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arXiv · 2404.09324

Mean Field Correlated Imitation Learning

Zhiyu Zhao·Qirui Mi·Ning Yang·Xue Yan·Haifeng Zhang·Jun Wang·Yaodong Yang
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Abstract

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.

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Zhiyu Zhao, Qirui Mi, Ning Yang, Xue Yan, Haifeng Zhang, Jun Wang, Yaodong Yang. 2024-10-03. Mean Field Correlated Imitation Learning. https://arxiv.org/abs/2404.09324

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