Deep Galerkin Method for Mean Field Control Problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866911774358372352 |
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| author | Sun, Jingruo |
| author_facet | Sun, Jingruo |
| contents | We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state space, continuous-time, and finite-horizon. The value function of the mean-field control problem is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the simplex. We apply the DGM to estimate the value function and the evolution of the distribution. We also prove the numerical solution approximated by a neural network converges to the analytical solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01719 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Deep Galerkin Method for Mean Field Control Problem Sun, Jingruo Optimization and Control Mathematical Finance We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state space, continuous-time, and finite-horizon. The value function of the mean-field control problem is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the simplex. We apply the DGM to estimate the value function and the evolution of the distribution. We also prove the numerical solution approximated by a neural network converges to the analytical solution. |
| title | Deep Galerkin Method for Mean Field Control Problem |
| topic | Optimization and Control Mathematical Finance |
| url | https://arxiv.org/abs/2212.01719 |