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When autonomous robots interact with humans, such as during autonomous driving, explicit safety guarantees are crucial in order to avoid potentially life-threatening accidents. Many data-driven methods have explored learning probabilistic bounds over human agents trajectories (i.e. confidence tubes that contain trajectories with probability $delta$), which can then be used to guarantee safety with probability $1-delta$. However, almost all existing works consider $delta geq 0.001$. The purpose of this paper is to argue that (1) in safety-critical applications, it is necessary to provide safety guarantees with $delta < 10^{-8}$, and (2) current learning-based methods are ill-equipped to compute accurate confidence bounds at such low $delta$. Using human driving data (from the highD dataset), as well as synthetically generated data, we show that current uncertainty models use inaccurate distributional assumptions to describe human behavior and/or require infeasible amounts of data to accurately learn confidence bounds for $delta leq 10^{-8}$. These two issues result in unreliable confidence bounds, which can have dangerous implications if deployed on safety-critical systems.
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Recent advances in Deep Machine Learning have shown promise in solving complex perception and control loops via methods such as reinforcement and imitation learning. However, guaranteeing safety for such learned deep policies has been a challenge due