{"paper":{"title":"Efficient Algorithms for Smooth Minimax Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Kiran Koshy Thekumparampil, Praneeth Netrapalli, Prateek Jain, Sewoong Oh","submitted_at":"2019-07-02T17:50:34Z","abstract_excerpt":"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 a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01543","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}