{"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/history-restricted-online-learning","title":"Online Learning with Bounded Recall","arxiv_id":"2205.14519","date":"2022-05-28","proceeding":null,"authors":["Jon Schneider","Kiran Vodrahalli"],"abstract":"We study the problem of full-information online learning in the \"bounded recall\" setting popular in the study of repeated games. An online learning algorithm $\\mathcal{A}$ is $M$-$\\textit{bounded-recall}$ if its output at time $t$ can be written as a function of the $M$ previous rewards (and not e.g. any other internal state of $\\mathcal{A}$). We first demonstrate that a natural approach to constructing bounded-recall algorithms from mean-based no-regret learning algorithms (e.g., running Hedge over the last $M$ rounds) fails, and that any such algorithm incurs constant regret per round. We then construct a stationary bounded-recall algorithm that achieves a per-round regret of $\\Theta(1/\\sqrt{M})$, which we complement with a tight lower bound. Finally, we show that unlike the perfect recall setting, any low regret bound bounded-recall algorithm must be aware of the ordering of the past $M$ losses -- any bounded-recall algorithm which plays a symmetric function of the past $M$ losses must incur constant regret per round.","url_abs":"https://arxiv.org/abs/2205.14519v2","url_pdf":"https://arxiv.org/pdf/2205.14519v2.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":"history-restricted-online-learning","repo_url":"https://github.com/kiranvodrahalli/history_restricted_online_learning","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2205.14519","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}