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

Youbang Sun · Tao Liu · Ruida Zhou · P. R. Kumar · Shahin Shahrampour

Great Hall & Hall B1+B2 (level 1) #1306
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[ Paper [ Poster [ OpenReview
Thu 14 Dec 8:45 a.m. PST — 10:45 a.m. PST

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.

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