[1911.11950] Trading Convergence Rate with Computational Budget in High Dimensional Bayesian Optimization Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:1911.11950 (stat) [Submitted on 27 Nov 2019 ( v1 ), last revised 28 Aug 2020 (this version, v2)] Title: Trading Convergence Rate with Computational Budget in High Dimensional Bayesian Optimization Authors: Hung Tran-The , Sunil Gupta , Santu Rana , Svetha Venkatesh View a PDF of the paper titled Trading Convergence Rate with Computational Budget in High Dimensional Bayesian Optimization, by Hung Tran-The and 3 other authors View PDF HTML (experimental) Abstract: Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find global maximisation of acquisition function, which itself is a non-convex optimization problem in the original search space. With growing dimensions, the computational budget for this maximisation gets increasingly short leading to inaccurate solution of the maximisation. This inaccuracy adversely affects both the convergence and the efficiency of BO. We propose a novel approach where the acquisition function only requires maximisation on a discrete set of low dimensional subspaces embedded in the original high-dimensional search space. Our method is free of any low dimensional structure assumption on the function unlike many recent high-dimensional BO methods. Optimising acquisition function in low dimensional subspaces allows our method to obtain accurate solutions within limited computational budget. We show that in spite of this convenience, our algorithm remains convergent. In particular, cumulative regret of our algorithm only grows sub-linearly with the number of iterations. More importantly, as evident from our regret bounds, our algorithm provides a way to trade the convergence rate with the number of subspaces used in the optimisation. Finally, when the number of subspaces is "sufficiently large", our algorithm's cumulative regret is at most $\mathcal{O}^{*}(\sqrt{T\gamma_T})$ as opposed to $\mathcal{O}^{*}(\sqrt{DT\gamma_T})$ for the GP-UCB of Srinivas et al. (2012), reducing a crucial factor $\sqrt{D}$ where $D$ being the dimensional number of input space. Comments: Our accepted paper (with Supplementary Material) at AAAI 2020 Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG) Cite as: arXiv:1911.11950 [stat.ML] (or arXiv:1911.11950v2 [stat.ML] for this version) https://doi.org/10.48550/arXiv.1911.11950 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1609/aaai.v34i03.5623 Focus to learn more DOI(s) linking to related resources Submission history From: Hung Tran-The [ view email ] [v1] Wed, 27 Nov 2019 04:49:12 UTC (468 KB) [v2] Fri, 28 Aug 2020 07:19:24 UTC (472 KB) Full-text links: Access Paper: View a PDF of the paper titled Trading Convergence Rate with Computational Budget in High Dimensional Bayesian Optimization, by Hung Tran-The and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2019-11 Change to browse by: cs cs.LG stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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