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High-dimensional Bayesian optimization using low-dimensional feature spaces

Moriconi, R; Deisenroth, MP; Sesh Kumar, KS; (2020) High-dimensional Bayesian optimization using low-dimensional feature spaces. Machine Learning , 109 pp. 1925-1943. 10.1007/s10994-020-05899-z. Green open access

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Abstract

Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to optimizing 10–20 parameters. To scale BO to high dimensions, we usually make structural assumptions on the decomposition of the objective and/or exploit the intrinsic lower dimensionality of the problem, e.g. by using linear projections. We could achieve a higher compression rate with nonlinear projections, but learning these nonlinear embeddings typically requires much data. This contradicts the BO objective of a relatively small evaluation budget. To address this challenge, we propose to learn a low-dimensional feature space jointly with (a) the response surface and (b) a reconstruction mapping. Our approach allows for optimization of BO’s acquisition function in the lower-dimensional subspace, which significantly simplifies the optimization problem. We reconstruct the original parameter space from the lower-dimensional subspace for evaluating the black-box function. For meaningful exploration, we solve a constrained optimization problem.

Type: Article
Title: High-dimensional Bayesian optimization using low-dimensional feature spaces
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10994-020-05899-z
Publisher version: https://doi.org/10.1007/s10994-020-05899-z
Language: English
Additional information: © 2020 Springer Nature Switzerland AG. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10107617
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