Probably Approximately Correct Greedy Maximization with Efficient Bounds on Information Gain for Sensor Selection

TL;DR

This paper introduces a probably approximately correct greedy maximization method that efficiently selects sensor data by using confidence bounds, reducing computational costs while maintaining near-optimal solutions.

Contribution

It proposes a novel PAC greedy algorithm that relies on cheap confidence bounds, especially for conditional entropy, to efficiently maximize submodular functions in sensor selection.

Findings

Achieves near-optimal sensor sets with high probability

Reduces computational cost compared to traditional methods

Performs well on real-world multi-camera tracking data

Abstract

Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being maximized. Unfortunately, in many realistic settings F is too expensive to evaluate exactly even once. We present probably approximately correct greedy maximization, which requires access only to cheap anytime confidence bounds on F and uses them to prune elements. We show that, with high probability, our method returns an approximately optimal set. We propose novel, cheap confidence bounds for conditional entropy, which appears in many common choices of F and for which it is difficult to find unbiased or bounded estimates. Finally, results on a real-world dataset from a multi-camera tracking system in a shopping mall demonstrate that our approach performs comparably to existing methods, but at a fraction of the computational cost.