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.

翻译：跨领域模仿学习研究如何利用一个智能体的专家演示来训练具有不同实现方式或形态的模仿智能体。由于专家智能体与模仿智能体处于不同系统（甚至可能具有不同维度），比较两者间的轨迹与稳态分布具有挑战性。我们提出Gromov-Wasserstein模仿学习（GWIL），这是一种跨领域模仿方法，它利用Gromov-Wasserstein距离在不同智能体的状态空间之间进行对齐与比较。我们的理论严格刻画了GWIL保持最优性的场景，揭示了其可能性与局限性。我们在非平凡连续控制领域中验证了GWIL的有效性，这些领域涵盖从专家域的简单刚性变换到状态-动作空间的任意变换。