{"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/near-optimal-algorithms-for-making-the","title":"Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization","arxiv_id":"2208.05925","date":"2022-08-11","proceeding":null,"authors":["Lesi Chen","Luo Luo"],"abstract":"We study the problem of finding a near-stationary point for smooth minimax optimization. The recent proposed extra anchored gradient (EAG) methods achieve the optimal convergence rate for the convex-concave minimax problem in deterministic setting. However, the direct extension of EAG to stochastic optimization is not efficient.In this paper, we design a novel stochastic algorithm called Recursive Anchored IteratioN (RAIN). We show that the RAIN achieves near-optimal stochastic first-order oracle (SFO) complexity for stochastic minimax optimization in both convex-concave and strongly-convex-strongly-concave cases. In addition, we extend the idea of RAIN to solve structured nonconvex-nonconcave minimax problem and it also achieves near-optimal SFO complexity.","url_abs":"https://arxiv.org/abs/2208.05925v3","url_pdf":"https://arxiv.org/pdf/2208.05925v3.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":"near-optimal-algorithms-for-making-the","repo_url":"https://github.com/TrueNobility303/RAIN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2208.05925","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}