A Robust Multi-Objective Bayesian Optimization Framework Considering Input Uncertainty

Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty into account to find a set of robust solutions. While this is...

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Bibliographic Details
Published inarXiv.org
Main Authors Qing, J, Couckuyt, I, Dhaene, T
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.02.2022
Subjects
Bayesian analysis
Design engineering
Gaussian process
Multiple objective analysis
Optimization
Pareto optimization
Robustness (mathematics)
Uncertainty
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Summary:Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty into account to find a set of robust solutions. While this is an active topic in single-objective Bayesian optimization, it is less investigated in the multi-objective case. We introduce a novel Bayesian optimization framework to efficiently perform multi-objective optimization considering input uncertainty. We propose a robust Gaussian Process model to infer the Bayes risk criterion to quantify robustness, and we develop a two-stage Bayesian optimization process to search for a robust Pareto frontier. The complete framework supports various distributions of the input uncertainty and takes full advantage of parallel computing. We demonstrate the effectiveness of the framework through numerical benchmarks.
ISSN:2331-8422