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 fits a reward model for preference scores and then optimizes the generating policy with an on-policy PPO algorithm to maximize the reward. The processing of RLHF is complex, time-consuming, and unstable. The Direct Preference Optimization (DPO) algorithm uses an off-policy algorithm to directly optimize the generating policy and eliminates the need for a reward model. DPO is more data-efficient and stable. However, DPO has a drawback of overfitting to the preference data and ignoring the KL-regularization term when the preference is deterministic. Identity mapping Preference Optimization(IPO) uses a root-finding MSE loss to incorporate KL-regularization. However, both DPO and IPO fail to properly address the KL-regularization term because the support of the preference distribution is not equal to the reference distribution. In this paper, we propose a simple and intuitive off-policy preference optimization algorithm from an importance sampling view, which we call Maximum Preference Optimization (MPO). MPO incorporates the off-policy KL-regularization term, making regularization truly effective. MPO achieves the best of both worlds by combining the objectives of RLHF and IPO while being an off-policy algorithm. Furthermore, MPO eliminates the need for a reward model and reference policy, simplifying the learning process and reducing memory usage.

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