{"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/doubly-optimal-no-regret-learning-in-monotone","title":"Doubly Optimal No-Regret Learning in Monotone Games","arxiv_id":"2301.13120","date":"2023-01-30","proceeding":null,"authors":["Yang Cai","Weiqiang Zheng"],"abstract":"We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow $O(\\frac{1}{\\sqrt{T}})$ last-iterate convergence rate to a Nash equilibrium. While the $O(\\frac{1}{\\sqrt{T}})$ rate is tight for a large class of algorithms including the well-studied extragradient algorithm and optimistic gradient algorithm, it is not optimal for all gradient-based algorithms. We propose the accelerated optimistic gradient (AOG) algorithm, the first doubly optimal no-regret learning algorithm for smooth monotone games. Namely, our algorithm achieves both (i) the optimal $O(\\sqrt{T})$ regret in the adversarial setting under smooth and convex loss functions and (ii) the optimal $O(\\frac{1}{T})$ last-iterate convergence rate to a Nash equilibrium in multi-player smooth monotone games. As a byproduct of the accelerated last-iterate convergence rate, we further show that each player suffers only an $O(\\log T)$ individual worst-case dynamic regret, providing an exponential improvement over the previous state-of-the-art $O(\\sqrt{T})$ bound.","url_abs":"https://arxiv.org/abs/2301.13120v2","url_pdf":"https://arxiv.org/pdf/2301.13120v2.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":"doubly-optimal-no-regret-learning-in-monotone","repo_url":"https://github.com/weiqiangzheng1999/doubly-optimal-no-regret-learning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2301.13120","atlas_url":"https://app.syntology.ai/?focus=2301.13120","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}