{"ID":2868336,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.16537","arxiv_id":"2509.16537","title":"Bayesian distributionally robust variational inequalities: regularization and quantification","abstract":"We propose a Bayesian distributionally robust variational inequality (DRVI) framework that models the data-generating distribution through a finite mixture family, which allows us to study the DRVI on a tractable finite-dimensional parametric ambiguity set. To address distributional uncertainty, we construct a data-driven ambiguity set with posterior coverage guarantees via Bayesian inference. We also employ a regularization approach to ensure numerical stability. We prove the existence of solutions to the Bayesian DRVI and the asymptotic convergence to a solution as sample size grows to infinity and the regularization parameter goes to zero. Moreover, we derive quantitative stability bounds and finite-sample guarantees under data scarcity and contamination. Numerical experiments on a distributionally robust multi-portfolio Nash equilibrium problem validate our theoretical results and demonstrate the robustness and reliability of Bayesian DRVI solutions in practice.","short_abstract":"We propose a Bayesian distributionally robust variational inequality (DRVI) framework that models the data-generating distribution through a finite mixture family, which allows us to study the DRVI on a tractable finite-dimensional parametric ambiguity set. To address distributional uncertainty, we construct a data-dri...","url_abs":"https://arxiv.org/abs/2509.16537","url_pdf":"https://arxiv.org/pdf/2509.16537v3","authors":"[\"Wentao Ma\",\"Zhiping Chen\",\"Xiaojun Chen\"]","published":"2025-09-20T04:55:32Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}