On the Statistical Efficiency of Mean Field Reinforcement Learning with
General Function Approximation
- URL: http://arxiv.org/abs/2305.11283v4
- Date: Fri, 13 Oct 2023 18:00:57 GMT
- Title: On the Statistical Efficiency of Mean Field Reinforcement Learning with
General Function Approximation
- Authors: Jiawei Huang, Batuhan Yardim, Niao He
- Abstract summary: 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.
- Score: 23.224683209113948
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 low MF-MBED
subsumes a rich family of Mean-Field RL problems. Additionally, we propose
algorithms based on maximal likelihood estimation, which can return an
$\epsilon$-optimal policy for MFC or an $\epsilon$-Nash Equilibrium policy for
MFG, with sample complexity polynomial w.r.t. relevant parameters and
independent of the number of states, actions and agents. Compared with previous
works, our results only require the minimal assumptions including realizability
and Lipschitz continuity.
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