A radial basis function method for noisy global optimisation
A radial basis function method for noisy global optimisation
We present a novel response surface method for global optimisation of an expensive and noisy (black-box) objective function, where error bounds on the deviation of the observed noisy function values from their true counterparts are available. The method is based on Gutmann’s well-established RBF method for minimising an expensive and deterministic objective function, which has become popular both from a theoretical and practical perspective. To construct suitable radial basis function approximants to the objective function and to determine new sample points for successive evaluation of the expensive noisy objective, the method uses a regularised least-squares criterion. In particular, new points are defined by means of a target value, analogous to the original RBF method. We provide essential convergence results, and provide a numerical illustration of the method by means of a simple test problem.
90C26, 90C30, Approximation, Controlled noise, Expensive noisy objective function, Global optimisation, Radial basis functions, Response surface methods
Banholzer, Dirk
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Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Werner, Ralf
056699b2-2ac9-4977-919e-da57a71f17cc
Banholzer, Dirk
1c6c11f7-6477-4463-b9f2-6786ce4aa280
Fliege, Jörg
54978787-a271-4f70-8494-3c701c893d98
Werner, Ralf
056699b2-2ac9-4977-919e-da57a71f17cc
Banholzer, Dirk, Fliege, Jörg and Werner, Ralf
(2024)
A radial basis function method for noisy global optimisation.
Mathematical Programming.
(doi:10.1007/s10107-024-02125-9).
Abstract
We present a novel response surface method for global optimisation of an expensive and noisy (black-box) objective function, where error bounds on the deviation of the observed noisy function values from their true counterparts are available. The method is based on Gutmann’s well-established RBF method for minimising an expensive and deterministic objective function, which has become popular both from a theoretical and practical perspective. To construct suitable radial basis function approximants to the objective function and to determine new sample points for successive evaluation of the expensive noisy objective, the method uses a regularised least-squares criterion. In particular, new points are defined by means of a target value, analogous to the original RBF method. We provide essential convergence results, and provide a numerical illustration of the method by means of a simple test problem.
Text
s10107-024-02125-9
- Version of Record
More information
Accepted/In Press date: 17 June 2024
e-pub ahead of print date: 8 August 2024
Keywords:
90C26, 90C30, Approximation, Controlled noise, Expensive noisy objective function, Global optimisation, Radial basis functions, Response surface methods
Identifiers
Local EPrints ID: 495039
URI: http://eprints.soton.ac.uk/id/eprint/495039
ISSN: 0025-5610
PURE UUID: ba794a89-e308-4e7f-8e4c-28071a3a365c
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Date deposited: 28 Oct 2024 17:44
Last modified: 29 Oct 2024 02:42
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Contributors
Author:
Dirk Banholzer
Author:
Ralf Werner
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