Planning with Submodular Objective Functions

TL;DR

This paper introduces a new planning framework that maximizes submodular objectives, unifying standard planning and submodular maximization, and demonstrates superior empirical performance on synthetic and navigation tasks.

Contribution

It proposes a novel algorithmic framework based on multilinear extension for planning with submodular functions, unifying existing approaches and improving performance.

Findings

Significant empirical improvements over baseline algorithms

Framework generalizes standard planning and submodular maximization

Effective on synthetic environments and navigation tasks

Abstract

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.