Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games
This addresses computational challenges in MFGs for applications like economics and control, though it appears incremental as it builds on variational and GAN-based approaches.
The authors tackled solving high-dimensional stochastic mean-field games (MFGs) beyond existing methods by proposing APAC-Net, which formulates MFGs as a convex-concave saddle point problem and trains neural networks akin to a GAN, achieving results on up to 100-dimensional problems.
We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are beyond reach with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying variational primal-dual structure that MFGs exhibit and phrase it as a convex-concave saddle point problem. Second, we parameterize the value and density functions by two neural networks, respectively. By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN). We show the potential of our method on up to 100-dimensional MFG problems.