The Many Faces of On-Policy Distillation: Pitfalls, Mechanisms, and Fixes

2026-05-11

AI Summary

This work systematically investigates the root causes of performance instability and degradation in on-policy distillation (OPD) and on-policy self-distillation (OPSD) during large language model post-training. Through empirical analysis across diverse tasks—including mathematical reasoning and system prompt internalization—the study identifies three primary failure mechanisms: distribution shift, optimization instability, and the absence of privileged information (PI). It further elucidates the critical conditions under which PI enhances self-distillation efficacy. To address these issues, the authors propose a unified remedy combining TopK reverse KL loss, stop-gradient operations, RLVR-adapted teacher models, and SFT-stabilized student models. Experiments demonstrate that this approach substantially mitigates the identified failure modes and significantly improves distillation performance, particularly in knowledge internalization tasks.

Abstract

On-policy distillation (OPD) and on-policy self-distillation (OPSD) have emerged as promising post-training methods for large language models, offering dense token-level supervision on trajectories sampled from the model's own policy. However, existing results on their effectiveness remain mixed: while OP(S)D has shown promise in system prompt and knowledge internalization, recent studies also report instability and degradation. In this work, we present a comprehensive empirical study of when OPD and OPSD work, when they fail, and why. We find that OPD on mathematical reasoning is highly sensitive to teacher choice and loss formulation, whereas OPSD fails in our tested settings due to test-time absence of instance-specific privileged information (PI). In contrast, OPSD is effective when PI represents a shared latent rule, such as a system prompt or alignment preference. We identify three failure mechanisms: (1) distribution mismatch between teacher and student caused by conditioning on student-generated prefixes, (2) optimization instability from biased TopK reverse-KL gradients, and (3) an OPSD-specific limitation where the student learns a PI-free policy that aggregates PI-conditioned teachers, which is insufficient when PI is instance-specific. We further show that stop-gradient TopK objectives, RLVR-adapted teachers, and SFT-stabilized students mitigate these failures.

Problem

• On-policy distillation
• self-distillation
• failure mechanisms
• privileged information
• distribution mismatch

Innovation

• on-policy distillation
• self-distillation
• privileged information
• distribution mismatch
• optimization stability