  Specifying complex task behaviours while ensuring good robot performance may
be difficult for untrained users. We study a framework for users to specify
rules for acceptable behaviour in a shared environment such as industrial
facilities. As non-expert users might have little intuition about how their
specification impacts the robot's performance, we design a learning system that
interacts with the user to find an optimal solution. Using active preference
learning, we iteratively show alternative paths that the robot could take on an
interface. From the user feedback ranking the alternatives, we learn about the
weights that users place on each part of their specification. We extend the
user model from our previous work to a discrete Bayesian learning model and
introduce a greedy algorithm for proposing alternative that operates on the
notion of equivalence regions of user weights. We prove that with this
algorithm the revision active learning process converges on the user-optimal
path. In simulations on realistic industrial environments, we demonstrate the
convergence and robustness of our approach.
