Generalization in Mean Field Games by Learning Master Policies

Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most the literature assumes a single initial distribution for agents, which limits practical applications MFGs. Machine Learning has potential solve wider diversity MFG problems thanks generalizations capacities. We study how leverage these generalization properties learn policies enabling typical agent behave optimally against any population distribution. In reference Master equation in MFGs, we coin term “Master policies” describe them and prove that policy provides Nash equilibrium, whatever propose method such policies. Our approach relies on three ingredients: adding current as part observation, approximating with neural networks, training via Reinforcement Fictitious Play. illustrate numerical examples not only efficiency learned but also its capabilities beyond distributions used training.