  In the past few years, there has been considerable interest in two prominent
approaches for Distributionally Robust Optimization (DRO): Divergence-based and
Wasserstein-based methods. The divergence approach models misspecification in
terms of likelihood ratios, while the latter models it through a measure of
distance or cost in actual outcomes. Building upon these advances, this paper
introduces a novel approach that unifies these methods into a single framework
based on optimal transport (OT) with conditional moment constraints. Our
proposed approach, for example, makes it possible for optimal adversarial
distributions to simultaneously perturb likelihood and outcomes, while
producing an optimal (in an optimal transport sense) coupling between the
baseline model and the adversarial model.Additionally, the paper investigates
several duality results and presents tractable reformulations that enhance the
practical applicability of this unified framework.
