  Informative path-planning is a well established approach to visual-servoing
and active viewpoint selection in robotics, but typically assumes that a
suitable cost function or goal state is known. This work considers the inverse
problem, where the goal of the task is unknown, and a reward function needs to
be inferred from exploratory example demonstrations provided by a demonstrator,
for use in a downstream informative path-planning policy. Unfortunately, many
existing reward inference strategies are unsuited to this class of problems,
due to the exploratory nature of the demonstrations. In this paper, we propose
an alternative approach to cope with the class of problems where these
sub-optimal, exploratory demonstrations occur. We hypothesise that, in tasks
which require discovery, successive states of any demonstration are
progressively more likely to be associated with a higher reward, and use this
hypothesis to generate time-based binary comparison outcomes and infer reward
functions that support these ranks, under a probabilistic generative model. We
formalise this \emph{probabilistic temporal ranking} approach and show that it
improves upon existing approaches to perform reward inference for autonomous
ultrasound scanning, a novel application of learning from demonstration in
medical imaging while also being of value across a broad range of goal-oriented
learning from demonstration tasks. \keywords{Visual servoing \and reward
inference \and probabilistic temporal ranking
