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Shortfall-Based Wasserstein Distributionally Robust Optimization
- Source :
- Mathematics, Volume 11, Issue 4, Pages: 849
- Publication Year :
- 2023
- Publisher :
- MDPI AG, 2023.
-
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.
Details
- ISSN :
- 22277390
- Volume :
- 11
- Database :
- OpenAIRE
- Journal :
- Mathematics
- Accession number :
- edsair.doi.dedup.....8dc2c21b07a932b3e5030faea80a2a00