๐ค AI Summary
This paper addresses the conceptual and methodological divide between ฯ-divergence-based (likelihood-ratio-centric) and Wasserstein-based (outcome-space-centric) paradigms in distributionally robust optimization (DRO). To bridge this gap, we propose the first unified DRO framework. Methodologically, we integrate optimal transport theory with conditional moment constraints to construct a novel DRO model capable of simultaneously perturbing both likelihood ratios and outcome distributions. Via Lagrangian duality analysis, we derive a computationally tractable closed-form dual reformulation, whose equivalent problem is solvable in polynomial time. Theoretical contributions include: (i) establishing a rigorous strong duality theorem under conditional moment constraints; and (ii) introducing a new modeling paradigm for optimal transport that explicitly incorporates such constraints. Empirical results demonstrate that the proposed framework significantly enhances generalization and robustness under distributional shifts.
๐ Abstract
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.
