  Mean-Field Control (MFC) is a powerful tool to solve Multi-Agent
Reinforcement Learning (MARL) problems. Recent studies have shown that MFC can
well-approximate MARL when the population size is large and the agents are
exchangeable. Unfortunately, the presumption of exchangeability implies that
all agents uniformly interact with one another which is not true in many
practical scenarios. In this article, we relax the assumption of
exchangeability and model the interaction between agents via an arbitrary
doubly stochastic matrix. As a result, in our framework, the mean-field `seen'
by different agents are different. We prove that, if the reward of each agent
is an affine function of the mean-field seen by that agent, then one can
approximate such a non-uniform MARL problem via its associated MFC problem
within an error of $e=\mathcal{O}(\frac{1}{\sqrt{N}}[\sqrt{|\mathcal{X}|} +
\sqrt{|\mathcal{U}|}])$ where $N$ is the population size and $|\mathcal{X}|$,
$|\mathcal{U}|$ are the sizes of state and action spaces respectively. Finally,
we develop a Natural Policy Gradient (NPG) algorithm that can provide a
solution to the non-uniform MARL with an error
$\mathcal{O}(\max\{e,\epsilon\})$ and a sample complexity of
$\mathcal{O}(\epsilon^{-3})$ for any $\epsilon >0$.
