cs.LGMay 6, 2026

Preference-Based Self-Distillation: Beyond KL Matching via Reward Regularization

Authors: Xin Yu, Liuchen Liao, Yiwen Zhang, Yingchen Yu, Lingzhou Xue, Qinzhen Guo

Organizations: 1The Pennsylvania State University · 2TikTok

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

On-policy distillation is an efficient alternative to reinforcement learning, offering dense token-level training signals. However, its reliance on a stronger external teacher has driven recent work on on-policy self-distillation, where the same model serves as both teacher and student under different prompt contexts. Yet, existing self-distillation methods largely reduce learning to KL matching toward the context-augmented teacher model. This approach often suffers from training instability and can degrade reasoning performance over time. Moreover, self-distillation from the same model with prompt augmentation lacks the exploratory diversity provided by a genuine external teacher. To address these limitations, we move beyond fixed-teacher KL matching and propose \textbf{P}reference-\textbf{B}ased \textbf{S}elf-\textbf{D}istillation (\textbf{PBSD}), which revisits on-policy self-distillation through a reward-regularized perspective. Instead of directly matching the teacher distribution, we derive a reward-regularized objective whose analytic optimum is a reward-reweighted teacher distribution, yielding a target policy provably superior to the original teacher under this objective. Practically, PBSD optimizes preference gaps between teacher and student samples while maintaining on-policy student sampling. We support this framework with a statistical analysis of the induced preference-learning problem, formally establishing when on policy self-distillation is preferable to learning from an external teacher in our setting. Experiments on mathematical reasoning and tool-use benchmarks across multiple model scales demonstrate that PBSD consistently achieves the strongest average performance among comparable baselines, showing improved training stability over prior self-distillation baselines while preserving token efficiency.

Explore similar work

CardsList
Jul 30, 2026cs.LG

ββ-OPSD: Deriving with Policy Optimization, Training with Self-Distillation

On-policy self-distillation (OPSD) is a promising approach to improve reasoning language models, but it remains brittle in practice: making it work reliably often requires substantial engineering effort. We identify a structural source of this difficulty: vanilla OPSD is precisely the β=1β=1 member of a broader policy-optimization family, where ββ weights the KL penalty anchoring the student to a reference policy. This equivalence turns ββ from an implicit value fixed at one into a controllable regularization parameter, yielding a more general formulation that trades off proximity to a reference policy against privileged teacher guidance. We introduce ββ-OPSD and derive its optimal policy as a geometric interpolation between the reference policy and the privileged teacher. Directly optimizing this objective with reinforcement learning, however, would be costly and high-variance. Rather than optimize the RL objective directly, we turn its closed-form solution into a distillation target. Each value of ββ selects a target along the reference-to-teacher path, which we implement efficiently by mixing their token-level logits. In this way, inexpensive distillation approximates the solution of expensive policy optimization. Return-to-go credit assignment further aligns token updates with the sequence-level objective while retaining the simplicity of OPSD. Experiments on mathematical reasoning benchmarks show that ββ-OPSD consistently outperforms vanilla OPSD, improving optimization stability and downstream reasoning performance. Our results provide a principled route from self-distillation to policy optimization and back without sacrificing the efficiency that makes OPSD practical.
Jiawei Xu, Minghui Liu, Juzheng Zhang +2
On-Policy DistillationRp-OpsdDownstream Reasoning
AskPDF
May 11, 2026cs.LG

Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why

On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically requires costly training runs whose aggregate performance metrics obscure the dynamics at the level of individual tokens. We introduce a training-free diagnostic framework that operates at the highest resolution: per token, per question, and per teacher. We derive an ideal per-node gradient defined as the parameter update that maximally increases the student's probability of success. We then develop a scalable targeted-rollout algorithm to estimate this gradient efficiently, even for long chains of intermediate thoughts. The gradient alignment score, defined as the cosine similarity between this ideal gradient and any given distillation gradient, quantifies the extent to which a particular configuration approximates the ideal signal. Across a range of self-distillation settings and external teacher models, we observe that distillation guidance exhibits substantially higher alignment with the ideal on incorrect rollouts than on correct ones, where the student already performs well and the teacher's signal tends to become noisy. Furthermore, we find that the optimal distillation context depends jointly on the student model's capacity and the target task, and that no single universally effective configuration emerges. These findings motivate the use of per-task, per-token diagnostic analyses for distillation.
Mohammadreza Armandpour, Fatih Ilhan, David Harrison +6
On-Policy DistillationToken-Level Supervision
AskPDF
Aug 10, 2026cs.LG

SR-OPSD: Self-Referenced On-Policy Self-Distillation

On-policy self-distillation (OPSD) converts feedback into dense token-level supervision on trajectories generated by the policy to be optimized, providing a useful complement to reinforcement learning with sparse outcome rewards. However, the self-teacher policy used in OPSD is typically a stop-gradient or exponential-moving-average copy of the policy conditioned on additional context information, and thus co-evolves with both the student policy and its on-policy context distribution. Directly matching such a moving target with a fixed projection objective can lead to unstable optimization or excessive distributional concentration. This nature of OPSD motivates the proposed \emph{Self-Referenced On-Policy Self-Distillation (SR-OPSD)}. At fixed student-generated contexts, a token-level variational characterization identifies the effective distillation target as a geometric interpolation between the self-teacher policy and a reference policy. Meanwhile, we use the Rényi divergence family to generalize the projection geometry. This formulation separates \emph{where} the adaptive target is placed from \emph{how} the student is projected toward it: the interpolation coefficient controls underlying target, while the Rényi order controls the projection geometry and its sensitivity to token-level density ratios. Extensive experiments across scientific evaluation, mathematical reasoning, and coding generation tasks with multiple large language models show that SR-OPSD achieves the state-of-the-art or competitive performance across various settings.
Zhuo Sun, Entong Li, Yanlong Zhao +7
Unsupervised On-Policy Self-DistillationOn-Policy DistillationToken-Level Uncertainty
AskPDF