Bayesian Optimization Under Uncertainty

We consider the problem of robust optimization, where it is sought to design a system such that it sustains a specified measure of performance under uncertainty. This problem is challenging since modeling a complex system under uncertainty can be expensive and for most real-world problems robust optimization will not be computationally viable. In this paper, we propose a Bayesian methodology to efficiently solve a class of robust optimization problems that arise in engineering design under uncertainty. The central idea is to use Gaussian process models of loss functions (or robustness metrics) together with appropriate acquisition functions to guide the search for a robust optimal solution. Numerical studies on a test problem are presented to demonstrate the efficacy of the proposed approach.

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