# Group-Relative REINFORCE Is Secretly an Off-Policy Algorithm: Demystifying Some Myths About GRPO and Its Friends

arXiv: https://arxiv.org/abs/2509.24203 · HTML: https://mlsanity.com/paper/2509.24203/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 70 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 21 of 21)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [Geometric-Mean Policy Optimization](https://mlsanity.com/paper/2507.20673/) (2025)
- [Reinforcement Learning Optimization for Large-Scale Learning: An Efficient and User-Friendly Scaling Library](https://mlsanity.com/paper/2506.06122/) (2025)
- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [OpenRLHF: An Easy-to-use, Scalable and High-performance RLHF Framework](https://mlsanity.com/paper/2405.11143/) (2024)
- [Part I: Tricks or Traps? A Deep Dive into RL for LLM Reasoning](https://mlsanity.com/paper/2508.08221/) (2025)
- [Offline Regularised Reinforcement Learning for Large Language Models Alignment](https://mlsanity.com/paper/2405.19107/) (2024)
- [SwS: Self-aware Weakness-driven Problem Synthesis in Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08989/) (2025)
- [Asymmetric REINFORCE for off-Policy Reinforcement Learning: Balancing positive and negative rewards](https://mlsanity.com/paper/2506.20520/) (2025)
- [Trinity-RFT: A General-Purpose and Unified Framework for Reinforcement Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2505.17826/) (2025)

## Built on by (most cited first, 15 of 15)

- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [R3L: Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification](https://mlsanity.com/paper/2601.03715/) (2026)
- [An Empirical Study on Preference Tuning Generalization and Diversity Under Domain Shift](https://mlsanity.com/paper/2601.05882/) (2026)
- [Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning](https://mlsanity.com/paper/2606.21943/) (2026)
- [Staleness-Learning Rate Scaling Laws for Asynchronous RLHF](https://mlsanity.com/paper/2607.01083/) (2026)
- [Learning Stateful Predictive Knowledge From Experience](https://mlsanity.com/paper/2607.28638/) (2026)
- [Transformation-Augmented GRPO for Enhancing Exploration in Reasoning of Large Language Models](https://mlsanity.com/paper/2601.22478/) (2026)
- [SCA: Segment-Wise CoT Compression with Answer Alignment](https://mlsanity.com/paper/2603.07598/) (2026)
- [Skip-Connected Policy Optimization for Implicit Advantage](https://mlsanity.com/paper/2604.08690/) (2026)
- [F-TIS: Harnessing Diverse Models in Collaborative GRPO](https://mlsanity.com/paper/2605.22537/) (2026)
- [Do Math Reasoning LLMs Help Predict the Impact of Public Transit Events?](https://mlsanity.com/paper/2511.00808/) (2025)
- [POETS: Uncertainty-Aware LLM Optimization via Compute-Efficient Policy Ensembles](https://mlsanity.com/paper/2605.07775/) (2026)
- [Connect the Dots: Training LLMs for Long-Lifecycle Agents with Cross-Domain Generalization Via Reinforcement Learning](https://mlsanity.com/paper/2606.20002/) (2026)
- [Understanding Enrichment in Reinforcement Learning](https://mlsanity.com/paper/2610.02846/) (2026)
- [Backpropagating Verifier Rewards Through Continuous Flow Language Models](https://mlsanity.com/paper/2610.19080/) (2026)

## Abstract (arXiv)

Off-policy reinforcement learning (RL) for large language models (LLMs) is attracting growing interest, driven by practical constraints in real-world applications, the complexity of LLM-RL infrastructure, and the need for further innovations of RL methodologies. While classic REINFORCE and its modern variants like Group Relative Policy Optimization (GRPO) are typically regarded as on-policy algorithms with limited tolerance of off-policyness, we present in this work a first-principles derivation for group-relative REINFORCE -- a REINFORCE variant that uses the within-group mean reward as the baseline for advantage calculation -- without assuming a specific training data distribution, showing that it admits a native off-policy interpretation. This perspective yields two general principles for adapting REINFORCE to truly off-policy settings: regularizing policy updates, and actively shaping the data distribution. Our analysis demystifies some myths about the roles of importance sampling and clipping in GRPO, unifies and reinterprets two recent algorithms -- Online Policy Mirror Descent and Asymmetric REINFORCE -- as regularized forms of the REINFORCE loss, and offers theoretical justification for seemingly heuristic data-weighting strategies. Our findings lead to actionable insights that are validated with extensive empirical studies, and open up new opportunities for principled algorithm design in off-policy RL for LLMs. Source code for this work is available at https://github.com/agentscope-ai/Trinity-RFT/tree/main/examples/rec_gsm8k.