Unbiased Top-$k$ Estimation for On-Policy Distillation

Linjian Meng, Siyuan Gan, YuHan Li, Xiran Wang, Ziyang Ding +3

On-policy distillation (OPD) is becoming an important component of large language model (LLM) post-training for transferring the reasoning capability of a strong teacher LLM to a weaker student LLM. OPD trains the student by minimizing the reverse KL divergence between the teacher and the student via rollouts generated by the student's policy. However, estimating the gradient of the reverse KL divergence in OPD remains a challenge. Using only the sampled token from the student-generated rollout is computationally cheap but provides limited distributional supervision, which will degrade accuracy. In addition, using the full vocabulary provides complete distributional supervision but is computationally expensive. Therefore, recent works propose Top-$k$ OPD (TK-OPD) that use selected top-$k$ tokens, which provides richer distributional supervision than sampled-token estimation at substantially lower computational cost than full-vocabulary estimation. Unfortunately, using only the selected top-$k$ tokens induces bias, leading to accuracy degradation, as the probability mass outside the selected top-$k$ tokens is discarded. To address the bias of TK-OPD, we propose Tail-Corrected…