Stop Summation: Min-Form Credit Assignment Is All Process Reward Model Needs for Reasoning

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. Code and models are available at https://github.com/CJReinforce/PURE.

Scaling Offline Model-Based RL via Jointly-Optimized World-Action Model Pretraining

A significant aspiration of offline reinforcement learning (RL) is to develop a generalist agent with high capabilities from large and heterogeneous datasets. However, prior approaches that scale offline RL either rely heavily on expert trajectories or struggle to generalize to diverse unseen tasks. Inspired by the excellent generalization of world model in conditional video generation, we explore the potential of image observation-based world model for scaling offline RL and enhancing generalization on novel tasks. In this paper, we introduce JOWA: Jointly-Optimized World-Action model, an offline model-based RL agent pretrained on multiple Atari games to learn general-purpose representation and decision-making ability. Our method jointly optimizes a world-action model through shared transformer backbone, which stabilize temporal difference learning with large models during pretraining. Moreover, we propose an provably efficient and parallelizable planning algorithm to compensate for the Q-value estimation error and thus search out better policies. Experimental results indicate that our largest agent, with 150 million parameters, achieves 78.9% human-level performance on pretrained games using only 10% subsampled offline data, outperforming existing state-of-the-art large-scale offline RL baselines by 31.6% on averange. Furthermore, JOWA scales favorably with model capacity and can sample-efficiently transfer to novel games using only 5k offline fine-tuning data corresponding to about 4 trajectories per game, which demonstrates superior generalization of JOWA. We will release codes at https://github.com/CJReinforce/JOWA.