Robust expected improvement for Bayesian optimization

Ryan B. Christianson and Robert B. Gramacy

IISE Transactions, 2024, vol. 56, issue 12, 1294-1306

Abstract: Bayesian Optimization (BO) links Gaussian Process (GP) surrogates with sequential design toward optimizing expensive-to-evaluate black-box functions. Example design heuristics, or so-called acquisition functions, like expected improvement, balance exploration and exploitation to furnish global solutions under stringent evaluation budgets. However, they fall short when solving for robust optima, meaning a preference for solutions in a wider domain of attraction. Robust solutions are useful when inputs are imprecisely specified, or where a series of solutions is desired. A common mathematical programming technique in such settings involves an adversarial objective, biasing a local solver away from “sharp” troughs. Here we propose a surrogate modeling and active learning technique called robust expected improvement that ports adversarial methodology into the BO/GP framework. After describing the methods, we illustrate and draw comparisons to several competitors on benchmark synthetic exercises and real problems of varying complexity.

Date: 2024
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DOI: 10.1080/24725854.2023.2275166

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