Interactive Submodular Set Cover

TL;DR

This paper introduces interactive submodular set cover, a generalization of submodular set cover and active learning, providing approximation guarantees, hardness results, and initial experimental insights.

Contribution

It defines the interactive submodular set cover problem, offers a greedy algorithm with approximation guarantees, and establishes matching hardness results.

Findings

Greedy algorithm achieves provable approximation bounds.

Hardness of approximation matches the algorithm's guarantees.

Early experiments show promising practical performance.

Abstract

We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover. Applications include advertising in social networks with hidden information. We give an approximation guarantee for a novel greedy algorithm and give a hardness of approximation result which matches up to constant factors. We also discuss negative results for simpler approaches and present encouraging early experimental results.