A Policy Iteration Method for Inverse Mean Field Games
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910019088285696 |
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| author | Ren, Kui Soedjak, Nathan Tong, Shanyin |
| author_facet | Ren, Kui Soedjak, Nathan Tong, Shanyin |
| contents | We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the optimal costs for agents. The proposed approach decouples this complex inverse problem, which is an optimization problem constrained by a coupled nonlinear forward and backward PDE system in the MFG, into several iterations of solving linear PDEs and linear inverse problems. This method can also be viewed as a fixed-point iteration that simultaneously solves the MFG system and inversion. We prove its linear rate of convergence. In addition, numerical examples in 1D and 2D, along with performance comparisons to a direct least-squares method, demonstrate the superior efficiency and accuracy of the proposed method for solving inverse MFGs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Policy Iteration Method for Inverse Mean Field Games Ren, Kui Soedjak, Nathan Tong, Shanyin Optimization and Control Computer Science and Game Theory Numerical Analysis Analysis of PDEs 35Q89, 35R30, 49L12, 49M41, 49N45 49N80, 65K10, 91A16 We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the optimal costs for agents. The proposed approach decouples this complex inverse problem, which is an optimization problem constrained by a coupled nonlinear forward and backward PDE system in the MFG, into several iterations of solving linear PDEs and linear inverse problems. This method can also be viewed as a fixed-point iteration that simultaneously solves the MFG system and inversion. We prove its linear rate of convergence. In addition, numerical examples in 1D and 2D, along with performance comparisons to a direct least-squares method, demonstrate the superior efficiency and accuracy of the proposed method for solving inverse MFGs. |
| title | A Policy Iteration Method for Inverse Mean Field Games |
| topic | Optimization and Control Computer Science and Game Theory Numerical Analysis Analysis of PDEs 35Q89, 35R30, 49L12, 49M41, 49N45 49N80, 65K10, 91A16 |
| url | https://arxiv.org/abs/2409.06184 |