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