# Understanding Off- vs On-Policy Distillation: A Tale of Distinct Training Objectives

arXiv: https://arxiv.org/abs/2609.38666 · HTML: https://mlsanity.com/paper/2609.38666/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 40 of its 65 references that are in the map.
- First posted on arXiv 29 Sep 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, 30 of 40)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [MiMo-V2-Flash Technical Report](https://mlsanity.com/paper/2601.02780/) (2026)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Entropy-Aware On-Policy Distillation of Language Models](https://mlsanity.com/paper/2603.07079/) (2026)
- [DistiLLM: Towards Streamlined Distillation for Large Language Models](https://mlsanity.com/paper/2402.03898/) (2024)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting](https://mlsanity.com/paper/2510.18874/) (2025)
- [DistiLLM-2: A Contrastive Approach Boosts the Distillation of LLMs](https://mlsanity.com/paper/2503.07067/) (2025)
- [MOPD: Multi-Teacher On-Policy Distillation for Capability Integration in LLM Post-Training](https://mlsanity.com/paper/2606.30406/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [SCOPE: Signal-Calibrated On-Policy Distillation Enhancement with Dual-Path Adaptive Weighting](https://mlsanity.com/paper/2604.10688/) (2026)
- [RL Fine-Tuning Heals OOD Forgetting in SFT](https://mlsanity.com/paper/2509.12235/) (2025)
- [Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models](https://mlsanity.com/paper/2604.08527/) (2026)
- [Trust Region On-Policy Distillation](https://mlsanity.com/paper/2606.01249/) (2026)
- [KL for a KL: On-Policy Distillation with Control Variate Baseline](https://mlsanity.com/paper/2605.07865/) (2026)
- [Logarithmic Regret for Online KL-Regularized Reinforcement Learning](https://mlsanity.com/paper/2502.07460/) (2025)
- [Demystifying On-Policy Distillation: Roles, Pathologies, and Regulations](https://mlsanity.com/paper/2607.13399/) (2026)
- [Achieving Logarithmic Regret in KL-Regularized Zero-Sum Markov Games](https://mlsanity.com/paper/2510.13060/) (2025)
- [VLA-OPD: Bridging Offline SFT and Online RL for Vision-Language-Action Models via On-Policy Distillation](https://mlsanity.com/paper/2603.26666/) (2026)
- [Escaping the KL Agreement Trap in On-Policy Distillation](https://mlsanity.com/paper/2606.09471/) (2026)
- [Hybrid Policy Distillation for LLMs](https://mlsanity.com/paper/2604.20244/) (2026)
- [Self-Distilled Policy Gradient](https://mlsanity.com/paper/2606.04036/) (2026)
- [PowerOPD: Stabilizing On-Policy Distillation with Bounded Power Transformation](https://mlsanity.com/paper/2606.17199/) (2026)
- [One Student, Many Teachers: Multi-Task On-Policy Distillation via Soft-Prompt Privileged Context](https://mlsanity.com/paper/2607.18293/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) learns from teacher feedback on student-generated responses and has shown promise in reducing forgetting relative to supervised fine-tuning (SFT). However, its benefits and fragility remain incompletely understood. We study sequential distillation from multiple teachers, where the student minimizes its average divergence from the teachers. Forward Kullback--Leibler (KL) divergence yields a weighted arithmetic mixture, while reverse KL yields a normalized weighted geometric aggregate. We develop algorithms that learn these targets under off-policy and on-policy feedback, respectively, establishing logarithmic regret bounds in the tabular setting and extending the analysis to function approximation. By analyzing these aggregation targets, we identify mechanisms that help explain both the benefits and fragility of OPD. Relative to forward KL, reverse KL can better retain a confident expert's preferences under uninformative feedback, but is more sensitive to teachers that assign very low probabilities to correct responses. Its token-level conditionals also reveal a dependence on continuation distributions that can favor incorrect prefixes over long horizons.