Mean Field Games Flock! The Reinforcement Learning Way

We present a method enabling a large number of agents to learn how to flock,\nwhich is a natural behavior observed in large populations of animals. This\nproblem has drawn a lot of interest but requires many structural assumptions\nand is tractable only in small dimensions. We phrase this problem as a Mean\nField Game (MFG), where each individual chooses its acceleration depending on\nthe population behavior. Combining Deep Reinforcement Learning (RL) and\nNormalizing Flows (NF), we obtain a tractable solution requiring only very weak\nassumptions. Our algorithm finds a Nash Equilibrium and the agents adapt their\nvelocity to match the neighboring flock's average one. We use Fictitious Play\nand alternate: (1) computing an approximate best response with Deep RL, and (2)\nestimating the next population distribution with NF. We show numerically that\nour algorithm learn multi-group or high-dimensional flocking with obstacles.\n