Treffer: Distributionally robust optimization with generalized total variation ambiguity sets.

This paper introduces a data-driven framework for distributionally robust optimization (DRO), founded on a new class of ambiguity sets termed generalized total variation (GTV) sets. In contrast to traditional DRO approaches, the proposed scheme constructs ambiguity sets whose geometry incorporates sample size, support, confidence level, empirical distribution, and cost function structure. Under this framework, we develop two tractable solution methods (first-order, gradient-based), each offering finite-sample statistical guarantees. The first-order approach employs sequential convex programming to construct a solution, followed by a linear program to determine a high-confidence upper bound (i.e., generalization bound) on the solution's unknown true risk. The gradient-based approach, applicable when the ambiguity set has a smoothly curved boundary, utilizes gradient information to establish a high-confidence upper bound through a sequence of convex programs, all linear except for the final step. We prove that both methods produce statistically consistent risk estimates. Then, we empirically validate the framework on two applications: a synthetic two-item Newsvendor problem and a real-world portfolio optimization problem using S&P 500 asset returns. Results demonstrate that for finite support problems, GTV ambiguity sets can deliver generalization bounds that are as tight as, or tighter than, those from popular alternatives such as Wasserstein and total variation ambiguity sets. We thus highlight the practical benefits of incorporating several types of information into ambiguity set construction, offering improved robustness-performance tradeoffs for data-driven decision-making under uncertainty. • Introduces GTV ambiguity sets adapting to sample size, support, and cost structure. • Proposes two tractable methods: first-order and gradient-based, with guarantees. • Gradient-based method exploits interior geometry of the ambiguity set. • Validated on synthetic Newsvendor problems and real S&P 500 portfolio data. • Outperforms Wasserstein and total variation sets in certain small-sample settings. [ABSTRACT FROM AUTHOR]

Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)