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arXiv · 2310.09727

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

Youbang Sun·Tao Liu·Ruida Zhou·P. R. Kumar·Shahin Shahrampour
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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 $ε$-Nash Equilibrium (NE) within $\mathcal{O}(1/ε)$ iterations. This improves upon the previous best result of $\mathcal{O}(1/ε^2)$ iterations and is of the same order, $\mathcal{O}(1/ε)$, 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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Youbang Sun, Tao Liu, Ruida Zhou, P. R. Kumar, Shahin Shahrampour. 2023-10-27. Provably Fast Convergence of Independent Natural Policy Gradient for Markov Potential Games. https://arxiv.org/abs/2310.09727

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