  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.
