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Two-timescale Extragradient for Finding Local Minimax Points

Jiseok Chae · Kyuwon Kim · Donghwan Kim

Halle B #144
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Wed 8 May 7:30 a.m. PDT — 9:30 a.m. PDT


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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