Learning from humans is challenging because people are imperfect teachers. When everyday humans show the robot a new task they want it to perform, humans inevitably make errors (e.g., inputting noisy actions) and provide suboptimal examples (e.g., overshooting the goal). Existing methods often learn by matching some or all of the human's behavior --- but this approach is fundamentally limited because the demonstrations themselves are imperfect. In this work we advance offline imitation learning by enabling robots to extrapolate across nearby actions, instead of only considering what the human actually showed. We achieve this by hypothesizing that all of the human's demonstrations are trying to convey an underlying policy, while the noise and sub-optimality within their behaviors obfuscates the data and introduces unintentional complexity. To recover the underlying policy and learn what the human teacher meant, we introduce Counter-BC, a generalized version of behavior cloning. Counter-BC expands the dataset to include actions close to behaviors the human demonstrated (i.e., counterfactual actions that the human teacher could have intended, but did not actually show). During training Counter-BC autonomously modifies the human's demonstrations within this expanded region to reach a simplified policy that explains the underlying trends in the human's dataset. Theoretically, we prove that Counter-BC can extract a simple and similar-to-demonstration policy from imperfect data, multiple users, and teachers of varying skill levels. Empirically, we compare Counter-BC to state-of-the-art alternatives in settings with noisy demonstrations, standardized datasets, and real human teachers. Overall, we find that trying to extrapolate what the human teacher meant by considering nearby actions can lead to more proficient learning from humans. See videos of our work here: https://youtu.be/XaeOZWhTt68

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