  We formulate an efficient approximation for multi-agent batch reinforcement
learning, the approximated multi-agent fitted Q iteration (AMAFQI). We present
a detailed derivation of our approach. We propose an iterative policy search
and show that it yields a greedy policy with respect to multiple approximations
of the centralized, learned Q-function. In each iteration and policy
evaluation, AMAFQI requires a number of computations that scales linearly with
the number of agents whereas the analogous number of computations increase
exponentially for the fitted Q iteration (FQI), a commonly used approaches in
batch reinforcement learning. This property of AMAFQI is fundamental for the
design of a tractable multi-agent approach. We evaluate the performance of
AMAFQI and compare it to FQI in numerical simulations. The simulations
illustrate the significant computation time reduction when using AMAFQI instead
of FQI in multi-agent problems and corroborate the similar performance of both
approaches.
