  We consider offline Imitation Learning from corrupted demonstrations where a
constant fraction of data can be noise or even arbitrary outliers. Classical
approaches such as Behavior Cloning assumes that demonstrations are collected
by an presumably optimal expert, hence may fail drastically when learning from
corrupted demonstrations. We propose a novel robust algorithm by minimizing a
Median-of-Means (MOM) objective which guarantees the accurate estimation of
policy, even in the presence of constant fraction of outliers. Our theoretical
analysis shows that our robust method in the corrupted setting enjoys nearly
the same error scaling and sample complexity guarantees as the classical
Behavior Cloning in the expert demonstration setting. Our experiments on
continuous-control benchmarks validate that our method exhibits the predicted
robustness and effectiveness, and achieves competitive results compared to
existing imitation learning methods.
