{"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/optimal-no-regret-learning-in-strongly","title":"Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedback","arxiv_id":"2112.02856","date":"2021-12-06","proceeding":null,"authors":["Wenjia Ba","Tianyi Lin","Jiawei Zhang","Zhengyuan Zhou"],"abstract":"We consider online no-regret learning in unknown games with bandit feedback, where each player can only observe its reward at each time -- determined by all players' current joint action -- rather than its gradient. We focus on the class of \\textit{smooth and strongly monotone} games and study optimal no-regret learning therein. Leveraging self-concordant barrier functions, we first construct a new bandit learning algorithm and show that it achieves the single-agent optimal regret of $\\tilde{\\Theta}(n\\sqrt{T})$ under smooth and strongly concave reward functions ($n \\geq 1$ is the problem dimension). We then show that if each player applies this no-regret learning algorithm in strongly monotone games, the joint action converges in the \\textit{last iterate} to the unique Nash equilibrium at a rate of $\\tilde{\\Theta}(nT^{-1/2})$. Prior to our work, the best-known convergence rate in the same class of games is $\\tilde{O}(n^{2/3}T^{-1/3})$ (achieved by a different algorithm), thus leaving open the problem of optimal no-regret learning algorithms (since the known lower bound is $\\Omega(nT^{-1/2})$). Our results thus settle this open problem and contribute to the broad landscape of bandit game-theoretical learning by identifying the first doubly optimal bandit learning algorithm, in that it achieves (up to log factors) both optimal regret in the single-agent learning and optimal last-iterate convergence rate in the multi-agent learning. We also present preliminary numerical results on several application problems to demonstrate the efficacy of our algorithm in terms of iteration count.","url_abs":"https://arxiv.org/abs/2112.02856v4","url_pdf":"https://arxiv.org/pdf/2112.02856v4.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":"optimal-no-regret-learning-in-strongly","repo_url":"https://github.com/tydlin/doubly_optimal_bandits","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"logistic-regression","method_name":"Logistic Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2112.02856","atlas_url":"https://app.syntology.ai/?focus=2112.02856","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}