# Trust Region On-Policy Distillation

arXiv: https://arxiv.org/abs/2606.01249 · HTML: https://mlsanity.com/paper/2606.01249/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 31 May 2026.

## Placed in

- 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, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [WildChat: 1M ChatGPT Interaction Logs in the Wild](https://mlsanity.com/paper/2405.01470/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [Are We Done with MMLU?](https://mlsanity.com/paper/2406.04127/) (2024)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [Scaling Reasoning Efficiently via Relaxed On-Policy Distillation](https://mlsanity.com/paper/2603.11137/) (2026)
- [Robin: A multi-agent system for automating scientific discovery](https://mlsanity.com/paper/2505.13400/) (2025)
- [Asymmetric On-Policy Distillation: Bridging Exploitation and Imitation at the Token Level](https://mlsanity.com/paper/2605.06387/) (2026)
- [100 Days After DeepSeek-R1: A Survey on Replication Studies and More Directions for Reasoning Language Models](https://mlsanity.com/paper/2505.00551/) (2025)
- [To Mix or To Merge: Toward Multi-Domain Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2602.12566/) (2026)
- [Aime: Towards Fully-Autonomous Multi-Agent Framework](https://mlsanity.com/paper/2507.11988/) (2025)
- [MobileLLM-R1: Exploring the Limits of Sub-Billion Language Model Reasoners with Open Training Recipes](https://mlsanity.com/paper/2509.24945/) (2025)

## Built on by (most cited first, 30 of 30)

- [On-policy Distillation with Verifiable Reward](https://mlsanity.com/paper/2608.24696/) (2026)
- [Does On-Policy Distillation Really Distill? From Noisy Teacher to Self-Improvement](https://mlsanity.com/paper/2608.31046/) (2026)
- [Mismatch Matters: On-Policy Distillation Beyond Token Agreement](https://mlsanity.com/paper/2608.09836/) (2026)
- [Weak-to-Strong On-Policy Distillation](https://mlsanity.com/paper/2607.26246/) (2026)
- [Towards Understanding On-Policy Distillation through the Lens of Test-Time Scaling](https://mlsanity.com/paper/2608.11829/) (2026)
- [Tail-Aware Top-k On-Policy Distillation](https://mlsanity.com/paper/2608.14728/) (2026)
- [Verify Before You Distill: Prompt-Level Teacher Gating for On-Policy Distillation](https://mlsanity.com/paper/2609.02998/) (2026)
- [RISE: Recursive Improvement via Self-Extrapolating Policy Distillation](https://mlsanity.com/paper/2609.05295/) (2026)
- [Reconciling Process Supervision with Outcome-Based Credit in Agentic Policy Optimization](https://mlsanity.com/paper/2608.31077/) (2026)
- [The Physics of Multi-Turn Long-Horizon Planning: From Pre-training to Post-training via Single- and Multi-Teacher On-Policy Agentic Distillation](https://mlsanity.com/paper/2607.24720/) (2026)
- [Who Teaches Which Token? Verifier-Gated Multi-Expert On-Policy Distillation for Scientific Reasoning](https://mlsanity.com/paper/2609.15404/) (2026)
- [RetireOPD: Self-Retiring On-Policy Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2609.20784/) (2026)
- [Geometric Self-Distillation for Reasoning Generalization](https://mlsanity.com/paper/2607.06855/) (2026)
- [Data-Free On-Policy Distillation: How Far Can We Go Without External Data?](https://mlsanity.com/paper/2609.14193/) (2026)
- [Blockwise Policy-Drift Gating for On-Policy Distillation](https://mlsanity.com/paper/2606.24084/) (2026)
- [One Symptom, Three Levers: A Critical Review of On-Policy Self-Distillation](https://mlsanity.com/paper/2608.25936/) (2026)
- [Teaching a Moving Student: Rethinking the Curriculum of On-Policy Distillation](https://mlsanity.com/paper/2609.25048/) (2026)
- [Understanding the Synergy between SFT, RLVR, and OPD in LLM Post-Training](https://mlsanity.com/paper/2609.31900/) (2026)
- [Expected Reasoning-Step Return Unifies On-Policy Learning from Rewards and Teachers](https://mlsanity.com/paper/2609.32674/) (2026)
- [Fisher-Informed Recalibration for Feedback-Based On-Policy Self-Distillation of LLMs](https://mlsanity.com/paper/2609.34009/) (2026)
- [No Pain, More Gain: Iterative Merging for Effective Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2609.34745/) (2026)
- [An RL View of OPD: Least Square Policy Distillation for Sample-Efficient LLM Reasoning](https://mlsanity.com/paper/2609.35505/) (2026)
- [Interactive-Policy Distillation with Bidirectional Propose-and-Verify](https://mlsanity.com/paper/2609.36546/) (2026)
- [SAKI: Maximal-Coupling-Routed Teacher Supervision for On-Policy Distillation](https://mlsanity.com/paper/2609.36601/) (2026)
- [Dr. OPD: Learning What to Follow for Optimal On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2609.38025/) (2026)
- [Understanding Off- vs On-Policy Distillation: A Tale of Distinct Training Objectives](https://mlsanity.com/paper/2609.38666/) (2026)
- [RISED: RubrIcs for agentic multi-environment Selection and sElf-Distillation](https://mlsanity.com/paper/2610.00979/) (2026)
- [Divergence controls entropy in distillation](https://mlsanity.com/paper/2610.03529/) (2026)
- [Towards Unbiased On-Policy Distillation for Block Diffusion Language Models](https://mlsanity.com/paper/2610.05373/) (2026)
- [When Do We Need On-Policy Distillation? Distilling on Offline Student Rollouts Is Often Better](https://mlsanity.com/paper/2610.11291/) (2026)

## Abstract (arXiv)

On-Policy Distillation (OPD) is a fundamental technique for efficient post-training of large language models (LLMs), with broad applications in agent learning, multi-task enhancement, and model compression. However, OPD training becomes unstable when the teacher and student distributions differ substantially, as teacher supervision on student-generated tokens may yield unreliable policy gradients and even cause optimization failure. This work addresses reliable on-policy token-level supervision through credit assignment strategies, and proposes Trust Region On-Policy Distillation, TrOPD. It features the following characteristics: 1) Trust-Region On-Policy Learning: TrOPD performs OPD only in regions where the teacher provides reliable supervision, mitigating the optimization difficulty of the K1 reverse-KL estimator under distribution mismatch. 2) Outlier Estimation: For outlier regions, we explore gradient clipping, masking, and forward-KL estimation to reduce the adverse effects of unreliable supervision. 3) Off-Policy Guidance: The student continues generation from teacher prefixes and uses forward KL to imitate off-policy guidance, encouraging on-policy exploration toward reliable regions. Experiments show that TrOPD consistently outperforms SoTA OPD baselines, including OPD, EOPD, and REOPOLD, across mathematical reasoning, code generation, and general-domain benchmarks.