Minimax problems are notoriously challenging to optimize. However, we present that two-timescale extragradient can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under mild conditions. This work provably improves upon all previous results as we eliminate a crucial assumption that the Hessian, with respect to the maximization variable, is nondegenerate.
Two-timescale Extragradient for Finding Local Minimax Points
Jiseok Chae Kyuwon Kim Donghwan Kim