Two-timescale Extragradient for Finding Local Minimax Points
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Keywords: Minimax optimization, Nonconvex-nonconcave optimization, Extragradient method, Dynamical systems
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TL;DR: We characterize to which points the extragradient method with timescale separation converges, and show that those points are related to local minimax points.
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 with respect to the maximization variable is nondegenerate.
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Primary Area: optimization
Submission Number: 5024
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