  Preventing poaching through ranger patrols protects endangered wildlife,
directly contributing to the UN Sustainable Development Goal 15 of life on
land. Combinatorial bandits have been used to allocate limited patrol
resources, but existing approaches overlook the fact that each location is home
to multiple species in varying proportions, so a patrol benefits each species
to differing degrees. When some species are more vulnerable, we ought to offer
more protection to these animals; unfortunately, existing combinatorial bandit
approaches do not offer a way to prioritize important species. To bridge this
gap, (1) We propose a novel combinatorial bandit objective that trades off
between reward maximization and also accounts for prioritization over species,
which we call ranked prioritization. We show this objective can be expressed as
a weighted linear sum of Lipschitz-continuous reward functions. (2) We provide
RankedCUCB, an algorithm to select combinatorial actions that optimize our
prioritization-based objective, and prove that it achieves asymptotic
no-regret. (3) We demonstrate empirically that RankedCUCB leads to up to 38%
improvement in outcomes for endangered species using real-world wildlife
conservation data. Along with adapting to other challenges such as preventing
illegal logging and overfishing, our no-regret algorithm addresses the general
combinatorial bandit problem with a weighted linear objective.
