  We study planning with submodular objective functions, where instead of
maximizing the cumulative reward, the goal is to maximize the objective value
induced by a submodular function. Our framework subsumes standard planning and
submodular maximization with cardinality constraints as special cases, and thus
many practical applications can be naturally formulated within our framework.
Based on the notion of multilinear extension, we propose a novel and
theoretically principled algorithmic framework for planning with submodular
objective functions, which recovers classical algorithms when applied to the
two special cases mentioned above. Empirically, our approach significantly
outperforms baseline algorithms on synthetic environments and navigation tasks.
