{"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/the-uncertainty-bellman-equation-and","title":"The Uncertainty Bellman Equation and Exploration","arxiv_id":"1709.05380","date":"2017-09-15","proceeding":"ICML 2018 7","authors":["Brendan O'Donoghue","Ian Osband","Remi Munos","Volodymyr Mnih"],"abstract":"We consider the exploration/exploitation problem in reinforcement learning.\nFor exploitation, it is well known that the Bellman equation connects the value\nat any time-step to the expected value at subsequent time-steps. In this paper\nwe consider a similar \\textit{uncertainty} Bellman equation (UBE), which\nconnects the uncertainty at any time-step to the expected uncertainties at\nsubsequent time-steps, thereby extending the potential exploratory benefit of a\npolicy beyond individual time-steps. We prove that the unique fixed point of\nthe UBE yields an upper bound on the variance of the posterior distribution of\nthe Q-values induced by any policy. This bound can be much tighter than\ntraditional count-based bonuses that compound standard deviation rather than\nvariance. Importantly, and unlike several existing approaches to optimism, this\nmethod scales naturally to large systems with complex generalization.\nSubstituting our UBE-exploration strategy for $\\epsilon$-greedy improves DQN\nperformance on 51 out of 57 games in the Atari suite.","url_abs":"http://arxiv.org/abs/1709.05380v4","url_pdf":"http://arxiv.org/pdf/1709.05380v4.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":"the-uncertainty-bellman-equation-and","repo_url":"https://github.com/stratismarkou/sample-efficient-bayesian-rl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1709.05380","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}