  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.
