  Cross-domain imitation learning studies how to leverage expert demonstrations
of one agent to train an imitation agent with a different embodiment or
morphology. Comparing trajectories and stationary distributions between the
expert and imitation agents is challenging because they live on different
systems that may not even have the same dimensionality. We propose
Gromov-Wasserstein Imitation Learning (GWIL), a method for cross-domain
imitation that uses the Gromov-Wasserstein distance to align and compare states
between the different spaces of the agents. Our theory formally characterizes
the scenarios where GWIL preserves optimality, revealing its possibilities and
limitations. We demonstrate the effectiveness of GWIL in non-trivial continuous
control domains ranging from simple rigid transformation of the expert domain
to arbitrary transformation of the state-action space.

Machine Learning;Artificial Intelligence;Robotics;Machine Learning