Unlocking the Critic: Reward-Free Policy Optimization for LLM Post-Training

arXiv:2609.37119 · cs.LG, cs.AI, cs.CL · Submitted 2026-09-29 · Read on arXiv

cs.LG, cs.AI, cs.CL

Submitted: 2026-09-29

Updated: 2026-09-29

Comments: 26 pages, 15 figures, 16 tables

Code: https://github.com/huggingface/open-r1

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 47× in this paper · explained in 1 episode
• Verifier — 47× in this paper · explained in 2 episodes
• AUC — 36× in this paper · explained in 2 episodes
• Actor — 32× in this paper · explained in 3 episodes
• Calibration — 25× in this paper · explained in 7 episodes
• Reinforcement Learning — 11× in this paper · explained in 4 episodes
• Reward-Free Policy Optimization — 5× in this paper
• Benchmark — 4× in this paper · explained in 2 episodes
• In International Conference on Learning Representations — 4× in this paper
• Trace — 4× in this paper · explained in 2 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Ablation — 2× in this paper · explained in 1 episode
• Credit assignment — 2× in this paper · explained in 3 episodes
• Fine-Tuning — 2× in this paper · explained in 5 episodes
• In Conference on Language Modeling — 2× in this paper
• Meeting of the Association for Computational Linguistics — 2× in this paper
• Reasoning Traces — 2× in this paper · explained in 3 episodes
• Agentic System — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• GRPO — 1× in this paper · explained in 6 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• In International Conference on Machine Learning — 1× in this paper
• Reinforcement Learning (RL) — 1× in this paper · explained in 25 episodes
• Reward Hacking — 1× in this paper · explained in 8 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Self-consistency — 1× in this paper · explained in 2 episodes
• Thinking mode — 1× in this paper · explained in 2 episodes
• Tokenization — 1× in this paper · explained in 2 episodes
• Verifiable Rewards — 1× in this paper · explained in 2 episodes

Sources

• Concrete Problems in AI Safety
• Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning
• Training Verifiers to Solve Math Word Problems
• Process Reinforcement through Implicit Rewards
• The Llama 3 Herd of Models
• REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization
• Kimi k1.5: Scaling Reinforcement Learning with LLMs
• Kimi K2: Open Agentic Intelligence
• MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention
• EVPO: Explained Variance Policy Optimization for Adaptive Critic Utilization in LLM Post-Training
• Proximal Policy Optimization Algorithms
• Bringing Value Models Back: Generative Critics for Value Modeling in LLM Reinforcement Learning
• Spurious Rewards: Rethinking Training Signals in RLVR
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• Reinforcing Chain-of-Thought Reasoning with Self-Evolving Rubrics
• Solving math word problems with process- and outcome-based feedback
• Qwen3 Technical Report
• What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret
• VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks
• Group Sequence Policy Optimization

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