# A Step Back: Prefix Importance Ratio Stabilizes Policy Optimization

arXiv: https://arxiv.org/abs/2601.22718 · HTML: https://mlsanity.com/paper/2601.22718/

## 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 26 of its 29 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [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)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [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)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [Asynchronous RLHF: Faster and More Efficient Off-Policy RL for Language Models](https://mlsanity.com/paper/2410.18252/) (2024)
- [Tapered Off-Policy REINFORCE: Stable and efficient reinforcement learning for LLMs](https://mlsanity.com/paper/2503.14286/) (2025)
- [Prosperity before Collapse: How Far Can Off-Policy RL Reach with Stale Data on LLMs?](https://mlsanity.com/paper/2510.01161/) (2025)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [DCPO: Dynamic Clipping Policy Optimization](https://mlsanity.com/paper/2509.02333/) (2025)
- [Laminar: A Scalable Asynchronous RL Post-Training Framework](https://mlsanity.com/paper/2510.12633/) (2025)
- [RollPacker: Mitigating Long-Tail Rollouts for Fast, Synchronous RL Post-Training](https://mlsanity.com/paper/2509.21009/) (2025)
- [When Importance Sampling Misallocates Credit: Asymmetric Ratios for Outcome-Supervised RL](https://mlsanity.com/paper/2510.06062/) (2025)
- [Revisiting LLM Reasoning via Information Bottleneck](https://mlsanity.com/paper/2507.18391/) (2025)
- [ESPO: Entropy Importance Sampling Policy Optimization](https://mlsanity.com/paper/2512.00499/) (2025)

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

- [CAPO: Critic-Guided Action-Aligned Policy Optimization for Advancing LLM Agent Capabilities](https://mlsanity.com/paper/2604.18401/) (2026)
- [Beyond Uniform Token-Level Trust Region in LLM Reinforcement Learning](https://mlsanity.com/paper/2606.10968/) (2026)
- [Turning Off-Policy Tokens On-Policy: A Plug-in Approach for Improving LLM Alignment](https://mlsanity.com/paper/2607.04728/) (2026)
- [From Trajectories to Prefixes: Reusing Teacher Trajectories via Replayed Prefixes and Online Continuation](https://mlsanity.com/paper/2607.19395/) (2026)
- [Reusing Rollouts under Policy Lag: Prefix-Normalized Policy Optimization for LLM Reinforcement Learning](https://mlsanity.com/paper/2608.01418/) (2026)
- [DenoiseRL: Bootstrapping Reasoning Models to Recover from Noisy Prefixes](https://mlsanity.com/paper/2605.28421/) (2026)
- [Free Everywhere, Exact on Trees: PPO's Dropped Correction Buys Sample Efficiency Under Aggressive Reuse](https://mlsanity.com/paper/2609.39634/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) post-training has increasingly demonstrated strong ability to elicit reasoning behaviors in large language models (LLMs). For training efficiency, rollouts are typically generated in an off-policy manner using an older sampling policy and then used to update the current target policy. To correct the resulting discrepancy between the sampling and target policies, most existing RL objectives rely on a token-level importance sampling ratio, primarily due to its computational simplicity and numerical stability. However, we observe that token-level correction often leads to unstable training dynamics when the degree of off-policyness is large. In this paper, we revisit LLM policy optimization under off-policy conditions and show that the theoretically rigorous correction term is the prefix importance ratio, and that relaxing it to a token-level approximation can induce instability in RL post-training. To stabilize LLM optimization under large off-policy drift, we propose a simple yet effective objective, Minimum Prefix Ratio (MinPRO). MinPRO replaces the unstable cumulative prefix ratio with a non-cumulative surrogate based on the minimum token-level ratio observed in the preceding prefix. Extensive experiments on both dense and mixture-of-experts LLMs, across multiple mathematical reasoning benchmarks, demonstrate that MinPRO substantially improves training stability and peak performance in off-policy regimes.