[2105.04332] Bayesian Optimistic Optimisation with Exponentially Decaying Regret Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2105.04332 (cs) [Submitted on 10 May 2021] Title: Bayesian Optimistic Optimisation with Exponentially Decaying Regret Authors: Hung Tran-The , Sunil Gupta , Santu Rana , Svetha Venkatesh View a PDF of the paper titled Bayesian Optimistic Optimisation with Exponentially Decaying Regret, by Hung Tran-The and 3 other authors View PDF HTML (experimental) Abstract: Bayesian optimisation (BO) is a well-known efficient algorithm for finding the global optimum of expensive, black-box functions. The current practical BO algorithms have regret bounds ranging from $\mathcal{O}(\frac{logN}{\sqrt{N}})$ to $\mathcal O(e^{-\sqrt{N}})$, where $N$ is the number of evaluations. This paper explores the possibility of improving the regret bound in the noiseless setting by intertwining concepts from BO and tree-based optimistic optimisation which are based on partitioning the search space. We propose the BOO algorithm, a first practical approach which can achieve an exponential regret bound with order $\mathcal O(N^{-\sqrt{N}})$ under the assumption that the objective function is sampled from a Gaussian process with a Matérn kernel with smoothness parameter $\nu > 4 +\frac{D}{2}$, where $D$ is the number of dimensions. We perform experiments on optimisation of various synthetic functions and machine learning hyperparameter tuning tasks and show that our algorithm outperforms baselines. Comments: To appear at ICML 2021 (21 pages) Subjects: Machine Learning (cs.LG) ; Machine Learning (stat.ML) Cite as: arXiv:2105.04332 [cs.LG] (or arXiv:2105.04332v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2105.04332 Focus to learn more arXiv-issued DOI via DataCite Journal reference: PMLR 139:10390-10400, 2021 Submission history From: Hung Tran-The [ view email ] [v1] Mon, 10 May 2021 13:07:44 UTC (1,011 KB) Full-text links: Access Paper: View a PDF of the paper titled Bayesian Optimistic Optimisation with Exponentially Decaying Regret, by Hung Tran-The and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2021-05 Change to browse by: cs stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar DBLP - CS Bibliography listing | bibtex Sunil Gupta Santu Rana Svetha Venkatesh 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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