Batch bayesian optimization via particle gradient flows
File(s)
Accepted version
Author(s)
Crovini, Enrico
Cotter, Simon L
Zygalakis, Konstantinos
Duncan, Andrew B
Type
Journal Article
Abstract
Bayesian optimization (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the uncertainty in that surrogate through Bayesian inference. Objective evaluations are sequentially determined by maximizing an acquisition function at each step. However, this ancilliary optimization problem can be highly nontrivial to solve, due to the nonconcavity of the acquisition function, particularly in the case of batch Bayesian optimization, where multiple points are selected in every step. In this work we reformulate batch BO as an optimization problem over the space of probability measures. We construct a new acquisition function based on multipoint expected improvement, which is concave over the space of probability measures. Practical schemes for solving this “inner" optimization problem arise naturally as gradient flows of this objective function. We demonstrate the efficacy of this new method on different benchmark functions and compare with state-of-the-art batch BO methods.
Date Issued
2026-03-31
Date Acceptance
2025-09-30
Citation
SIAM-ASA Journal on Uncertainty Quantification, 2026, 14 (1), pp.197-220
ISSN
2166-2525
Publisher
Society for Industrial and Applied Mathematics
Start Page
197
End Page
220
Journal / Book Title
SIAM-ASA Journal on Uncertainty Quantification
Volume
14
Issue
1
Copyright Statement
Copyright © 2026 Copyright Owner. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
License URL
Publication Status
Published
Date Publish Online
2026-03-05