# Multi-Turn On-Policy Distillation with Prefix Replay

arXiv: https://arxiv.org/abs/2607.04763 · HTML: https://mlsanity.com/paper/2607.04763/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 67 of its 78 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 67)

- [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)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)

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

- [Look Ahead Before You Distill: Future Trajectory Validation of Teacher Guidance for Agentic On-Policy Distillation](https://mlsanity.com/paper/2608.01953/) (2026)
- [Mismatch Matters: On-Policy Distillation Beyond Token Agreement](https://mlsanity.com/paper/2608.09836/) (2026)
- [Step-Level On-Policy Distillation: Interpolating Between On-Policy Distillation and Supervised Fine-Tuning](https://mlsanity.com/paper/2608.16333/) (2026)
- [When Privileged Guidance Misaligns: State-Matched Routing and Contextualized Self-Distillation for Multi-Turn Agents](https://mlsanity.com/paper/2608.05219/) (2026)
- [DART-SD: Diamond-topology Aware Retrieval and Tuning for Self-Distillation of Multi-Turn Tool-Calling Agents](https://mlsanity.com/paper/2608.18524/) (2026)
- [MiMo-V2.6: Scaling Reinforcement Learning Towards Self-Improvement](https://mlsanity.com/paper/2610.11959/) (2026)
- [Hints, Critics, and Teachers: Prior Injection for Sparse-Reward RL in Vision-Language Math Reasoning](https://mlsanity.com/paper/2608.21811/) (2026)
- [UOPD: Uncertainty-Aware Intervention for On-Policy Distillation of Multi-Turn Agents](https://mlsanity.com/paper/2609.34036/) (2026)
- [WAM-OPD: Sharpening World Action Models via On-Policy Distillation](https://mlsanity.com/paper/2609.34250/) (2026)
- [Teacher-Student Gaps Are Not Enough: Outcome-Guided On-Policy Distillation for Multi-Turn Autonomous Agents](https://mlsanity.com/paper/2609.35319/) (2026)
- [Act First, Reason Later: Accelerating On-Policy Distillation for Multi-Turn Agents via Reference-Conditioned Inverse Dynamics](https://mlsanity.com/paper/2609.36608/) (2026)
- [Distilling Agentic Systems: A Roadmap across Models, Artifacts, and Harnesses](https://mlsanity.com/paper/2609.36630/) (2026)
- [Rethinking Self-Distillation for Multi-Teacher Capability Merging](https://mlsanity.com/paper/2610.04272/) (2026)
- [State-OPD: State-Grounded On-Policy Distillation for Multi-Turn Agents](https://mlsanity.com/paper/2610.13238/) (2026)
- [Beyond Corrected Actions: Training LLM Agents on Textual Critiques](https://mlsanity.com/paper/2610.19367/) (2026)

## Abstract (arXiv)

We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4× faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.