On-Policy Delta Distillation
Machine LearningComputation and Language
Summary
The authors studied a way to improve reinforcement learning where a smaller model learns from a larger teacher model after initial training. Instead of copying the teacher's exact outputs, they suggest learning from the difference between the teacher's reasoning-tuned model and its original version, which they call the delta signal. This new signal helps the smaller model better gain reasoning skills during post-training. They tested their method, named OPD², on tasks in math, science, and coding, showing it works better and faster than traditional methods.
Authors
Byeongho Heo, Jaehui Hwang, Sangdoo Yun, Dongyoon Han
Abstract
On-policy distillation is an alternative post-training method in reinforcement learning that alleviates the constraints imposed by reward models by providing token-level supervision from a teacher model. Although on-policy distillation has been studied and applied across various settings, its fundamental design remains underexplored. In this paper, we introduce a new distillation reward, termed the delta signal, instead of directly imitating the teacher's output distribution. The delta signal is defined as the difference between the teacher model and its base model prior to instruction tuning for reasoning capability. It therefore captures the changes induced by reasoning tuning and provides a more direct signal for transferring reasoning capabilities. Using extensive empirical evidence, we show that the delta signal substantially improves on-policy distillation and refer to the new distillation method as On-Policy Delta Distillation (OPD$^2$). Experiments across mathematics, science, and code-reasoning benchmarks demonstrate that OPD$^2$ consistently outperforms conventional on-policy distillation, enabling reasoning LLMs to achieve strong performance with only a short post-training period. Code will be available at https://github.com/naver-ai/opd2