Online optimization with costly and noisy measurements using random Fourier expansions

Journal article (2016)

Authors

L. Bliek Algorithmics - EEMCS , Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
H.R.G.W. Verstraete Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
M.H.G. Verhaegen Team Michel Verhaegen - Mechanical, Maritime and Materials Engineering
S. Wahls Team Sander Wahls - Mechanical, Maritime and Materials Engineering
Research Group
Team Sander Wahls (Mechanical, Maritime and Materials Engineering) (TU Delft)
More Info
expand_more

Published Date

2016

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Sander Wahls

Abstract

This paper analyzes data-based online nonlinear extremum-seeker (DONE), an online optimization algorithm that iteratively minimizes an unknown function based on costly and noisy measurements. The algorithm maintains a surrogate of the unknown function in the form of a random Fourier expansion. The surrogate is updated whenever a new measurement is available, and then used to determine the next measurement point. The algorithm is comparable with Bayesian optimization algorithms, but its computational complexity per iteration does not depend on the number of measurements. We derive several theoretical results that provide insight on how the hyperparameters of the algorithm should be chosen. The algorithm is compared with a Bayesian optimization algorithm for an analytic benchmark problem and three applications, namely, optical coherence tomography, optical beam-forming network tuning, and robot arm control. It is found that the DONE algorithm is significantly faster than Bayesian optimization in the discussed problems while achieving a similar or better performance.

Files

Online_optimization_costly.pdf
(pdf | 0.483 Mb)
Unknown license

Download not available