We examine the problem of determining demonstration sufficiency: how can a robot self-assess whether it has received enough demonstrations from an expert to ensure a desired level of performance? To address this problem, we propose a novel self-assessment approach based on Bayesian inverse reinforcement learning and value-at-risk, enabling learning-from-demonstration ("LfD") robots to compute high-confidence bounds on their performance and use these bounds to determine when they have a sufficient number of demonstrations. We propose and evaluate two definitions of sufficiency: (1) normalized expected value difference, which measures regret with respect to the human's unobserved reward function, and (2) percent improvement over a baseline policy. We demonstrate how to formulate high-confidence bounds on both of these metrics. We evaluate our approach in simulation for both discrete and continuous state-space domains and illustrate the feasibility of developing a robotic system that can accurately evaluate demonstration sufficiency. We also show that the robot can utilize active learning in asking for demonstrations from specific states which results in fewer demos needed for the robot to still maintain high confidence in its policy. Finally, via a user study, we show that our approach successfully enables robots to perform at users' desired performance levels, without needing too many or perfectly optimal demonstrations.

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