  In this paper, we study the well-known team orienteering problem where a
fleet of robots collects rewards by visiting locations. Usually, the rewards
are assumed to be known to the robots; however, in applications such as
environmental monitoring or scene reconstruction, the rewards are often
subjective and specifying them is challenging. We propose a framework to learn
the unknown preferences of the user by presenting alternative solutions to
them, and the user provides a ranking on the proposed alternative solutions. We
consider the two cases for the user: 1) a deterministic user which provides the
optimal ranking for the alternative solutions, and 2) a noisy user which
provides the optimal ranking according to an unknown probability distribution.
For the deterministic user we propose a framework to minimize a bound on the
maximum deviation from the optimal solution, namely regret. We adapt the
approach to capture the noisy user and minimize the expected regret. Finally,
we demonstrate the importance of learning user preferences and the performance
of the proposed methods in an extensive set of experimental results using real
world datasets for environmental monitoring problems.
