{"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/minimax-regret-bounds-for-reinforcement","title":"Minimax Regret Bounds for Reinforcement Learning","arxiv_id":"1703.05449","date":"2017-03-16","proceeding":"ICML 2017 8","authors":["Mohammad Gheshlaghi Azar","Ian Osband","Rémi Munos"],"abstract":"We consider the problem of provably optimal exploration in reinforcement\nlearning for finite horizon MDPs. We show that an optimistic modification to\nvalue iteration achieves a regret bound of $\\tilde{O}( \\sqrt{HSAT} +\nH^2S^2A+H\\sqrt{T})$ where $H$ is the time horizon, $S$ the number of states,\n$A$ the number of actions and $T$ the number of time-steps. This result\nimproves over the best previous known bound $\\tilde{O}(HS \\sqrt{AT})$ achieved\nby the UCRL2 algorithm of Jaksch et al., 2010. The key significance of our new\nresults is that when $T\\geq H^3S^3A$ and $SA\\geq H$, it leads to a regret of\n$\\tilde{O}(\\sqrt{HSAT})$ that matches the established lower bound of\n$\\Omega(\\sqrt{HSAT})$ up to a logarithmic factor. Our analysis contains two key\ninsights. We use careful application of concentration inequalities to the\noptimal value function as a whole, rather than to the transitions probabilities\n(to improve scaling in $S$), and we define Bernstein-based \"exploration\nbonuses\" that use the empirical variance of the estimated values at the next\nstates (to improve scaling in $H$).","url_abs":"http://arxiv.org/abs/1703.05449v2","url_pdf":"http://arxiv.org/pdf/1703.05449v2.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":"minimax-regret-bounds-for-reinforcement","repo_url":"https://github.com/seanrsinclair/AdaptiveQLearning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1703.05449","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}