Probably Approximately Correct Greedy Maximization with Efficient Bounds on Information Gain for Sensor Selection
This addresses the computational bottleneck in sensor selection and similar decision-making problems for applications like surveillance, but it is incremental as it builds on existing greedy methods with new bounds.
The paper tackles the problem of submodular function maximization in settings where evaluating the function is computationally expensive, by introducing a probably approximately correct greedy maximization method that uses cheap confidence bounds to prune elements. It demonstrates on a real-world multi-camera tracking dataset that the approach performs comparably to existing methods at a fraction of the computational cost.
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.