Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation
Knowledge distillation is central to LLM post-training, yet its design space remains poorly understood, especially alongside reinforcement learning (RL). We show that the prevailing paradigms, off-policy distillation and on-policy distillation (OPD), implicitly couple two orthogonal choices: prefix source and token-level KL direction. This follows from decomposing sequence-level KL over autoregressive response distributions: forward KL pairs teacher prefixes with token-level forward KL, and reverse KL pairs student prefixes with token-level reverse KL. We argue this coupling is not intrinsic: decoupling the two axes yields four valid objectives. We establish gradient-level identities show...
| Authors | Anhao Zhao, Haoran Xin, Yingqi Fan et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 May 2026 |
| Last updated at source | 16 May 2026 |
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