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We present APAC-Net, an alternating population and agent control neuralnetwork for solving stochastic mean field games (MFGs). Our algorithm is gearedtoward high-dimensional instances of MFGs that are beyond reach with existingsolution methods. We achieve this in two steps. First, we take advantage of theunderlying variational primal-dual structure that MFGs exhibit and phrase it asa convex-concave saddle point problem. Second, we parameterize the value anddensity functions by two neural networks, respectively. By phrasing the problemin this manner, solving the MFG can be interpreted as a special case oftraining a generative adversarial network (GAN). We show the potential of ourmethod on up to 100-dimensional MFG problems.

Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games