  Established approaches to obtain generalization bounds in data-driven
optimization and machine learning mostly build on solutions from empirical risk
minimization (ERM), which depend crucially on the functional complexity of the
hypothesis class. In this paper, we present an alternate route to obtain these
bounds on the solution from distributionally robust optimization (DRO), a
recent data-driven optimization framework based on worst-case analysis and the
notion of ambiguity set to capture statistical uncertainty. In contrast to the
hypothesis class complexity in ERM, our DRO bounds depend on the ambiguity set
geometry and its compatibility with the true loss function. Notably, when using
statistical distances such as maximum mean discrepancy, Wasserstein distance,
or $\phi$-divergence in the DRO, our analysis implies generalization bounds
whose dependence on the hypothesis class appears the minimal possible: The
bound depends solely on the true loss function, independent of any other
candidates in the hypothesis class. To our best knowledge, it is the first
generalization bound of this type in the literature, and we hope our findings
can open the door for a better understanding of DRO, especially its benefits on
loss minimization and other machine learning applications.
