{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-algorithms-for-smooth-minimax","title":"Efficient Algorithms for Smooth Minimax Optimization","arxiv_id":"1907.01543","date":"2019-07-02","proceeding":"NeurIPS 2019 12","authors":["Kiran Koshy Thekumparampil","Prateek Jain","Praneeth Netrapalli","Sewoong Oh"],"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., $\\min_x \\max_{1\\leq i\\leq m} f_i(x)$, 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.","url_abs":"https://arxiv.org/abs/1907.01543v1","url_pdf":"https://arxiv.org/pdf/1907.01543v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"efficient-algorithms-for-smooth-minimax","repo_url":"https://github.com/POLane16/DIAG","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"efficient-algorithms-for-smooth-minimax","repo_url":"https://github.com/tkkiran/DIAG","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1907.01543","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1907.01543"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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