On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation

Fuente: arXiv
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Autores principales: Huang, Jiawei, Yardim, Batuhan, He, Niao
Formato: Preprint
Publicado: 2023
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author Huang, Jiawei
Yardim, Batuhan
He, Niao
author_facet Huang, Jiawei
Yardim, Batuhan
He, Niao
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2305_11283
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation
Huang, Jiawei
Yardim, Batuhan
He, Niao
Machine Learning
Artificial Intelligence
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.
title On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2305.11283