{"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/fundamental-benefit-of-alternating-updates-in","title":"Fundamental Benefit of Alternating Updates in Minimax Optimization","arxiv_id":"2402.10475","date":"2024-02-16","proceeding":null,"authors":["Jaewook Lee","Hanseul Cho","Chulhee Yun"],"abstract":"The Gradient Descent-Ascent (GDA) algorithm, designed to solve minimax optimization problems, takes the descent and ascent steps either simultaneously (Sim-GDA) or alternately (Alt-GDA). While Alt-GDA is commonly observed to converge faster, the performance gap between the two is not yet well understood theoretically, especially in terms of global convergence rates. To address this theory-practice gap, we present fine-grained convergence analyses of both algorithms for strongly-convex-strongly-concave and Lipschitz-gradient objectives. Our new iteration complexity upper bound of Alt-GDA is strictly smaller than the lower bound of Sim-GDA; i.e., Alt-GDA is provably faster. Moreover, we propose Alternating-Extrapolation GDA (Alex-GDA), a general algorithmic framework that subsumes Sim-GDA and Alt-GDA, for which the main idea is to alternately take gradients from extrapolations of the iterates. We show that Alex-GDA satisfies a smaller iteration complexity bound, identical to that of the Extra-gradient method, while requiring less gradient computations. We also prove that Alex-GDA enjoys linear convergence for bilinear problems, for which both Sim-GDA and Alt-GDA fail to converge at all.","url_abs":"https://arxiv.org/abs/2402.10475v2","url_pdf":"https://arxiv.org/pdf/2402.10475v2.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":"fundamental-benefit-of-alternating-updates-in","repo_url":"https://github.com/hanseuljo/alex-gda","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"image-generation","task_name":"Image Generation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-generation-on-lsun-bedroom-64-x-64","task":"Image Generation","dataset":"LSUN Bedroom 64 x 64","model":"WGAN-GP + TTUR + Alex-Adam","rank_in_archive_order":1,"of":3,"metrics":{"FID":"6.3"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2402.10475","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2402.10475"}},"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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