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.

翻译：近年来，基于散度的方法和基于Wasserstein的方法作为分布鲁棒优化（DRO）的两种主流范式引起了广泛关注。散度方法通过似然比刻画模型错误设定，而后者则通过实际结果中的距离或成本度量来建模。在前述研究基础上，本文提出了一种创新方法，通过引入带有条件矩约束的最优输运（OT）理论，将两种方法统一到同一框架内。例如，我们提出的方法使得最优对抗分布能够同时扰动似然与结果，同时在基线模型与对抗模型之间建立（从最优输运意义下的）最优耦合。此外，本文还探讨了若干对偶性质，并提出了可处理的重构形式，从而增强了该统一框架的实际应用性。