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This paper presents a Gaussian Process (GP) framework, a non-parametrictechnique widely acknowledged for regression and classification tasks, toaddress inverse problems in mean field games (MFGs). By leveraging GPs, we aimto recover agents' strategic actions and the environment's configurations frompartial and noisy observations of the population of agents and the setup of theenvironment. Our method is a probabilistic tool to infer the behaviors ofagents in MFGs from data in scenarios where the comprehensive dataset is eitherinaccessible or contaminated by noises.

Decoding Mean Field Games from Population and Environment Observations By Gaussian Processes