Preference as Reward, Maximum Preference Optimization with Importance Sampling

Preference learning is a key technology for aligning language models with human values. Reinforcement Learning from Human Feedback (RLHF) is a model based algorithm to optimize preference learning, which first fitting a reward model for preference score, and then optimizing generating policy with on-policy PPO algorithm to maximize the reward. The processing of RLHF is complex, time-consuming and unstable. Direct Preference Optimization (DPO) algorithm using off-policy algorithm to direct optimize generating policy and eliminating the need for reward model, which is data efficient and stable. DPO use Bradley-Terry model and log-loss which leads to over-fitting to the preference data at the expense of ignoring KL-regularization term when preference is deterministic. IPO uses a root-finding MSE loss to solve the ignoring KL-regularization problem. In this paper, we'll figure out, although IPO fix the problem when preference is deterministic, but both DPO and IPO fails the KL-regularization term because the support of preference distribution not equal to reference distribution. Then, we design a simple and intuitive off-policy preference optimization algorithm from an importance sampling view, which we call Maximum Preference Optimization (MPO), and add off-policy KL-regularization terms which makes KL-regularization truly effective. The objective of MPO bears resemblance to RLHF's objective, and likes IPO, MPO is off-policy. So, MPO attains the best of both worlds. To simplify the learning process and save memory usage, MPO eliminates the needs for both reward model and reference policy.