{"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/a-computationally-efficient-approach-to-black","title":"A Domain-Shrinking based Bayesian Optimization Algorithm with Order-Optimal Regret Performance","arxiv_id":"2010.13997","date":"2020-10-27","proceeding":"NeurIPS 2021 12","authors":["Sudeep Salgia","Sattar Vakili","Qing Zhao"],"abstract":"We consider sequential optimization of an unknown function in a reproducing kernel Hilbert space. We propose a Gaussian process-based algorithm and establish its order-optimal regret performance (up to a poly-logarithmic factor). This is the first GP-based algorithm with an order-optimal regret guarantee. The proposed algorithm is rooted in the methodology of domain shrinking realized through a sequence of tree-based region pruning and refining to concentrate queries in increasingly smaller high-performing regions of the function domain. The search for high-performing regions is localized and guided by an iterative estimation of the optimal function value to ensure both learning efficiency and computational efficiency. Compared with the prevailing GP-UCB family of algorithms, the proposed algorithm reduces computational complexity by a factor of $O(T^{2d-1})$ (where $T$ is the time horizon and $d$ the dimension of the function domain).","url_abs":"https://arxiv.org/abs/2010.13997v3","url_pdf":"https://arxiv.org/pdf/2010.13997v3.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":"a-computationally-efficient-approach-to-black","repo_url":"https://github.com/sudeepsalgia/gp_threds","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"},{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"},{"method_slug":"pruning","method_name":"Pruning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2010.13997","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}