The growing interest in addressing minimax optimization problem has been fueled by recent applications in machine learning. Although extensively studied in the convex-concave regime, where a global solution can be eff...
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The growing interest in addressing minimax optimization problem has been fueled by recent applications in machine learning. Although extensively studied in the convex-concave regime, where a global solution can be efficiently computed, this paper delves into the minimax problem within the nonconvex-concave setup. We propose an alternating gradient projection algorithm with momentum (M-AGP), belonging to single-loop algorithms that not only are easier to implement but also require only the computation of gradient projection updates. We demonstrate that the proposed algorithm identifies an epsilon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-stationary point of the nonconvex-strongly concave minimax problem in O(epsilon-2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\varepsilon <^>{-2})$$\end{document} iterations, representing the best-known rate in the literature. Finally, we utilize two test problems, namely robust nonlinear regression and an image classification problem, to showcase the efficacy of the proposed algorithm.
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