  Learning from previously collected datasets of expert data offers the promise
of acquiring robotic policies without unsafe and costly online explorations.
However, a major challenge is a distributional shift between the states in the
training dataset and the ones visited by the learned policy at the test time.
While prior works mainly studied the distribution shift caused by the policy
during the offline training, the problem of recovering from out-of-distribution
states at the deployment time is not very well studied yet. We alleviate the
distributional shift at the deployment time by introducing a recovery policy
that brings the agent back to the training manifold whenever it steps out of
the in-distribution states, e.g., due to an external perturbation. The recovery
policy relies on an approximation of the training data density and a learned
equivariant mapping that maps visual observations into a latent space in which
translations correspond to the robot actions. We demonstrate the effectiveness
of the proposed method through several manipulation experiments on a real
robotic platform. Our results show that the recovery policy enables the agent
to complete tasks while the behavioral cloning alone fails because of the
distributional shift problem.
