Robust expected improvement for Bayesian optimization

TL;DR

This paper introduces robust expected improvement (REI), a new Bayesian optimization method that enhances the search for solutions stable under input uncertainties by integrating adversarial techniques into Gaussian process-based optimization.

Contribution

The paper proposes a novel REI method that incorporates adversarial strategies into Bayesian optimization to find robust solutions, addressing limitations of traditional acquisition functions.

Findings

REI outperforms standard EI in robustness to input perturbations

REI demonstrates effectiveness on synthetic and real-world problems

The method provides more stable solutions under input uncertainty

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 (EI), 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 (REI) 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.