Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games
Abstract
Mean-field games (MFGs) is an emerging field that models large populations of agents. They play a central role in many disciplines, such as economics, data science, and engineering. Since many applications come in the form of high-dimensional stochastic MFGs, numerical methods that use spatial grids are prone to the curse of dimensionality. To this end, we exploit the variational structure of potential MFGs and reformulate it as a generative adversarial network (GAN) training problem. This reformulation allays a bit the curse of dimensionality when solving high-dimensional MFGs in the stochastic setting, by avoiding spatial grids or uniform sampling in high dimensions, and instead utilizes the structure of the MFG and its connection with GANs.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 30, 2021
- Source ID
- 10.1073/pnas.2024713118
Entities
People
- A. T. Lin
- Levon Nurbekyan
- Samy Wu Fung
- Stanley Osher
- Wuchen Li
Organizations
- Air Force Office of Scientific Research
- Colorado School of Mines
- Office of Naval Research
- University of California
- University of South Carolina