  This paper studies a distributed policy gradient in collaborative multi-agent
reinforcement learning (MARL), where agents over a communication network aim to
find the optimal policy to maximize the average of all agents' local returns.
Due to the non-concave performance function of policy gradient, the existing
distributed stochastic optimization methods for convex problems cannot be
directly used for policy gradient in MARL. This paper proposes a distributed
policy gradient with variance reduction and gradient tracking to address the
high variances of policy gradient, and utilizes importance weight to solve the
{distribution shift} problem in the sampling process. We then provide an upper
bound on the mean-squared stationary gap, which depends on the number of
iterations, the mini-batch size, the epoch size, the problem parameters, and
the network topology. We further establish the sample and communication
complexity to obtain an $\epsilon$-approximate stationary point. Numerical
experiments are performed to validate the effectiveness of the proposed
algorithm.
