Two-timescale Extragradient for Finding Local Minimax Points
Jiseok Chae Kyuwon Kim Donghwan Kim
Minimax problems are notoriously challenging to optimize. However, we
demonstrate that the 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 a
mild condition. This work surpasses all previous results as we eliminate a
crucial assumption that the Hessian, with respect to the maximization variable,
is nondegenerate.