  Policy learning using historical observational data is an important problem
that has found widespread applications. Examples include selecting offers,
prices, advertisements to send to customers, as well as selecting which
medication to prescribe to a patient. However, existing literature rests on the
crucial assumption that the future environment where the learned policy will be
deployed is the same as the past environment that has generated the data -- an
assumption that is often false or too coarse an approximation. In this paper,
we lift this assumption and aim to learn a distributionally robust policy with
incomplete observational data. We first present a policy evaluation procedure
that allows us to assess how well the policy does under the worst-case
environment shift. We then establish a central limit theorem type guarantee for
this proposed policy evaluation scheme. Leveraging this evaluation scheme, we
further propose a novel learning algorithm that is able to learn a policy that
is robust to adversarial perturbations and unknown covariate shifts with a
performance guarantee based on the theory of uniform convergence. Finally, we
empirically test the effectiveness of our proposed algorithm in synthetic
datasets and demonstrate that it provides the robustness that is missing using
standard policy learning algorithms. We conclude the paper by providing a
comprehensive application of our methods in the context of a real-world voting
dataset.
