Shortfall-Based Wasserstein Distributionally Robust Optimization

In this paper, we study a distributionally robust optimization (DRO) problem with affine decision rules. particular, construct an ambiguity set based on new family of Wasserstein metrics, shortfall–Wasserstein which apply normalized utility-based shortfall risk measures to summarize the transportation cost random variables. demonstrate that multi-dimensional ball can be affinely projected onto one-dimensional one. A noteworthy result reformulation is our program benefits from finite sample guarantee without dependence dimension nominal distribution. This also has computational tractability, and provide dual formulation verify strong duality enables direct concise problem. Our results offer DRO framework applied in numerous contexts such as regression portfolio optimization.