Bounds for Distributionally Robust Optimization Problems

[2504.06381] Bounds for Distributionally Robust Optimization Problems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2504.06381 (math) [Submitted on 8 Apr 2025 ( v1 ), last revised 14 Aug 2026 (this version, v4)] Title: Bounds for Distributionally Robust Optimization Problems Authors: Brandon Tam , Silvana M. Pesenti View a PDF of the paper titled Bounds for Distributionally Robust Optimization Problems, by Brandon Tam and Silvana M. Pesenti View PDF HTML (experimental) Abstract: We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when the images of these sets under scalar-valued aggregation functions are contained in and contain uncertainty sets of univariate random variables defined via a univariate Wasserstein distance. This provides lower and upper bounds for the solution to general multivariate DRO problems that are computationally tractable. Furthermore, we generalize the results to uncertainty sets characterized by Bregman-Wasserstein divergences, which allows for asymmetric deviations from the reference random vector. Moreover, for DRO problems with risk measure criterion in the class of signed Choquet integrals, we derive semi-analytic formulae for the upper and lower bounds and the distribution that attains these bounds. Comments: 43 pages, 4 figures, 3 tables Subjects: Optimization and Control (math.OC) ; Risk Management (q-fin.RM) MSC classes: 90B99 Cite as: arXiv:2504.06381 [math.OC] (or arXiv:2504.06381v4 [math.OC] for this version) https://doi.org/10.48550/arXiv.2504.06381 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Brandon Tam [ view email ] [v1] Tue, 8 Apr 2025 19:05:52 UTC (490 KB) [v2] Mon, 3 Nov 2025 16:06:09 UTC (276 KB) [v3] Wed, 28 Jan 2026 19:44:01 UTC (272 KB) [v4] Fri, 14 Aug 2026 18:41:54 UTC (204 KB) Full-text links: Access Paper: View a PDF of the paper titled Bounds for Distributionally Robust Optimization Problems, by Brandon Tam and Silvana M. Pesenti View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-04 Change to browse by: math q-fin q-fin.RM References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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