# Squeeze the Soaked Sponge: Efficient Off-policy Reinforcement Finetuning for Large Language Model

arXiv: https://arxiv.org/abs/2507.06892 · HTML: https://mlsanity.com/paper/2507.06892/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 47 of its 58 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Placed in

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

## Builds on (most cited first, 30 of 47)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning](https://mlsanity.com/paper/2503.04697/) (2025)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)

## Built on by (most cited first, 14 of 14)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [ADHint: Adaptive Hints with Difficulty Priors for Reinforcement Learning](https://mlsanity.com/paper/2512.13095/) (2025)
- [Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning](https://mlsanity.com/paper/2605.02913/) (2026)
- [RLVR without Ineffective Samples: Group Prioritized Off-Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2606.01281/) (2026)
- [Buffer Matters: Unleashing the Power of Off-Policy Reinforcement Learning in Large Language Model Reasoning](https://mlsanity.com/paper/2602.20722/) (2026)
- [OP-GRPO: Efficient Off-Policy GRPO for Flow-Matching Models](https://mlsanity.com/paper/2604.04142/) (2026)
- [DyJR: Preserving Diversity in Reinforcement Learning with Verifiable Rewards via Dynamic Jensen-Shannon Replay](https://mlsanity.com/paper/2603.16157/) (2026)
- [Learning Agentic Policy from Action Guidance](https://mlsanity.com/paper/2605.12004/) (2026)
- [From P(y|x) to P(y): Investigating Reinforcement Learning in Pre-train Space](https://mlsanity.com/paper/2604.14142/) (2026)
- [Experience Augmented Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2606.30420/) (2026)
- [Scaling DRL for Decision Making: A Survey on Data, Network, and Training Budget Strategies](https://mlsanity.com/paper/2508.03194/) (2025)
- [RSPO: Reward-Swap Policy Optimization for Multi-Turn LLM Agents](https://mlsanity.com/paper/2607.04713/) (2026)
- [ARMOR: Stabilizing On-Policy LLM RL with Off-Policy Anchor Samples](https://mlsanity.com/paper/2607.10481/) (2026)

## Abstract (arXiv)

Reinforcement Learning (RL) has demonstrated its potential to improve the reasoning ability of Large Language Models (LLMs). One major limitation of most existing Reinforcement Finetuning (RFT) methods is that they are on-policy RL in nature, i.e., data generated during the past learning process is not fully utilized. This inevitably comes at a significant cost of compute and time, posing a stringent bottleneck on continuing economic and efficient scaling. To this end, we launch the renaissance of off-policy RL and propose Reincarnating Mix-policy Proximal Policy Gradient (ReMix), a general approach to enable on-policy RFT methods like PPO and GRPO to leverage off-policy data. ReMix consists of three major components: (1) Mix-policy proximal policy gradient with an increased Update-To-Data (UTD) ratio for efficient training; (2) KL-Convex policy constraint to balance the trade-off between stability and flexibility; (3) Policy reincarnation to achieve a seamless transition from efficient early-stage learning to steady asymptotic improvement. In our experiments, we train a series of ReMix models upon PPO, GRPO and 1.5B, 7B base models. ReMix shows an average Pass@1 accuracy of 52.10% (for 1.5B model) with 0.079M response rollouts, 350 training steps and achieves 63.27%/64.39% (for 7B model) with 0.007M/0.011M response rollouts, 50/75 training steps, on five math reasoning benchmarks (i.e., AIME'24, AMC'23, Minerva, OlympiadBench, and MATH500). Compared with 15 recent advanced models, ReMix shows SOTA-level performance with an over 30x to 450x reduction in training cost in terms of rollout data volume. In addition, we reveal insightful findings via multifaceted analysis, including the implicit preference for shorter responses due to the Whipping Effect of off-policy discrepancy, the collapse mode of self-reflection behavior under the presence of severe off-policyness, etc.