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Lookup NU author(s): Mike Diessner, Dr Kevin Wilson, Dr Richard Whalley
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
Bayesian optimization provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g. in machine learning to optimize hyperparameters of neural networks, and in engineering, e.g. in fluid dynamics to optimize control strategies that maximize drag reduction. This paper empirically studies and compares the performance and the robustness of common Bayesian optimization algorithms on a range of synthetic test functions to provide general guidance on the design of Bayesian optimization algorithms for specific problems. It investigates the choice of acquisition function, the effect of different numbers of training samples, the exact and Monte Carlo based calculation of acquisition functions, and both single-point and multi-point optimization. The test functions considered cover a wide selection of challenges and therefore serve as a ideal test bed to understand the performance of Bayesian optimization to specific challenges, and in general. To illustrate how these findings can be used to inform a Bayesian optimization setup tailored to a specific problem, two simulations in the area of computational fluid dynamics are optimized, giving evidence that suitable solutions can be found in a small number of evaluations of the objective function for complex, real problems. The results of our investigation can similarly be applied to other areas, such as machine learning and physical experiments, where objective functions are expensive to evaluate and their mathematical expressions are unknown.
Author(s): Diessner M, O'Connor J, Wynn A, Laizet S, Guan Y, Wilson K, Whalley RD
Publication type: Article
Publication status: Published
Journal: Frontiers in Applied Mathematics and Statistics
Year: 2022
Volume: 8
Online publication date: 08/12/2022
Acceptance date: 11/11/2022
Date deposited: 14/11/2022
ISSN (electronic): 2297-4687
Publisher: Frontiers Research Foundation
URL: https://doi.org/10.3389/fams.2022.1076296
DOI: 10.3389/fams.2022.1076296
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