  Cell-free Massive MIMO systems consist of a large number of geographically
distributed access points (APs) that serve users by coherent joint
transmission. Downlink power allocation is important in these systems, to
determine which APs should transmit to which users and with what power. If the
system is implemented correctly, it can deliver a more uniform user performance
than conventional cellular networks. To this end, previous works have shown how
to perform system-wide max-min fairness power allocation when using maximum
ratio precoding. In this paper, we first generalize this method to arbitrary
precoding, and then train a neural network to perform approximately the same
power allocation but with reduced computational complexity. Finally, we train
one neural network per AP to mimic system-wide max-min fairness power
allocation, but using only local information. By learning the structure of the
local propagation environment, this method outperforms the state-of-the-art
distributed power allocation method from the Cell-free Massive MIMO literature.
