Kinetic variable-sample methods for stochastic optimization problems
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912467462914048 |
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| author | Bonandin, Sabrina Herty, Michael |
| author_facet | Bonandin, Sabrina Herty, Michael |
| contents | We discuss kinetic-based particle optimization methods and variable-sample strategies for problems where the cost function represents the expected value of a random mapping. Kinetic-based optimization methods rely on a consensus mechanism targeting the global minimizer, and they exploit tools of kinetic theory to establish a rigorous framework for proving convergence to that minimizer. Variable-sample strategies replace the expected value by an approximation at each iteration of the optimization algorithm. We combine these approaches and introduce a novel algorithm based on instantaneous collisions governed by a linear Boltzmann-type equation. After proving the convergence of the resulting kinetic method under appropriate parameter constraints, we establish a connection to a recently introduced consensus-based method for solving the random problem in a suitable scaling. Finally, we showcase its enhanced computational efficiency compared to the aforementioned algorithm and validate the consistency of the proposed modeling approaches through several numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kinetic variable-sample methods for stochastic optimization problems Bonandin, Sabrina Herty, Michael Optimization and Control Mathematical Physics 82B40, 65K10, 60K35, 90C26 We discuss kinetic-based particle optimization methods and variable-sample strategies for problems where the cost function represents the expected value of a random mapping. Kinetic-based optimization methods rely on a consensus mechanism targeting the global minimizer, and they exploit tools of kinetic theory to establish a rigorous framework for proving convergence to that minimizer. Variable-sample strategies replace the expected value by an approximation at each iteration of the optimization algorithm. We combine these approaches and introduce a novel algorithm based on instantaneous collisions governed by a linear Boltzmann-type equation. After proving the convergence of the resulting kinetic method under appropriate parameter constraints, we establish a connection to a recently introduced consensus-based method for solving the random problem in a suitable scaling. Finally, we showcase its enhanced computational efficiency compared to the aforementioned algorithm and validate the consistency of the proposed modeling approaches through several numerical experiments. |
| title | Kinetic variable-sample methods for stochastic optimization problems |
| topic | Optimization and Control Mathematical Physics 82B40, 65K10, 60K35, 90C26 |
| url | https://arxiv.org/abs/2502.17982 |