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arXiv · 2002.04131

Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis

Haotian Gu·Xin Guo·Xiaoli Wei·Renyuan Xu
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Abstract

Multi-agent reinforcement learning (MARL), despite its popularity and empirical success, suffers from the curse of dimensionality. This paper builds the mathematical framework to approximate cooperative MARL by a mean-field control (MFC) approach, and shows that the approximation error is of $\mathcal{O}(\frac{1}{\sqrt{N}})$. By establishing an appropriate form of the dynamic programming principle for both the value function and the Q function, it proposes a model-free kernel-based Q-learning algorithm (MFC-K-Q), which is shown to have a linear convergence rate for the MFC problem, the first of its kind in the MARL literature. It further establishes that the convergence rate and the sample complexity of MFC-K-Q are independent of the number of agents $N$, which provides an $\mathcal{O}(\frac{1}{\sqrt{N}})$ approximation to the MARL problem with $N$ agents in the learning environment. Empirical studies for the network traffic congestion problem demonstrate that MFC-K-Q outperforms existing MARL algorithms when $N$ is large, for instance when $N>50$.

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BibTeXRIS

Haotian Gu, Xin Guo, Xiaoli Wei, Renyuan Xu. 2020-02-10. Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis. https://arxiv.org/abs/2002.04131

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