Leveraging the Turnpike Effect for Mean Field Games Numerics
Recently, a deep-learning algorithm referred to as Deep Galerkin Method (DGM), has gained a lot of attention among those trying to solve numerically Mean Field Games with finite horizon, even if the performance seems to be decreasing significantly with increasing horizon. On the other hand, it has b...
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IEEE
2024-01-01
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| Series: | IEEE Open Journal of Control Systems |
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| Online Access: | https://ieeexplore.ieee.org/document/10572276/ |
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| author | Rene A. Carmona Claire Zeng |
| author_facet | Rene A. Carmona Claire Zeng |
| author_sort | Rene A. Carmona |
| collection | DOAJ |
| description | Recently, a deep-learning algorithm referred to as Deep Galerkin Method (DGM), has gained a lot of attention among those trying to solve numerically Mean Field Games with finite horizon, even if the performance seems to be decreasing significantly with increasing horizon. On the other hand, it has been proven that some specific classes of Mean Field Games enjoy some form of the turnpike property identified over seven decades ago by economists. The gist of this phenomenon is a proof that the solution of an optimal control problem over a long time interval spends most of its time near the stationary solution of the ergodic version of the corresponding infinite horizon optimization problem. After reviewing the implementation of DGM for finite horizon Mean Field Games, we introduce a “turnpike-accelerated” version that incorporates the turnpike estimates in the loss function to be optimized, and we perform a comparative numerical analysis to show the advantages of this accelerated version over the baseline DGM algorithm. We demonstrate on some of the Mean Field Game models with local-couplings known to have the turnpike property, as well as a new class of linear-quadratic models for which we derive explicit turnpike estimates. |
| format | Article |
| id | doaj-art-d5a2eee6867949b1a9b7f5e5ec3c3ecc |
| institution | Kabale University |
| issn | 2694-085X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Control Systems |
| spelling | doaj-art-d5a2eee6867949b1a9b7f5e5ec3c3ecc2025-01-09T00:03:08ZengIEEEIEEE Open Journal of Control Systems2694-085X2024-01-01338940410.1109/OJCSYS.2024.341964210572276Leveraging the Turnpike Effect for Mean Field Games NumericsRene A. Carmona0https://orcid.org/0000-0003-1359-711XClaire Zeng1https://orcid.org/0009-0003-5062-3994Department of Operations Research and Financial Engineering, and the Bendheim Center for Finance, Princeton University, Princeton, NJ, USADepartment of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, USARecently, a deep-learning algorithm referred to as Deep Galerkin Method (DGM), has gained a lot of attention among those trying to solve numerically Mean Field Games with finite horizon, even if the performance seems to be decreasing significantly with increasing horizon. On the other hand, it has been proven that some specific classes of Mean Field Games enjoy some form of the turnpike property identified over seven decades ago by economists. The gist of this phenomenon is a proof that the solution of an optimal control problem over a long time interval spends most of its time near the stationary solution of the ergodic version of the corresponding infinite horizon optimization problem. After reviewing the implementation of DGM for finite horizon Mean Field Games, we introduce a “turnpike-accelerated” version that incorporates the turnpike estimates in the loss function to be optimized, and we perform a comparative numerical analysis to show the advantages of this accelerated version over the baseline DGM algorithm. We demonstrate on some of the Mean Field Game models with local-couplings known to have the turnpike property, as well as a new class of linear-quadratic models for which we derive explicit turnpike estimates.https://ieeexplore.ieee.org/document/10572276/Turnpike propertymean field gameexponential convergencedeep galerkin method |
| spellingShingle | Rene A. Carmona Claire Zeng Leveraging the Turnpike Effect for Mean Field Games Numerics IEEE Open Journal of Control Systems Turnpike property mean field game exponential convergence deep galerkin method |
| title | Leveraging the Turnpike Effect for Mean Field Games Numerics |
| title_full | Leveraging the Turnpike Effect for Mean Field Games Numerics |
| title_fullStr | Leveraging the Turnpike Effect for Mean Field Games Numerics |
| title_full_unstemmed | Leveraging the Turnpike Effect for Mean Field Games Numerics |
| title_short | Leveraging the Turnpike Effect for Mean Field Games Numerics |
| title_sort | leveraging the turnpike effect for mean field games numerics |
| topic | Turnpike property mean field game exponential convergence deep galerkin method |
| url | https://ieeexplore.ieee.org/document/10572276/ |
| work_keys_str_mv | AT reneacarmona leveragingtheturnpikeeffectformeanfieldgamesnumerics AT clairezeng leveragingtheturnpikeeffectformeanfieldgamesnumerics |