Interactions with either environments or expert policies during training are needed for most of the current imitation learning (IL) algorithms. For IL problems with no interactions, a typical approach is Behavior Cloning (BC). However, BC-like methods tend to be affected by distribution shift. To mitigate this problem, we come up with a Robust Model-Based Imitation Learning (RMBIL) framework that casts imitation learning as an end-to-end differentiable nonlinear closed-loop tracking problem. RMBIL applies Neural ODE to learn a precise multi-step dynamics and a robust tracking controller via Nonlinear Dynamics Inversion (NDI) algorithm. Then, the learned NDI controller will be combined with a trajectory generator, a conditional VAE, to imitate an experts behavior. Theoretical derivation shows that the controller network can approximate an NDI when minimizing the training loss of Neural ODE. Experiments on Mujoco tasks also demonstrate that RMBIL is competitive to the state-of-the-art generative adversarial method (GAIL) and achieves at least 30% performance gain over BC in uneven surfaces.
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