We consider the problem of learning to perform a task from demonstrations given by teachers or experts, when some of the experts' demonstrations might be adversarial and demonstrate an incorrect way to perform the task. We propose a novel technique that can identify parts of demonstrated trajectories that have not been significantly modified by the adversary and utilize them for learning, using temporally extended policies or options. We first define a trajectory divergence measure based on the spatial and temporal features of demonstrated trajectories to detect and discard parts of the trajectories that have been significantly modified by an adversarial expert, and, could degrade the learner's performance, if used for learning, We then use an options-based algorithm that partitions trajectories and learns only from the parts of trajectories that have been determined as admissible. We provide theoretical results of our technique to show that repairing partial trajectories improves the sample efficiency of the demonstrations without degrading the learner's performance. We then evaluate the proposed algorithm for learning to play an Atari-like, computer-based game called LunarLander in the presence of different types and degrees of adversarial attacks of demonstrated trajectories. Our experimental results show that our technique can identify adversarially modified parts of the demonstrated trajectories and successfully prevent the learning performance from degrading due to adversarial demonstrations.

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