Model-Based RL for Mean-Field Games is not Statistically Harder than
  Single-Agent RL
Jiawei Huang Niao He Andreas Krause
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.