Abstract
Here, we study machine learning (ML) architectures to solve a mean-field games (MFGs) system arising in price formation models. We formulate a training process that relies on a min–max characterization of the optimal control and price variables. Our main theoretical contribution is the development of a posteriori estimates as a tool to evaluate the convergence of the training process. We illustrate our results with numerical experiments for linear dynamics and both quadratic and non-quadratic models.
Original language | English (US) |
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Article number | 23 |
Journal | Applied Mathematics and Optimization |
Volume | 88 |
Issue number | 1 |
DOIs | |
State | Published - Aug 2023 |
Bibliographical note
Publisher Copyright:© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Lagrange multiplier
- Mean field games
- Neural networks
- Price formation
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics