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.

@inproceedings{kirschner2020distributionally,
	author = {Johannes Kirschner and Ilija Bogunovic and Stefanie Jegelka and Andreas Krause},
	booktitle = {Proc. International Conference on Artificial Intelligence and Statistics (AISTATS)},
	month = {June},
	title = {Distributionally Robust Bayesian Optimization},
	year = {2020}}