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The paper introduces Generalized On-Policy Distillation (G-OPD), a framework extending standard on-policy distillation by allowing a flexible reference model and a reward scaling factor to control the reward term's weight against KL regularization. They theoretically demonstrate that standard OPD is a specific instance of dense KL-constrained RL. Through experiments on math reasoning and code generation, they find that reward extrapolation (ExOPD), where the reward scaling factor is greater than 1, consistently improves performance, even enabling the student to surpass the teacher, and that reward correction using the teacher's base model further enhances distillation in strong-to-weak scenarios.
Students can surpass their teachers in on-policy distillation by extrapolating rewards and merging knowledge from domain experts, challenging the conventional wisdom that students are inherently limited by their teachers' capabilities.
On-policy distillation (OPD), which aligns the student with the teacher's logit distribution on student-generated trajectories, has demonstrated strong empirical gains in improving student performance and often outperforms off-policy distillation and reinforcement learning (RL) paradigms. In this work, we first theoretically show that OPD is a special case of dense KL-constrained RL where the reward function and the KL regularization are always weighted equally and the reference model can by any model. Then, we propose the Generalized On-Policy Distillation (G-OPD) framework, which extends the standard OPD objective by introducing a flexible reference model and a reward scaling factor that controls the relative weight of the reward term against the KL regularization. Through comprehensive experiments on math reasoning and code generation tasks, we derive two novel insights: (1) Setting the reward scaling factor to be greater than 1 (i.e., reward extrapolation), which we term ExOPD, consistently improves over standard OPD across a range of teacher-student size pairings. In particular, in the setting where we merge the knowledge from different domain experts, obtained by applying domain-specific RL to the same student model, back into the original student, ExOPD enables the student to even surpass the teacher's performance boundary and outperform the domain teachers. (2) Building on ExOPD, we further find that in the strong-to-weak distillation setting (i.e., distilling a smaller student from a larger teacher), performing reward correction by choosing the reference model as the teacher's base model before RL yields a more accurate reward signal and further improves distillation performance. However, this choice assumes access to the teacher's pre-RL variant and incurs more computational overhead. We hope our work offers new insights for future research on OPD.
