[2009.02539] Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2009.02539 (stat) [Submitted on 5 Sep 2020 ( v1 ), last revised 1 Nov 2020 (this version, v4)] Title: Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces Authors: Hung Tran-The , Sunil Gupta , Santu Rana , Huong Ha , Svetha Venkatesh View a PDF of the paper titled Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces, by Hung Tran-The and 4 other authors View PDF HTML (experimental) Abstract: Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a hyperharmonic series. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space. Comments: 34th Conference on Neural Information Processing Systems (NeurIPS 2020) Subjects: Machine Learning (stat.ML) ; Information Theory (cs.IT); Machine Learning (cs.LG) Cite as: arXiv:2009.02539 [stat.ML] (or arXiv:2009.02539v4 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2009.02539 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.5555/3495724.3497089 Focus to learn more DOI(s) linking to related resources Submission history From: Hung Tran-The [ view email ] [v1] Sat, 5 Sep 2020 14:24:40 UTC (478 KB) [v2] Tue, 8 Sep 2020 00:26:20 UTC (478 KB) [v3] Wed, 9 Sep 2020 00:31:27 UTC (478 KB) [v4] Sun, 1 Nov 2020 12:38:20 UTC (872 KB) Full-text links: Access Paper: View a PDF of the paper titled Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces, by Hung Tran-The and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2020-09 Change to browse by: cs cs.IT cs.LG math math.IT stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from