Distributionally Robust Optimization over Wasserstein Balls with i.i.d. Structure

[2503.23543] Distributionally Robust Optimization over Wasserstein Balls with i.i.d. Structure Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2503.23543 (math) [Submitted on 30 Mar 2025 ( v1 ), last revised 11 Apr 2026 (this version, v3)] Title: Distributionally Robust Optimization over Wasserstein Balls with i.i.d. Structure Authors: Andrey Kharitenko , Marta Fochesato , Anastasios Tsiamis , Niklas Schmid , John Lygeros View a PDF of the paper titled Distributionally Robust Optimization over Wasserstein Balls with i.i.d. Structure, by Andrey Kharitenko and 4 other authors View PDF HTML (experimental) Abstract: We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a Wasserstein ball centered at an empirical distribution $\widehat{P}$. This structure reflects the assumption of independent and identically distributed (i.i.d.) uncertainty components and yields a non-convex ambiguity set that is strictly contained in its unstructured counterpart, thereby reducing conservatism. The resulting optimization problem is generally intractable due to the loss of convexity. We address this by introducing a sequence of tractable convex relaxations, each admitting strong duality, and prove that this sequence converges to the original problem value under suitable conditions. Numerical examples are provided to illustrate the effectiveness of the proposed approach. As a byproduct of our proofs, we establish a novel formula, of independent interest, relating the Wasserstein distance of a mixture of product distributions to the Wasserstein distance between its constituent measures. Comments: 52 pages Subjects: Optimization and Control (math.OC) MSC classes: 90C15, 90C25 Cite as: arXiv:2503.23543 [math.OC] (or arXiv:2503.23543v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2503.23543 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Andrey Kharitenko [ view email ] [v1] Sun, 30 Mar 2025 18:03:52 UTC (664 KB) [v2] Thu, 22 May 2025 11:28:41 UTC (1,968 KB) [v3] Sat, 11 Apr 2026 18:36:08 UTC (1,180 KB) Full-text links: Access Paper: View a PDF of the paper titled Distributionally Robust Optimization over Wasserstein Balls with i.i.d. Structure, by Andrey Kharitenko and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-03 Change to browse by: math 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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