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• W2954249541 abstract "This paper studies first order methods for solving smooth minimax optimization problems $min_x max_y g(x,y)$ where $g(cdot,cdot)$ is smooth and $g(x,cdot)$ is concave for each $x$. In terms of $g(cdot,y)$, we consider two settings -- strongly convex and nonconvex -- and improve upon the best known rates in both. For strongly-convex $g(cdot, y), forall y$, we propose a new algorithm combining Mirror-Prox and Nesterov's AGD, and show that it can find global optimum in $tilde{O}(1/k^2)$ iterations, improving over current state-of-the-art rate of $O(1/k)$. We use this result along with an inexact proximal point method to provide $tilde{O}(1/k^{1/3})$ rate for finding stationary points in the nonconvex setting where $g(cdot, y)$ can be nonconvex. This improves over current best-known rate of $O(1/k^{1/5})$. Finally, we instantiate our result for finite nonconvex minimax problems, i.e., $min_x max_{1leq ileq m} f_i(x)$, with nonconvex $f_i(cdot)$, to obtain convergence rate of $O(m(log m)^{3/2}/k^{1/3})$ total gradient evaluations for finding a stationary point." @default.
• W2954249541 created "2019-07-12" @default.
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• W2954249541 date "2019-07-02" @default.
• W2954249541 modified "2023-09-24" @default.
• W2954249541 title "Efficient Algorithms for Smooth Minimax Optimization" @default.
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• W2954249541 hasPublicationYear "2019" @default.
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