Two-timescale Extragradient for Finding Local Minimax Points

arXiv:2305.16242v2 Announce Type: replace-cross
Abstract: Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method 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 that the two-timescale gradient descent ascent fails to work. This work provably improves upon all previous results on finding local minimax points, by eliminating a crucial assumption that the Hessian …

abstract arxiv cs.lg however math.oc minimax show solution systems theory timescale type