  In a single-agent setting, reinforcement learning (RL) tasks can be cast into
an inference problem by introducing a binary random variable o, which stands
for the "optimality". In this paper, we redefine the binary random variable o
in multi-agent setting and formalize multi-agent reinforcement learning (MARL)
as probabilistic inference. We derive a variational lower bound of the
likelihood of achieving the optimality and name it as Regularized Opponent
Model with Maximum Entropy Objective (ROMMEO). From ROMMEO, we present a novel
perspective on opponent modeling and show how it can improve the performance of
training agents theoretically and empirically in cooperative games. To optimize
ROMMEO, we first introduce a tabular Q-iteration method ROMMEO-Q with proof of
convergence. We extend the exact algorithm to complex environments by proposing
an approximate version, ROMMEO-AC. We evaluate these two algorithms on the
challenging iterated matrix game and differential game respectively and show
that they can outperform strong MARL baselines.
