In this paper, we study the fundamental statistical efficiency of Reinforcement Learning in Mean-Field Control (MFC) and Mean-Field Game (MFG) with general model-based function approximation. We introduce a new concept called Mean-Field Model-Based Eluder Dimension (MF-MBED), which characterizes the inherent complexity of mean-field model classes. We show that a rich family of Mean-Field RL problems exhibits low MF-MBED. Additionally, we propose algorithms based on maximal likelihood estimation, which can return an ϵ-optimal policy for MFC or an ϵ-Nash Equilibrium policy for MFG. The overall sample complexity depends only polynomially on MF-MBED, which is potentially much lower than the size of state-action space. Compared with previous works, our results only require the minimal assumptions including realizability and Lipschitz continuity.
@article{arxiv.2305.11283,
title = {On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation},
author = {Jiawei Huang and Batuhan Yardim and Niao He},
journal= {arXiv preprint arXiv:2305.11283},
year = {2024}
}