Multi-Step Alignment as Markov Games: An Optimistic Online Gradient Descent Approach with Convergence Guarantees
This addresses the problem of aligning large language models with human preferences in multi-turn conversational settings, offering a novel theoretical framework with convergence guarantees, though it is incremental in advancing RLHF methods.
The paper tackles the limitations of existing RLHF methods like DPO by modeling alignment as a two-player constant-sum Markov game to handle multi-turn conversations and non-transitive human preferences, resulting in the OMPO method that converges to an ε-approximate Nash equilibrium with O(ε⁻¹) policy updates and is validated on datasets.
Reinforcement Learning from Human Feedback (RLHF) has been highly successful in aligning large language models with human preferences. While prevalent methods like DPO have demonstrated strong performance, they frame interactions with the language model as a bandit problem, which limits their applicability in real-world scenarios where multi-turn conversations are common. Additionally, DPO relies on the Bradley-Terry model assumption, which does not adequately capture the non-transitive nature of human preferences. In this paper, we address these challenges by modeling the alignment problem as a two-player constant-sum Markov game, where each player seeks to maximize their winning rate against the other across all steps of the conversation. Our approach Optimistic Multi-step Preference Optimization (OMPO) is built upon the optimistic online mirror descent algorithm~\citep{rakhlin2013online,joulani17a}. Theoretically, we provide a rigorous analysis for the convergence of OMPO and show that OMPO requires $\mathcal{O}(ε^{-1})$ policy updates to converge to an $ε$-approximate Nash equilibrium. We also validate the effectiveness of our method on multi-turn conversations dataset and math reasoning dataset.