Can Mean Field Control (MFC) Approximate Cooperative Multi Agent Reinforcement Learning (MARL) with Non-Uniform Interaction?
This addresses a limitation in MARL for scenarios where agents do not interact uniformly, offering a theoretical framework and algorithm for more practical applications.
The paper tackles the problem of approximating cooperative multi-agent reinforcement learning (MARL) with non-uniform interactions, relaxing the exchangeability assumption by modeling interactions via a doubly stochastic matrix, and proves an approximation error of O(1/√N[√|X| + √|U|]) and develops a Natural Policy Gradient algorithm with sample complexity O(ε^{-3}).
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 $\mathcal{O}(\max\{e,ε\})$ and a sample complexity of $\mathcal{O}(ε^{-3})$ for any $ε>0$.