# Slow-Fast Policy Optimization: Reposition-Before-Update for LLM Reasoning

arXiv: https://arxiv.org/abs/2510.04072 · HTML: https://mlsanity.com/paper/2510.04072/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 31)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [Reinforcement Learning with Verifiable Rewards: GRPO's Effective Loss, Dynamics, and Success Amplification](https://mlsanity.com/paper/2503.06639/) (2025)
- [Concise Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2504.05185/) (2025)
- [Active Preference Optimization for Sample Efficient RLHF](https://mlsanity.com/paper/2402.10500/) (2024)
- [Active Preference Learning for Large Language Models](https://mlsanity.com/paper/2402.08114/) (2024)
- [History Rhymes: Accelerating LLM Reinforcement Learning with RhymeRL](https://mlsanity.com/paper/2508.18588/) (2025)
- [Large-Scale Data Selection for Instruction Tuning](https://mlsanity.com/paper/2503.01807/) (2025)
- [Revisiting Group Relative Policy Optimization: Insights into On-Policy and Off-Policy Training](https://mlsanity.com/paper/2505.22257/) (2025)
- [Stable Reinforcement Learning for Efficient Reasoning](https://mlsanity.com/paper/2505.18086/) (2025)
- [Data-Efficient Finetuning Using Cross-Task Nearest Neighbors](https://mlsanity.com/paper/2212.00196/) (2022)
- [AlpaGasus: Training A Better Alpaca with Fewer Data](https://mlsanity.com/paper/2307.08701/) (2023)
- [Enabling Weak LLMs to Judge Response Reliability via Meta Ranking](https://mlsanity.com/paper/2402.12146/) (2024)

## Built on by (most cited first, 4 of 4)

- [From Efficiency to Adaptivity: A Deeper Look at Adaptive Reasoning in Large Language Models](https://mlsanity.com/paper/2511.10788/) (2025)
- [On the Hidden Objective Biases of Group-based Reinforcement Learning](https://mlsanity.com/paper/2601.05002/) (2026)
- [Gradient Extrapolation-Based Policy Optimization](https://mlsanity.com/paper/2605.06755/) (2026)
- [CRPO: Character-centric Group Relative Policy Optimization for Role-aware Reasoning in Role-playing Agents](https://mlsanity.com/paper/2605.25511/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has become central to enhancing reasoning in large language models (LLMs). Yet on-policy algorithms such as Group Relative Policy Optimization (GRPO) often suffer in early training: noisy gradients from low-quality rollouts lead to unstable updates and inefficient exploration. We introduce Slow-Fast Policy Optimization (SFPO), a simple yet efficient framework to address the above limitations via decomposing each step into three stages: a short fast trajectory of inner steps on the same batch, a reposition mechanism to control off-policy drift, and a final slow correction. This reposition-before-update design preserves the objective and rollout process unchanged, making SFPO plug-compatible with existing policy-gradient pipelines. Extensive experiments demonstrate that SFPO consistently improves stability, reduces number of rollouts, and accelerates convergence of reasoning RL training. Specifically, it outperforms GRPO by up to 2.80 points in average on math reasoning benchmarks. It also achieves up to 4.93texttimes fewer rollouts and an up to 4.19texttimes reduction in wall-clock time to match GRPO's best accuracy. Project website is available at https://slow-fast-po.github.io/.