[2203.07875] Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2203.07875 (cs) [Submitted on 15 Mar 2022] Title: Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization Authors: Hung Tran-The , Sunil Gupta , Santu Rana , Svetha Venkatesh View a PDF of the paper titled Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization, by Hung Tran-The and Sunil Gupta and Santu Rana and Svetha Venkatesh View PDF HTML (experimental) Abstract: The expected improvement (EI) algorithm is one of the most popular strategies for optimization under uncertainty due to its simplicity and efficiency. Despite its popularity, the theoretical aspects of this algorithm have not been properly analyzed. In particular, whether in the noisy setting, the EI strategy with a standard incumbent converges is still an open question of the Gaussian process bandit optimization problem. We aim to answer this question by proposing a variant of EI with a standard incumbent defined via the GP predictive mean. We prove that our algorithm converges, and achieves a cumulative regret bound of $\mathcal O(\gamma_T\sqrt{T})$, where $\gamma_T$ is the maximum information gain between $T$ observations and the Gaussian process model. Based on this variant of EI, we further propose an algorithm called Improved GP-EI that converges faster than previous counterparts. In particular, our proposed variants of EI do not require the knowledge of the RKHS norm and the noise's sub-Gaussianity parameter as in previous works. Empirical validation in our paper demonstrates the effectiveness of our algorithms compared to several baselines. Comments: AISTATS 2022 Subjects: Machine Learning (cs.LG) ; Optimization and Control (math.OC) Cite as: arXiv:2203.07875 [cs.LG] (or arXiv:2203.07875v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2203.07875 Focus to learn more arXiv-issued DOI via DataCite Journal reference: PMLR 151:8715-8737, 2022 Submission history From: Hung Tran-The [ view email ] [v1] Tue, 15 Mar 2022 13:17:53 UTC (1,599 KB) Full-text links: Access Paper: View a PDF of the paper titled Regret Bounds for Expected Improvement Algorithms in Gaussian Process Bandit Optimization, by Hung Tran-The and Sunil Gupta and Santu Rana and Svetha Venkatesh View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2022-03 Change to browse by: cs math math.OC 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? ) 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