# REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization

arXiv: https://arxiv.org/abs/2501.03262 · HTML: https://mlsanity.com/paper/2501.03262/

## Key facts

- Cited by 241 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 4 Jan 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 7 of 7)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [ChatGPT for Robotics: Design Principles and Model Abilities](https://mlsanity.com/paper/2306.17582/) (2023)

## Built on by (most cited first, 30 of 241)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [GPG: A Simple and Strong Reinforcement Learning Baseline for Model Reasoning](https://mlsanity.com/paper/2504.02546/) (2025)
- [TempFlow-GRPO: When Timing Matters for GRPO in Flow Models](https://mlsanity.com/paper/2508.04324/) (2025)
- [Tool-Star: Empowering LLM-Brained Multi-Tool Reasoner via Reinforcement Learning](https://mlsanity.com/paper/2505.16410/) (2025)
- [Can Large Reasoning Models Self-Train?](https://mlsanity.com/paper/2505.21444/) (2025)
- [EnvScaler: Scaling Tool-Interactive Environments for LLM Agent via Programmatic Synthesis](https://mlsanity.com/paper/2601.05808/) (2026)
- [Part I: Tricks or Traps? A Deep Dive into RL for LLM Reasoning](https://mlsanity.com/paper/2508.08221/) (2025)
- [Can Prompt Difficulty be Online Predicted for Accelerating RL Finetuning of Reasoning Models?](https://mlsanity.com/paper/2507.04632/) (2025)
- [Graph-R1: Towards Agentic GraphRAG Framework via End-to-end Reinforcement Learning](https://mlsanity.com/paper/2507.21892/) (2025)
- [Stop Summation: Min-Form Credit Assignment Is All Process Reward Model Needs for Reasoning](https://mlsanity.com/paper/2504.15275/) (2025)
- [VLM-R3: Region Recognition, Reasoning, and Refinement for Enhanced Multimodal Chain-of-Thought](https://mlsanity.com/paper/2505.16192/) (2025)
- [ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2506.18896/) (2025)
- [Think or Not Think: A Study of Explicit Thinking in Rule-Based Visual Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.16188/) (2025)
- [RL Tango: Reinforcing Generator and Verifier Together for Language Reasoning](https://mlsanity.com/paper/2505.15034/) (2025)
- [Chasing Moving Targets with Online Self-Play Reinforcement Learning for Safer Language Models](https://mlsanity.com/paper/2506.07468/) (2025)
- [MMR1: Enhancing Multimodal Reasoning with Variance-Aware Sampling and Open Resources](https://mlsanity.com/paper/2509.21268/) (2025)
- [LLMs are Single-threaded Reasoners: Demystifying the Working Mechanism of Soft Thinking](https://mlsanity.com/paper/2508.03440/) (2025)
- [Look Back to Reason Forward: Revisitable Memory for Long-Context LLM Agents](https://mlsanity.com/paper/2509.23040/) (2025)
- [No Free Lunch: Rethinking Internal Feedback for LLM Reasoning](https://mlsanity.com/paper/2506.17219/) (2025)
- [Search and Refine During Think: Facilitating Knowledge Refinement for Improved Retrieval-Augmented Reasoning](https://mlsanity.com/paper/2505.11277/) (2025)
- [Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation](https://mlsanity.com/paper/2604.13010/) (2026)
- [100 Days After DeepSeek-R1: A Survey on Replication Studies and More Directions for Reasoning Language Models](https://mlsanity.com/paper/2505.00551/) (2025)
- [On the Design of KL-Regularized Policy Gradient Algorithms for LLM Reasoning](https://mlsanity.com/paper/2505.17508/) (2025)
- [SPEED-RL: Faster Training of Reasoning Models via Online Curriculum Learning](https://mlsanity.com/paper/2506.09016/) (2025)
- [SPELL: Self-Play Reinforcement Learning for Evolving Long-Context Language Models](https://mlsanity.com/paper/2509.23863/) (2025)
- [Promoting Efficient Reasoning with Verifiable Stepwise Reward](https://mlsanity.com/paper/2508.10293/) (2025)
- [Synergizing RAG and Reasoning: A Systematic Review](https://mlsanity.com/paper/2504.15909/) (2025)
- [CAPO: Towards Enhancing LLM Reasoning through Generative Credit Assignment](https://mlsanity.com/paper/2508.02298/) (2025)

## Abstract (arXiv)

Reinforcement Learning from Human Feedback~(RLHF) plays a crucial role in aligning Large Language Models~(LLMs). The dominant algorithm, Proximal Policy Optimization~(PPO), employs a critic network to estimate advantages, which introduces significant computational and memory overhead. To address this, a family of critic-free algorithms (e.g., GRPO, RLOO) has emerged. However, these methods typically rely on textitprompt-level (local) advantage normalization, which suffers from inaccurate advantage estimation, a tendency to overfit, and, as we show, is a theoretically biased estimator. To solve these challenges, we introduce REINFORCE++, a critic-free framework centered on Global Advantage Normalization. By normalizing advantages across the entire global batch rather than small, prompt-specific groups, our method provides a more stable and theoretically sound, textiteffectively unbiased estimate (whose bias vanishes as batch size increases). We introduce two variants: REINFORCE++, a highly efficient and general algorithm (k ≥ 1) for general-domain RLHF, and REINFORCE++ /w baseline, a robust group-sampling variant (k > 1) for complex reasoning tasks. Our empirical evaluation demonstrates that each variant shows superior stability and performance in its respective domain, outperforming existing methods and even PPO in complex agentic settings.