Planning with Submodular Objective Functions
This work addresses planning problems for applications like robotics and resource allocation by generalizing standard planning and submodular maximization, though it appears incremental as it builds on existing concepts.
The paper tackles planning with submodular objective functions, proposing a novel algorithmic framework based on multilinear extension, and empirically shows it significantly outperforms baseline algorithms on synthetic and navigation tasks.
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.