Imitation learning has achieved great success in many sequential decision-making tasks, in which a neural agent is learned by imitating collected human demonstrations. However, existing algorithms typically require a large number of high-quality demonstrations that are difficult and expensive to collect. Usually, a trade-off needs to be made between demonstration quality and quantity in practice. Targeting this problem, in this work we consider the imitation of sub-optimal demonstrations, with both a small clean demonstration set and a large noisy set. Some pioneering works have been proposed, but they suffer from many limitations, e.g., assuming a demonstration to be of the same optimality throughout time steps and failing to provide any interpretation w.r.t knowledge learned from the noisy set. Addressing these problems, we propose {\method} by evaluating and imitating at the sub-demonstration level, encoding action primitives of varying quality into different skills. Concretely, {\method} consists of a high-level controller to discover skills and a skill-conditioned module to capture action-taking policies, and is trained following a two-phase pipeline by first discovering skills with all demonstrations and then adapting the controller to only the clean set. A mutual-information-based regularization and a dynamic sub-demonstration optimality estimator are designed to promote disentanglement in the skill space. Extensive experiments are conducted over two gym environments and a real-world healthcare dataset to demonstrate the superiority of {\method} in learning from sub-optimal demonstrations and its improved interpretability by examining learned skills.
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