@@ -158,3 +158,4 @@ This implementation of OPD is relatively simple, as illustrated in Figure~\ref{f
Here, the KL divergence measures the discrepancy between the teacher and student distributions at each student-visited state. For optimization, we can treat the negative KL divergence at each token position as a token-level reward, such that a smaller discrepancy between the student and teacher distributions yields a higher reward. Based on these dense token-level rewards, standard RL algorithms can then be directly applied to optimize the student model.
From the perspective of reward construction, OPD provides more fine-grained supervision than conventional outcome-based approaches, which assign rewards only after the complete response is generated. In contrast, OPD provides token-level feedback throughout generation, making the supervision denser. However, this benefit comes with additional computational cost. The teacher model must evaluate student-generated states and produce next-token distributions during training, which requires extra forward passes and increases both memory and computation overhead.
