the student agent, with limited observations, enhances its performance by learning from the teacher agent, who has full observational capabilities in the SDN environment. AdaDoS represents the first application of RL to develop DoS-like attack sequences, capable of adaptively evading both machine learning-based and rule-based DoS-like attack detectors.

Zero-shot reinforcement learning (RL) has emerged as a setting for developing general agents in an unsupervised manner, capable of solving downstream tasks without additional training or planning at test-time. Unlike conventional RL, which optimizes policies for a fixed reward, zero-shot RL requires agents to encode representations rich enough to support immediate adaptation to any objective, drawing parallels to vision and language foundation models. Despite growing interest, the field lacks a common analytical lens. We present the first unified framework for zero-shot RL. Our formulation introduces a consistent notation and taxonomy that organizes existing approaches and allows direct comparison between them. Central to our framework is the classification of algorithms into two families: direct representations, which learn end-to-end mappings from rewards to policies, and compositional representations, which decompose the representation leveraging the substructure of the value function. Within this framework, we highlight shared principles and key differences across methods, and we derive an extended bound for successor-feature methods, offering a new perspective on their performance in the zero-shot regime. By consolidating existing work under a common lens, our framework provides a principled foundation for future research in zero-shot RL and outlines a clear path toward developing more general agents.

Autonomous control of multi-stage industrial processes requires both local specialization and global coordination. Reinforcement learning (RL) offers a promising approach, but its industrial adoption remains limited due to challenges such as reward design, modularity, and action space management. Many academic benchmarks differ markedly from industrial control problems, limiting their transferability to real-world applications. This study introduces an enhanced industry-inspired benchmark environment that combines tasks from two existing benchmarks, SortingEnv and ContainerGym, into a sequential recycling scenario with sorting and pressing operations. We evaluate two control strategies: a modular architecture with specialized agents and a monolithic agent governing the full system, while also analyzing the impact of action masking. Our experiments show that without action masking, agents struggle to learn effective policies, with the modular architecture performing better. When action masking is applied, both architectures improve substantially, and the performance gap narrows considerably. These results highlight the decisive role of action space constraints and suggest that the advantages of specialization diminish as action complexity is reduced. The proposed benchmark thus provides a valuable testbed for exploring practical and robust multi-agent RL solutions in industrial automation, while contributing to the ongoing debate on centralization versus specialization.