Bayesian distributionally robust variational inequalities: regularization and quantification
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912985980600320 |
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| author | Ma, Wentao Chen, Zhiping Chen, Xiaojun |
| author_facet | Ma, Wentao Chen, Zhiping Chen, Xiaojun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian distributionally robust variational inequalities: regularization and quantification Ma, Wentao Chen, Zhiping Chen, Xiaojun Optimization and Control 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. |
| title | Bayesian distributionally robust variational inequalities: regularization and quantification |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.16537 |