Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RL
This provides a theoretical foundation for efficient learning in multi-agent systems, extending to broader Markov Games via mean-field approximation, though it is incremental in refining complexity measures.
The paper tackles the sample complexity of reinforcement learning in Mean-Field Games (MFGs) by introducing the Partial Model-Based Eluder Dimension (P-MBED), showing that learning Nash Equilibrium in MFGs is statistically no harder than solving a logarithmic number of single-agent RL problems, with polynomial sample complexity results.
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.