Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RL

• URL: http://arxiv.org/abs/2402.05724v2
• Date: Mon, 3 Jun 2024 15:29:09 GMT
• Title: Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RL
• Authors: Jiawei Huang, Niao He, Andreas Krause,
• Abstract summary: We study the sample complexity of reinforcement learning in Mean-Field Games (MFGs) with model-based function approximation. We introduce the Partial Model-Based Eluder Dimension (P-MBED), a more effective notion to characterize the model class complexity.
• Score: 57.745700271150454
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the sample complexity of reinforcement learning (RL) in Mean-Field Games (MFGs) with model-based function approximation that requires strategic exploration to find a Nash Equilibrium policy. We introduce the Partial Model-Based Eluder Dimension (P-MBED), a more effective notion to characterize the model class complexity. Notably, P-MBED measures the complexity of the single-agent model class converted from the given mean-field model class, and potentially, can be exponentially lower than the MBED proposed by \citet{huang2023statistical}. We contribute a model elimination algorithm featuring a novel exploration strategy and establish sample complexity results polynomial w.r.t.~P-MBED. Crucially, our results reveal that, under the basic realizability and Lipschitz continuity assumptions, \emph{learning Nash Equilibrium in MFGs is no more statistically challenging than solving a logarithmic number of single-agent RL problems}. We further extend our results to Multi-Type MFGs, generalizing from conventional MFGs and involving multiple types of agents. This extension implies statistical tractability of a broader class of Markov Games through the efficacy of mean-field approximation. Finally, inspired by our theoretical algorithm, we present a heuristic approach with improved computational efficiency and empirically demonstrate its effectiveness.

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