  An unmanned autonomous vehicle (UAV) is sent on a mission to explore and
reconstruct an unknown environment from a series of measurements collected by
Bayesian optimization. The success of the mission is judged by the UAV's
ability to faithfully reconstruct any anomalous features present in the
environment, with emphasis on the extremes (e.g., extreme topographic
depressions or abnormal chemical concentrations). We show that the criteria
commonly used for determining which locations the UAV should visit are
ill-suited for this task. We introduce a number of novel criteria that guide
the UAV towards regions of strong anomalies by leveraging previously collected
information in a mathematically elegant and computationally tractable manner.
We demonstrate superiority of the proposed approach in several applications,
including reconstruction of seafloor topography from real-world bathymetry
data, as well as tracking of dynamic anomalies. A particularly attractive
property of our approach is its ability to overcome adversarial conditions,
that is, situations in which prior beliefs about the locations of the extremes
are imprecise or erroneous.
