Mind the Gap: Data Rewriting for Stable off-Policy Supervised Fine-Tuning

Supervised fine-tuning (SFT) of large language models can be viewed as an off-policy learning problem, where expert demonstrations come from a fixed behavior policy while training aims to optimize a target policy. Importance sampling is the standard tool for correcting this distribution mismatch, but large policy gaps lead to high variance and training instability. Existing approaches mitigate this issue using KL penalties or clipping, which passively constrain updates rather than actively reducing the gap. We propose a simple yet effective data rewriting framework that proactively shrinks the policy gap by keeping correct solutions as on-policy data and rewriting incorrect ones with guided resolving, falling back to expert demonstrations only when needed. This aligns the training distribution with the target policy before optimization, reducing importance sampling variance and stabilizing off-policy fine-tuning. Experiments on five mathematical reasoning benchmarks demonstrate consistent and significant gains over both vanilla SFT and the state-of-the-art Dynamic Fine-Tuning (DFT) approach. Data and code are available at https://github.com/NKU-HLT/Off-Policy-SFT.