KL for a KL: On-Policy Distillation with Control Variate Baseline
On-Policy Distillation (OPD) has emerged as a dominant post-training paradigm for large language models, especially for reasoning domains. However, OPD remains unstable in practice due to the high gradient variance of its single-sample Monte Carlo estimator, and recipes for stable training are still immature. We propose vOPD (On-Policy Distillation with a control variate baseline), which casts OPD as policy-gradient RL and stabilizes it by introducing a control variate baseline-canonically a value function -- from the RL literature. We show that the OPD value function admits a closed form as the per-token negative reverse KL divergence between the student and the teacher, available direct...
| Authors | Minjae Oh, Sangjun Song, Gyubin Choi et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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