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.

翻译：我们提出APAC-Net，一种交替种群与智能体控制神经网络，用于求解随机平均场博弈（MFGs）。该算法专门针对现有求解方法无法处理的高维MFG实例。我们通过两个步骤实现这一目标：首先，利用MFG潜在的变分原始-对偶结构，将其表述为一个凸-凹鞍点问题；其次，分别用两个神经网络参数化值函数和密度函数。通过这种问题表述，求解MFG可被解释为生成对抗网络（GAN）训练的一个特例。我们展示了该方法在高达100维的MFG问题上的潜力。