Coupled Alternating Neural Networks for Solving Multi-Population High-Dimensional Mean-Field Games

Multi-population mean-field game is a critical subclass of mean-field games (MFGs). It is a theoretically feasible multi-agent model for simulating and analyzing the game between multiple heterogeneous populations of interacting massive agents. Due to the factors of game complexity, dimensionality disaster and disturbances should be taken into account simultaneously to solve the multi-population high-dimensional stochastic MFG problem, which is a great challenge. We present CA-Net, a coupled alternating neural network approach for tractably solving multi-population high-dimensional MFGs. First, we provide a universal modeling framework for large-scale heterogeneous multi-agent game systems, which is strictly expressed as a multi-population MFG problem. Next, we generalize the potential variational primal–dual structure that MFGs exhibit, then phrase the multi-population MFG problem as a convex–concave saddle-point problem. Last but not least, we design a generative adversarial network (GAN) with multiple generators and multiple discriminators—the solving network—which parameterizes the value functions and the density functions of multiple populations by two sets of neural networks, respectively. In multi-group quadcopter trajectory-planning numerical experiments, the convergence results of HJB residuals, control, and average speed show the effectiveness of the CA-Net algorithm, and the comparison with baseline methods—cluster game, HJB-NN, Lax–Friedrichs, ML, and APAC-Net—shows the progressiveness of our solution method.