Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914189751091200 |
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| author | Hinds, P. D. Sharma, A. Tretyakov, M. V. |
| author_facet | Hinds, P. D. Sharma, A. Tretyakov, M. V. |
| contents | 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 and two reflected consensus-based optimization (CBO) models, respectively. We utilize reflection coupling to study long-time behaviour 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20247 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications Hinds, P. D. Sharma, A. Tretyakov, M. V. Probability Numerical Analysis Optimization and Control Statistics Theory 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 and two reflected consensus-based optimization (CBO) models, respectively. We utilize reflection coupling to study long-time behaviour 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. |
| title | Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications |
| topic | Probability Numerical Analysis Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2412.20247 |