# How Off-Policy Can GRPO Be? Mu-GRPO for Efficient LLM Reinforcement Learning

arXiv: https://arxiv.org/abs/2605.17570 · HTML: https://mlsanity.com/paper/2605.17570/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 17 May 2026.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [Defeating the Training-Inference Mismatch via FP16](https://mlsanity.com/paper/2510.26788/) (2025)
- [Tapered Off-Policy REINFORCE: Stable and efficient reinforcement learning for LLMs](https://mlsanity.com/paper/2503.14286/) (2025)
- [StreamRL: Scalable, Heterogeneous, and Elastic RL for LLMs with Disaggregated Stream Generation](https://mlsanity.com/paper/2504.15930/) (2025)
- [AsyncFlow: An Asynchronous Streaming RL Framework for Efficient LLM Post-Training](https://mlsanity.com/paper/2507.01663/) (2025)
- [History Rhymes: Accelerating LLM Reinforcement Learning with RhymeRL](https://mlsanity.com/paper/2508.18588/) (2025)

## Built on by (most cited first, 7 of 7)

- [Staleness-Learning Rate Scaling Laws for Asynchronous RLHF](https://mlsanity.com/paper/2607.01083/) (2026)
- [Performance, Efficiency and Collapse -- Advantages and Challenges in Offline Post-training of Code LLMs](https://mlsanity.com/paper/2609.11956/) (2026)
- [Rollout Efficiency in Reinforcement Learning for Reasoning Large Language Models: A Taxonomy and Future Directions](https://mlsanity.com/paper/2609.25463/) (2026)
- [Cool the Sampler, Not the Learner: Sampling Temperature Moves the Staleness Cliff of Importance-Corrected GRPO](https://mlsanity.com/paper/2609.36953/) (2026)
- [Asynchronous LLM Post-Training: Group-Mass Capping and Convergence Analysis](https://mlsanity.com/paper/2610.01896/) (2026)
- [Probe the Harness: Setup Checks for Stale-Data RL Comparisons in Language Models](https://mlsanity.com/paper/2610.02911/) (2026)
- [Two Clocks: Why Larger Rollout Batches Learn Slower but Fail on Schedule in Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2610.18853/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) has been a key driver of recent progress in reinforcement learning with verifiable rewards (RLVR) for large language models, but it is typically trained in a low-staleness, near-on-policy regime that incurs substantial system overhead. We ask a simple question: How off-policy can GRPO be? We show that GRPO-style algorithms can tolerate substantially larger rollout staleness than previously assumed, and propose Mu-GRPO, an RL training framework that organizes training into a small number (e.g., four) of large sequential generation-optimization stages. This design induces high rollout staleness while greatly reducing rollout-optimization switching overhead. To stabilize learning under stale data, Mu-GRPO combines relaxed clipping, which preserves useful stale-rollout gradients, with negative-advantage veto, which removes destabilizing post-trigger suffix updates in negative-advantage responses. Across five language models and multiple math reasoning benchmarks, Mu-GRPO matches or exceeds the performance of standard GRPO while achieving around 2x speedup in wall-clock training time, establishing a substantially improved performance-efficiency trade-off for LLM reinforcement learning.