Self-Play Probabilistic Preference Optimization for Language Model Alignment

Traditional reinforcement learning from human feedback (RLHF) approaches relying on parametric models like the Bradley-Terry model fall short in capturing the intransitivity and irrationality in human preferences. Recent advancements suggest that directly working with preference probabilities can yield a more accurate reflection of human preferences, enabling more flexible and accurate language model alignment. In this paper, we propose a self-play-based method for language model alignment, which treats the problem as a constant-sum two-player game aimed at identifying the Nash equilibrium policy. Our approach, dubbed \textit{Self-play Probabilistic Preference Optimization} (SPPO), approximates the Nash equilibrium through iterative policy updates and enjoys a theoretical convergence guarantee. Our method can effectively increase the log-likelihood of the chosen response and decrease that of the rejected response, which cannot be trivially achieved by symmetric pairwise loss such as Direct Preference Optimization (DPO) and Identity Preference Optimization (IPO). In our experiments, using only 60k prompts (without responses) from the UltraFeedback dataset and without any prompt augmentation, by leveraging a pre-trained preference model PairRM with only 0.4B parameters, SPPO can obtain a model from fine-tuning Mistral-7B-Instruct-v0.2 that achieves the state-of-the-art length-controlled win-rate of 28.53\% against GPT-4-Turbo on AlpacaEval 2.0. It also outperforms the (iterative) DPO and IPO on MT-Bench and the Open LLM Leaderboard. Notably, the strong performance of SPPO is achieved without additional external supervision (e.g., responses, preferences, etc.) from GPT-4 or other stronger language models.