Cross-Domain Imitation Learning via Optimal Transport

Arnaud Fickinger, Samuel Cohen, Stuart Russell, Brandon Amos

Keywords: transfer, imitation, deep reinforcement learning, continuous control, optimal transport

TL;DR: We provably achieve strong transfer in non-trivial continuous control domains by minimizing the Gromov-Wasserstein distance with deep reinforcement learning.

Abstract: 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.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2110.03684/code)