Fast Online Distributionally Robust Optimization via Data Compression

[2504.08097] Fast Online Distributionally Robust Optimization via Data Compression Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2504.08097 (math) [Submitted on 10 Apr 2025 ( v1 ), last revised 14 Aug 2026 (this version, v3)] Title: Fast Online Distributionally Robust Optimization via Data Compression Authors: Irina Wang , Bartolomeo Stellato View a PDF of the paper titled Fast Online Distributionally Robust Optimization via Data Compression, by Irina Wang and 1 other authors View PDF HTML (experimental) Abstract: We propose an online data compression approach for efficiently solving Wasserstein distributionally robust optimization (DRO) problems with streaming data. Our method constructs adaptive ambiguity sets around a compressed distribution obtained by online clustering, so the problem size stays fixed as data accumulate. We construct a dynamic regret bound with respect to a one-step-ahead non-compressed DRO oracle, and establish online clustering conditions such that, with high probability, the regret converges sublinearly to a clustering-discrepancy-based performance gap. This gap is defined in terms of the discrepancies between the true and compressed distributions, so that by varying the number of clusters, our method trades off robustness against computational effort. We additionally provide fast subgradient-based updates that replace direct solutions of both the full and compressed problems, and extend the regret analysis to this setting. Numerical experiments on portfolio optimization and sparse support vector machine problems, including mixed-integer formulations, show over an order of magnitude reduction in cumulative computation time, even compared to non-robust methods, with minimal loss in solution quality. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2504.08097 [math.OC] (or arXiv:2504.08097v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2504.08097 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Bartolomeo Stellato [ view email ] [v1] Thu, 10 Apr 2025 19:48:50 UTC (1,434 KB) [v2] Wed, 10 Sep 2025 20:41:52 UTC (963 KB) [v3] Fri, 14 Aug 2026 21:17:53 UTC (788 KB) Full-text links: Access Paper: View a PDF of the paper titled Fast Online Distributionally Robust Optimization via Data Compression, by Irina Wang and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-04 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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