Your Self-Play Algorithm is Secretly an Adversarial Imitator: Understanding LLM Self-Play through the Lens of Imitation Learning

Self-play post-training methods has emerged as an effective approach for finetuning large language models and turn the weak language model into strong language model without preference data. However, the theoretical foundations for self-play finetuning remain underexplored. In this work, we tackle this by connecting self-play finetuning with adversarial imitation learning by formulating finetuning procedure as a min–max game between the model and a regularized implicit reward player parameterized by the model itself. This perspective unifies self-play imitation and general preference alignment within a common framework. Under this formulation, we present a game-theoretic analysis showing that the self-play finetuning will converge to it's equilibrium. Guided by this theoretical formulation, we propose a new self-play imitation finetuning algorithm based on the $\chi^2$-divergence variational objective with bounded rewards and improved stability. Experiments on various of language model finetuning tasks demonstrate consistent improvements over existing self-play methods and validate our theoretical insights.