Robust Nash Alignment under Preference Uncertainty

Shihab Ahmed, Debamita Ghosh, David Tang, Yudan Wang, Alvaro Velasquez +1

Preference-based alignment methods typically optimize against a single preference model, and can therefore be brittle when pairwise preferences are uncertain: noisy, heterogeneous, or shift after deployment. To address these issues, we propose Robust Nash Alignment, a game-theoretic framework for alignment to uncertain pairwise preferences. Our formulation has a major learner seeking a policy with a large worst-case win rate against both an adversarial competitor and any preference kernel lying in an ambiguity set around a nominal preference. When the ambiguity set captures the uncertainty in preferences, the resulting robust objective of the game directly yields a certified lower bound on worst-case performance. However, we note this problem is computationally challenging to optimize, and to address this, we introduce a four-player primal-dual proxy game involving the leader policy, follower policy, adversarial kernel, and dual variable, and develop a single-loop optimistic mirror descent-ascent algorithm for it. We show that the proxy always lower-bounds the truncated hard-constrained objective, quantify the proxy-to-hard gap, and characterize an exactness condition under which…