{"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/lenient-regret-and-good-action-identification","title":"Lenient Regret and Good-Action Identification in Gaussian Process Bandits","arxiv_id":"2102.05793","date":"2021-02-11","proceeding":null,"authors":["Xu Cai","Selwyn Gomes","Jonathan Scarlett"],"abstract":"In this paper, we study the problem of Gaussian process (GP) bandits under relaxed optimization criteria stating that any function value above a certain threshold is \"good enough\". On the theoretical side, we study various {\\em lenient regret} notions in which all near-optimal actions incur zero penalty, and provide upper bounds on the lenient regret for GP-UCB and an elimination algorithm, circumventing the usual $O(\\sqrt{T})$ term (with time horizon $T$) resulting from zooming extremely close towards the function maximum. In addition, we complement these upper bounds with algorithm-independent lower bounds. On the practical side, we consider the problem of finding a single \"good action\" according to a known pre-specified threshold, and introduce several good-action identification algorithms that exploit knowledge of the threshold. We experimentally find that such algorithms can often find a good action faster than standard optimization-based approaches.","url_abs":"https://arxiv.org/abs/2102.05793v2","url_pdf":"https://arxiv.org/pdf/2102.05793v2.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":"lenient-regret-and-good-action-identification","repo_url":"https://github.com/caitree/GoodAction","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2102.05793","atlas_url":"https://app.syntology.ai/?focus=2102.05793","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}