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Informative path-planning is a well established approach to visual-servoingand active viewpoint selection in robotics, but typically assumes that asuitable cost function or goal state is known. This work considers the inverseproblem, where the goal of the task is unknown, and a reward function needs tobe inferred from exploratory example demonstrations provided by a demonstrator,for use in a downstream informative path-planning policy. Unfortunately, manyexisting reward inference strategies are unsuited to this class of problems,due to the exploratory nature of the demonstrations. In this paper, we proposean alternative approach to cope with the class of problems where thesesub-optimal, exploratory demonstrations occur. We hypothesise that, in taskswhich require discovery, successive states of any demonstration areprogressively more likely to be associated with a higher reward, and use thishypothesis to generate time-based binary comparison outcomes and infer rewardfunctions that support these ranks, under a probabilistic generative model. Weformalise this \emph{probabilistic temporal ranking} approach and show that itimproves upon existing approaches to perform reward inference for autonomousultrasound scanning, a novel application of learning from demonstration inmedical imaging while also being of value across a broad range of goal-orientedlearning from demonstration tasks. \keywords{Visual servoing \and rewardinference \and probabilistic temporal ranking

Learning rewards for robotic ultrasound scanning using probabilistic temporal ranking