  We examine global non-asymptotic convergence properties of policy gradient
methods for multi-agent reinforcement learning (RL) problems in Markov
potential games (MPG). To learn a Nash equilibrium of an MPG in which the size
of state space and/or the number of players can be very large, we propose new
independent policy gradient algorithms that are run by all players in tandem.
When there is no uncertainty in the gradient evaluation, we show that our
algorithm finds an $\epsilon$-Nash equilibrium with $O(1/\epsilon^2)$ iteration
complexity which does not explicitly depend on the state space size. When the
exact gradient is not available, we establish $O(1/\epsilon^5)$ sample
complexity bound in a potentially infinitely large state space for a
sample-based algorithm that utilizes function approximation. Moreover, we
identify a class of independent policy gradient algorithms that enjoys
convergence for both zero-sum Markov games and Markov cooperative games with
the players that are oblivious to the types of games being played. Finally, we
provide computational experiments to corroborate the merits and the
effectiveness of our theoretical developments.
