  We investigate multi-agent imitation learning (IL) within the framework of
mean field games (MFGs), considering the presence of time-varying correlated
signals. Existing MFG IL algorithms assume demonstrations are sampled from Mean
Field Nash Equilibria (MFNE), limiting their adaptability to real-world
scenarios. For example, in the traffic network equilibrium influenced by public
routing recommendations, recommendations introduce time-varying correlated
signals into the game, not captured by MFNE and other existing correlated
equilibrium concepts. To address this gap, we propose Adaptive Mean Field
Correlated Equilibrium (AMFCE), a general equilibrium incorporating
time-varying correlated signals. We establish the existence of AMFCE under mild
conditions and prove that MFNE is a subclass of AMFCE. We further propose
Correlated Mean Field Imitation Learning (CMFIL), a novel IL framework designed
to recover the AMFCE, accompanied by a theoretical guarantee on the quality of
the recovered policy. Experimental results, including a real-world traffic flow
prediction problem, demonstrate the superiority of CMFIL over state-of-the-art
IL baselines, highlighting the potential of CMFIL in understanding large
population behavior under correlated signals.
