Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation
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.
698e8f46cace060ff123ac51
Wenkai Yang
claimed_verified
2026-02-17T15:51:04.413Z
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/avatars/e24e7769188d441317b3b7d10ef8fd60.svg
Wenkai Yang
Keven16
user
Keven16
698e8f46cace060ff123ac52
Weijie Liu
698e8f46cace060ff123ac53
Ruobing Xie
698e8f46cace060ff123ac54
Kai Yang
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2026-03-05T09:58:58.820Z
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/avatars/b341feaf8779b39c225c5b044f29e671.svg
Kai Yang
yangkaiSIGS
user
yangkaiSIGS
698e8f46cace060ff123ac55
Saiyong Yang
698e8f46cace060ff123ac56
Yankai Lin
Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation
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.
On-policy distillation is extended through a generalized framework that introduces flexible reference models and reward scaling factors, demonstrating improved performance through reward extrapolation and reward correction techniques.
on-policy distillation logit distribution dense KL-constrained RL reward scaling factor reward extrapolation reward correction teacher-student size pairings domain-specific RL strong-to-weak distillation