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

• URL: http://arxiv.org/abs/2310.09727v2
• Date: Fri, 27 Oct 2023 16:28:19 GMT
• Title: Provably Fast Convergence of Independent Natural Policy Gradient for Markov Potential Games
• Authors: Youbang Sun, Tao Liu, Ruida Zhou, P. R. Kumar, Shahin Shahrampour
• Abstract summary: 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, the independent NPG method with an oracle providing exact policy evaluationally reaches an $epsilon$-Nash Equilibrium (NE) within $mathcalO (1/epsilon)$ iterations.
• Score: 18.11805544026393
• License: http://creativecommons.org/licenses/by/4.0/
• 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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