Process Rewards for Outcome-Guided Reasoning Steps in LLM Reinforcement Learning

arXiv:2604.02341 · cs.LG, cs.AI · Submitted 2026-02-08 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-02-08

Updated: 2026-10-13

Terminology

• Reinforcement Learning — 2× in this paper · explained in 4 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• GRPO — 1× in this paper · explained in 6 episodes
• Group Relative Policy Optimization (GRPO) — 1× in this paper · explained in 5 episodes
• Process Reward Models (PRMs) — 1× in this paper · explained in 3 episodes
• Reward Hacking — 1× in this paper · explained in 8 episodes
• Systematic Bias — 1× in this paper · explained in 3 episodes
• Verifiable Rewards — 1× in this paper · explained in 2 episodes

Sources

• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• Reinforcement Learning for Reasoning in Large Language Models with One Training Example
• Towards Hierarchical Multi-Step Reward Models for Enhanced Reasoning in Large Language Models
• The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models
• Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner
• Future-KL Regularized GRPO: Process-Level Credit Assignment from $f$-Divergence Regularization
• Beyond Correctness: Harmonizing Process and Outcome Rewards through RL Training
• Know What You Don't Know: Uncertainty Calibration of Process Reward Models
• High-Dimensional Continuous Control Using Generalized Advantage Estimation
• Proximal Policy Optimization Algorithms
• Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback
• DAPO: An Open-Source LLM Reinforcement Learning System at Scale
• Beyond the First Error: Process Reward Models for Reflective Mathematical Reasoning
• An Efficient and Precise Training Data Construction Framework for Process-supervised Reward Model in Mathematical Reasoning
• Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement
• Hard Examples Are All You Need: Maximizing GRPO Post-Training Under Annotation Budgets
• Measuring Mathematical Problem Solving With the MATH Dataset
• OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems

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