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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.20510 |
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| _version_ | 1866912975589212160 |
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| author | Picarelli, Athena Scaratti, Marco Tam, Jonathan |
| author_facet | Picarelli, Athena Scaratti, Marco Tam, Jonathan |
| contents | We investigate the global numerical approximation of a class of extended mean field control problems (MFC), where the dynamics and costs depend on the joint distribution of the state and the control. We propose a framework to approximate the value function globally over the Wasserstein space, moving beyond the restriction of fixed initial conditions. Our approach exploits the propagation of chaos by approximating the infinite-dimensional MFC problem by an $N$-player cooperative game, together with the usage of finite-dimensional solvers. This method avoids the need to parametrise functions on an infinite-dimensional space, offering a balance between probabilistic rigor and computational efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended mean field control: a global numerical solution via finite-dimensional approximation Picarelli, Athena Scaratti, Marco Tam, Jonathan Optimization and Control 49N80, 65D15, 93E20 We investigate the global numerical approximation of a class of extended mean field control problems (MFC), where the dynamics and costs depend on the joint distribution of the state and the control. We propose a framework to approximate the value function globally over the Wasserstein space, moving beyond the restriction of fixed initial conditions. Our approach exploits the propagation of chaos by approximating the infinite-dimensional MFC problem by an $N$-player cooperative game, together with the usage of finite-dimensional solvers. This method avoids the need to parametrise functions on an infinite-dimensional space, offering a balance between probabilistic rigor and computational efficiency. |
| title | Extended mean field control: a global numerical solution via finite-dimensional approximation |
| topic | Optimization and Control 49N80, 65D15, 93E20 |
| url | https://arxiv.org/abs/2503.20510 |