1. Shortfall-Based Wasserstein Distributionally Robust Optimization.
- Author
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Li, Ruoxuan, Lv, Wenhua, and Mao, Tiantian
- Subjects
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ROBUST optimization , *AMBIGUITY , *RANDOM variables , *TRANSPORTATION costs , *STATISTICAL decision making , *VARIABLE costs - Abstract
In this paper, we study a distributionally robust optimization (DRO) problem with affine decision rules. In particular, we construct an ambiguity set based on a new family of Wasserstein metrics, shortfall–Wasserstein metrics, which apply normalized utility-based shortfall risk measures to summarize the transportation cost random variables. In this paper, we demonstrate that the multi-dimensional shortfall–Wasserstein ball can be affinely projected onto a one-dimensional one. A noteworthy result of this reformulation is that our program benefits from finite sample guarantee without a dependence on the dimension of the nominal distribution. This distributionally robust optimization problem also has computational tractability, and we provide a dual formulation and verify the strong duality that enables a direct and concise reformulation of this problem. Our results offer a new DRO framework that can be applied in numerous contexts such as regression and portfolio optimization. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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