  Imitation learning trains a policy from expert demonstrations. Imitation
learning approaches have been designed from various principles, such as
behavioral cloning via supervised learning, apprenticeship learning via inverse
reinforcement learning, and GAIL via generative adversarial learning. In this
paper, we propose a framework to analyze the theoretical property of imitation
learning approaches based on discrepancy propagation analysis. Under the
infinite-horizon setting, the framework leads to the value discrepancy of
behavioral cloning in an order of O((1-\gamma)^{-2}). We also show that the
framework leads to the value discrepancy of GAIL in an order of
O((1-\gamma)^{-1}). It implies that GAIL has less compounding errors than
behavioral cloning, which is also verified empirically in this paper. To the
best of our knowledge, we are the first one to analyze GAIL's performance
theoretically. The above results indicate that the proposed framework is a
general tool to analyze imitation learning approaches. We hope our theoretical
results can provide insights for future improvements in imitation learning
algorithms.
