Robustness to distributional shift is one of the key challenges of
contemporary machine learning. Attaining such robustness is the goal of
distributionally robust optimization, which seeks a solution to an optimization
problem that is worst-case robust under a specified distributional shift of an
uncontrolled covariate. In this paper, we study such a problem when the
distributional shift is measured via the maximum mean discrepancy (MMD). For
the setting of zeroth-order, noisy optimization, we present a novel
distributionally robust Bayesian optimization algorithm (DRBO). Our algorithm
provably obtains sub-linear robust regret in various settings that differ in
how the uncertain covariate is observed. We demonstrate the robust performance
of our method on both synthetic and real-world benchmarks.Comment: Accepted at AISTATS 202