Spectral Representation of Robustness Measures for Optimization Under Input Uncertainty

Jixiang Qing, Tom Dhaene, Ivo Couckuyt
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:18096-18121, 2022.

Abstract

We study the inference of mean-variance robustness measures to quantify input uncertainty under the Gaussian Process (GP) framework. These measures are widely used in applications where the robustness of the solution is of interest, for example, in engineering design. While the variance is commonly used to characterize the robustness, Bayesian inference of the variance using GPs is known to be challenging. In this paper, we propose a Spectral Representation of Robustness Measures based on the GP’s spectral representation, i.e., an analytical approach to approximately infer both robustness measures for normal and uniform input uncertainty distributions. We present two approximations based on different Fourier features and compare their accuracy numerically. To demonstrate their utility and efficacy in robust Bayesian Optimization, we integrate the analytical robustness measures in three standard acquisition functions for various robust optimization formulations. We show their competitive performance on numerical benchmarks and real-life applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-qing22a, title = {Spectral Representation of Robustness Measures for Optimization Under Input Uncertainty}, author = {Qing, Jixiang and Dhaene, Tom and Couckuyt, Ivo}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {18096--18121}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/qing22a/qing22a.pdf}, url = {https://proceedings.mlr.press/v162/qing22a.html}, abstract = {We study the inference of mean-variance robustness measures to quantify input uncertainty under the Gaussian Process (GP) framework. These measures are widely used in applications where the robustness of the solution is of interest, for example, in engineering design. While the variance is commonly used to characterize the robustness, Bayesian inference of the variance using GPs is known to be challenging. In this paper, we propose a Spectral Representation of Robustness Measures based on the GP’s spectral representation, i.e., an analytical approach to approximately infer both robustness measures for normal and uniform input uncertainty distributions. We present two approximations based on different Fourier features and compare their accuracy numerically. To demonstrate their utility and efficacy in robust Bayesian Optimization, we integrate the analytical robustness measures in three standard acquisition functions for various robust optimization formulations. We show their competitive performance on numerical benchmarks and real-life applications.} }
Endnote
%0 Conference Paper %T Spectral Representation of Robustness Measures for Optimization Under Input Uncertainty %A Jixiang Qing %A Tom Dhaene %A Ivo Couckuyt %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-qing22a %I PMLR %P 18096--18121 %U https://proceedings.mlr.press/v162/qing22a.html %V 162 %X We study the inference of mean-variance robustness measures to quantify input uncertainty under the Gaussian Process (GP) framework. These measures are widely used in applications where the robustness of the solution is of interest, for example, in engineering design. While the variance is commonly used to characterize the robustness, Bayesian inference of the variance using GPs is known to be challenging. In this paper, we propose a Spectral Representation of Robustness Measures based on the GP’s spectral representation, i.e., an analytical approach to approximately infer both robustness measures for normal and uniform input uncertainty distributions. We present two approximations based on different Fourier features and compare their accuracy numerically. To demonstrate their utility and efficacy in robust Bayesian Optimization, we integrate the analytical robustness measures in three standard acquisition functions for various robust optimization formulations. We show their competitive performance on numerical benchmarks and real-life applications.
APA
Qing, J., Dhaene, T. & Couckuyt, I.. (2022). Spectral Representation of Robustness Measures for Optimization Under Input Uncertainty. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:18096-18121 Available from https://proceedings.mlr.press/v162/qing22a.html.

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