Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games

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 not approachable 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.