Proximal Supervised Fine-Tuning

Supervised fine-tuning (SFT) of foundation models often leads to poor generalization, where prior capabilities deteriorate after tuning on specific tasks. Inspired by trust-region policy optimization (TRPO) and proximal policy optimization (PPO) in reinforcement learning (RL), we propose Proximal SFT (PSFT), a fine-tuning objective that incorporates the benefits of trust-region, effectively constraining policy drift during SFT while maintaining competitive tuning. By viewing SFT as a special case of policy gradient methods with constant positive advantages, we derive PSFT that stabilizes optimization and leads to generalization, while leaving room for further optimization in subsequent post-training stages. Experiments across mathematical, human-value, and multimodal domains show that PSFT matches standard SFT in-domain, outperforms it in out-of-domain generalization, remains stable under prolonged training without causing entropy collapse, and provides a stronger foundation for the subsequent optimization.