  We present a novel POMDP problem formulation for a robot that must
autonomously decide where to go to collect new and scientifically relevant
images given a limited ability to communicate with its human operator. From
this formulation we derive constraints and design principles for the
observation model, reward model, and communication strategy of such a robot,
exploring techniques to deal with the very high-dimensional observation space
and scarcity of relevant training data. We introduce a novel active reward
learning strategy based on making queries to help the robot minimize path
"regret" online, and evaluate it for suitability in autonomous visual
exploration through simulations. We demonstrate that, in some bandwidth-limited
environments, this novel regret-based criterion enables the robotic explorer to
collect up to 17% more reward per mission than the next-best criterion.
