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

Understand

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.