Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications

Hinds, Piers D.; Sharma, Akash; Tretyakov, Michael V.

Abstract

In this paper, we establish well-posedness of reflected McKean-Vlasov SDEs and their particle approximations in smooth non-convex domains. We prove convergence of the interacting particle system to the corresponding mean-field limit with the optimal rate of convergence. We motivate this study with applications to sampling and optimization in constrained domains by considering reflected mean-field Langevin SDEs for sampling and two reflected consensus-based optimization (CBO) models. We utilize reflection coupling to study long-time behavior of reflected mean-field SDEs and also investigate convergence of the reflected CBO models to the global minimum of a constrained optimization problem. We numerically test reflected CBO models on benchmark constrained optimization problems and an inverse problem.

Citation

Hinds, P. D., Sharma, A., & Tretyakov, M. V. (2025). Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications. Mathematical Models and Methods in Applied Sciences, 35(8), 1845-1887. https://doi.org/10.1142/S0218202525500241

• Journal Article Type: Article
• Acceptance Date: Apr 3, 2025
• Online Publication Date: May 16, 2025
• Publication Date: May 16, 2025
• Deposit Date: Apr 7, 2025
• Publicly Available Date: Apr 7, 2025
• Journal: Mathematical Models and Methods in Applied Sciences
• Electronic ISSN: 0218-2025
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 35
• Issue: 8
• Pages: 1845-1887
• DOI: https://doi.org/10.1142/S0218202525500241
• Public URL: https://nottingham-repository.worktribe.com/output/47546855
• Publisher URL: https://www.worldscientific.com/doi/10.1142/S0218202525500241?srsltid=AfmBOoqutlpID8W__uUEphqmubmlWh0KSlxH_zu4Ah4w3BQiG23lvDS5