  Many decision problems in science, engineering and economics are affected by
uncertain parameters whose distribution is only indirectly observable through
samples. The goal of data-driven decision-making is to learn a decision from
finitely many training samples that will perform well on unseen test samples.
This learning task is difficult even if all training and test samples are drawn
from the same distribution---especially if the dimension of the uncertainty is
large relative to the training sample size. Wasserstein distributionally robust
optimization seeks data-driven decisions that perform well under the most
adverse distribution within a certain Wasserstein distance from a nominal
distribution constructed from the training samples. In this tutorial we will
argue that this approach has many conceptual and computational benefits. Most
prominently, the optimal decisions can often be computed by solving tractable
convex optimization problems, and they enjoy rigorous out-of-sample and
asymptotic consistency guarantees. We will also show that Wasserstein
distributionally robust optimization has interesting ramifications for
statistical learning and motivates new approaches for fundamental learning
tasks such as classification, regression, maximum likelihood estimation or
minimum mean square error estimation, among others.
