{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/coresets-for-wasserstein-distributionally","title":"Coresets for Wasserstein Distributionally Robust Optimization Problems","arxiv_id":"2210.04260","date":"2022-10-09","proceeding":null,"authors":["Ruomin Huang","Jiawei Huang","Wenjie Liu","Hu Ding"],"abstract":"Wasserstein distributionally robust optimization (\\textsf{WDRO}) is a popular model to enhance the robustness of machine learning with ambiguous data. However, the complexity of \\textsf{WDRO} can be prohibitive in practice since solving its ``minimax'' formulation requires a great amount of computation. Recently, several fast \\textsf{WDRO} training algorithms for some specific machine learning tasks (e.g., logistic regression) have been developed. However, the research on designing efficient algorithms for general large-scale \\textsf{WDRO}s is still quite limited, to the best of our knowledge. \\textit{Coreset} is an important tool for compressing large dataset, and thus it has been widely applied to reduce the computational complexities for many optimization problems. In this paper, we introduce a unified framework to construct the $\\epsilon$-coreset for the general \\textsf{WDRO} problems. Though it is challenging to obtain a conventional coreset for \\textsf{WDRO} due to the uncertainty issue of ambiguous data, we show that we can compute a ``dual coreset'' by using the strong duality property of \\textsf{WDRO}. Also, the error introduced by the dual coreset can be theoretically guaranteed for the original \\textsf{WDRO} objective. To construct the dual coreset, we propose a novel grid sampling approach that is particularly suitable for the dual formulation of \\textsf{WDRO}. Finally, we implement our coreset approach and illustrate its effectiveness for several \\textsf{WDRO} problems in the experiments.","url_abs":"https://arxiv.org/abs/2210.04260v3","url_pdf":"https://arxiv.org/pdf/2210.04260v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"coresets-for-wasserstein-distributionally","repo_url":"https://github.com/h305142/wdro_coreset","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}