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

Youbang Sun, Tao Liu, Ruida Zhou, Panganamala Kumar, Shahin Shahrampour

Keywords: Multi Agent Reinforcement Learning, Markov Potential Games, Natural Policy Gradient, Nash Equilibrium

TL;DR: This paper proves fast convergence of independent natural policy gradient algorithm for multi-agent reinforcement learning in Markov potential games.

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

Submission Number: 9570