EXOTIC: An Exact, Optimistic, Tree-Based Algorithm for Min-Max Optimization 文章

arXiv:2508.12479v2 Announce Type: replace-cross Abstract: Min-max optimization arises in many domains such as game theory, adversarial machine learning, etc. For these problems, gradient-based methods are well understood and enjoy strong guarantees. However, in the absence of convexity or concavity, existing approaches study convergence to an approximate saddle point or first-order stationary points, which may be arbitrarily far from global optima. In this work, we present an algorithmic framework for computing the global minimax value in convex--non-concave and non-convex--concave min-max optimization. For convex--non-concave min-max problems, we use a reformulation that transforms the problem into a non-concave--convex max-min optimization problem with suitably defined feasible sets and objective function. This reformulation can be viewed as an extension of Sion's minimax theorem to the convex--non-concave setting.