Moriconi, R;
Kumar, KSS;
Deisenroth, MP;
(2019)
High-dimensional Bayesian optimization with projections using quantile Gaussian processes.
Optimization Letters
10.1007/s11590-019-01433-w.
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Abstract
Key challenges of Bayesian optimization in high dimensions are both learning the response surface and optimizing an acquisition function. The acquisition function selects a new point to evaluate the black-box function. Both challenges can be addressed by making simplifying assumptions, such as additivity or intrinsic lower dimensionality of the expensive objective. In this article, we exploit the effective lower dimensionality with axis-aligned projections and optimize on a partitioning of the input space. Axis-aligned projections introduce a multiplicity of outputs for a single input that we refer to as inconsistency. We model inconsistencies with a Gaussian process (GP) derived from quantile regression. We show that the quantile GP and the partitioning of the input space increases data-efficiency. In particular, by modeling only a quantile function, we overcome issues of GP hyper-parameter learning in the presence of inconsistencies.
| Type: | Article |
|---|---|
| Title: | High-dimensional Bayesian optimization with projections using quantile Gaussian processes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11590-019-01433-w |
| Publisher version: | https://doi.org/10.1007/s11590-019-01433-w |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | High dimensional, Bayesian optimization, Gaussian processes, Quantile regression |
| 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/10083587 |
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