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This work studies an independent natural policy gradient (NPG) algorithm forthe multi-agent reinforcement learning problem in Markov potential games. It isshown that, under mild technical assumptions and the introduction of the\textit{suboptimality gap}, the independent NPG method with an oracle providingexact policy evaluation asymptotically reaches an $\epsilon$-Nash Equilibrium(NE) within $\mathcal{O}(1/\epsilon)$ iterations. This improves upon theprevious best result of $\mathcal{O}(1/\epsilon^2)$ iterations and is of thesame order, $\mathcal{O}(1/\epsilon)$, that is achievable for the single-agentcase. Empirical results for a synthetic potential game and a congestion gameare presented to verify the theoretical bounds.

Provably Fast Convergence of Independent Natural Policy Gradient for Markov Potential Games