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# Adaptive Discretization for Evaluation of Probabilistic Cost Functions

*Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics*, PMLR 108:2098-2108, 2020.

#### Abstract

In many real-world planning applications, e.g. dynamic design of experiments, autonomous driving and robot manipulation, it is necessary to evaluate candidate movement paths with respect to a safety cost function. Here, the continuous candidate paths need to be discretized first and, subsequently, evaluated onthe discretization points. The resulting quality of planned paths, thus, highly depends on the definition of the safety cost functions, and the resolution of the discretization. In this paper, we propose an approach for evaluating continuous candidate paths by employing an adaptive discretization scheme, with a probabilistic cost function learned from observations. The obtained path is then guaranteed to be epsilon-safe, i.e. the remaining risk of still finding an unsafe point on the trajectory is smaller than epsilon. The proposed approach is investigated theoretically, as well as empirically validated on several robotic path planning scenarios.