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

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Τίτλος: Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications
Συγγραφείς: Hinds, Piers D., Sharma, Akash, 1994, Tretyakov, Michael V.
Πηγή: Mathematical Models and Methods in Applied Sciences. 35(8):1845-1887
Θεματικοί όροι: consensus-based optimization, reflected stochastic differential equations, constrained sampling, reflected mean-field diffusion, mean-field Langevin dynamics, propagation of chaos, constrained optimization, Interacting particle system
Περιγραφή: In this paper, we establish well-posedness of reflected McKean-Vlasov stochastic differential equations (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.
Περιγραφή αρχείου: electronic
Σύνδεσμος πρόσβασης: https://research.chalmers.se/publication/546695
https://research.chalmers.se/publication/546695/file/546695_Fulltext.pdf
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  Data: Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications
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  Data: <searchLink fieldCode="AR" term="%22Hinds%2C+Piers+D%2E%22">Hinds, Piers D.</searchLink><br /><searchLink fieldCode="AR" term="%22Sharma%2C+Akash%22">Sharma, Akash</searchLink>, 1994<br /><searchLink fieldCode="AR" term="%22Tretyakov%2C+Michael+V%2E%22">Tretyakov, Michael V.</searchLink>
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  Data: <i>Mathematical Models and Methods in Applied Sciences</i>. 35(8):1845-1887
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  Data: <searchLink fieldCode="DE" term="%22consensus-based+optimization%22">consensus-based optimization</searchLink><br /><searchLink fieldCode="DE" term="%22reflected+stochastic+differential+equations%22">reflected stochastic differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22constrained+sampling%22">constrained sampling</searchLink><br /><searchLink fieldCode="DE" term="%22reflected+mean-field+diffusion%22">reflected mean-field diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22mean-field+Langevin+dynamics%22">mean-field Langevin dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22propagation+of+chaos%22">propagation of chaos</searchLink><br /><searchLink fieldCode="DE" term="%22constrained+optimization%22">constrained optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Interacting+particle+system%22">Interacting particle system</searchLink>
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  Data: In this paper, we establish well-posedness of reflected McKean-Vlasov stochastic differential equations (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.
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        Value: 10.1142/S0218202525500241
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      – SubjectFull: reflected stochastic differential equations
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      – SubjectFull: constrained sampling
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      – SubjectFull: reflected mean-field diffusion
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      – SubjectFull: constrained optimization
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      – SubjectFull: Interacting particle system
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              Y: 2025
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