{"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/moment-relaxations-for-data-driven","title":"Moment Relaxations for Data-Driven Wasserstein Distributionally Robust Optimization","arxiv_id":"2505.19278","date":"2025-05-25","proceeding":null,"authors":["Shixuan Zhang","Suhan Zhong"],"abstract":"We propose moment relaxations for data-driven $p$-Wasserstein distributionally robust optimization ($p$-WDRO) problems that are defined by polynomials. The proposed moment relaxations admit Benders-type decomposition with parallel evaluation of the subgradients using each sample subproblem, which enables efficient solution for larger training sets. We then identify conditions on $p$ and the defining polynomial degrees such that the proposed $k$-th order moment relaxations preserve the asymptotic consistency of the original $p$-WDRO (i.e., the relaxation gap is bounded at most linearly by the Wasserstein radius). In particular, these conditions translate to effective bounds on $k$, which lead to polynomially sized semidefinite optimization formulations that are compatible with existing solvers. Numerical experiments on a box-constrained regression problem and a two-stage production problem are included to demonstrate the scalability and the effectiveness of the proposed moment relaxations.","url_abs":"https://arxiv.org/abs/2505.19278v1","url_pdf":"https://arxiv.org/pdf/2505.19278v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"moment-relaxations-for-data-driven","repo_url":"https://github.com/shixuan-zhang/mowdro.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}