  Sample-efficient domain adaptation is an open problem in robotics. In this
paper, we present affine transport -- a variant of optimal transport, which
models the mapping between state transition distributions between the source
and target domains with an affine transformation. First, we derive the affine
transport framework; then, we extend the basic framework with Procrustes
alignment to model arbitrary affine transformations. We evaluate the method in
a number of OpenAI Gym sim-to-sim experiments with simulation environments, as
well as on a sim-to-real domain adaptation task of a robot hitting a hockeypuck
such that it slides and stops at a target position. In each experiment, we
evaluate the results when transferring between each pair of dynamics domains.
The results show that affine transport can significantly reduce the model
adaptation error in comparison to using the original, non-adapted dynamics
model.
