Identity Preference Optimization (IPO): How Exact Loss Inversion Prevents Overfitting in Direct Alignment
The post-training alignment of large language models underwent a structural shift with the introduction of Direct Preference Optimization (Rafailov et al., 2023). By reparameterizing the closed-form optimal policy under a Kullback-Leibler (KL) constrained Reinforcement Learning from Human Feedback (RLHF) objective, DPO eliminated the need to fit an explicit reward model or maintain complex actor-critic rollout loops. However, standard DPO introduces a distinct mathematical pathology: under dete








