Submodularity issues in value-of-information-based sensor placement

摘要： The value of information represents a rational metric for guiding the optimization of sensing efforts to support infrastructure system management under uncertainty. Unfortunately, this metric lacks the property of submodularity. Submodularity can be intuitively understood as a diminishing returns property, whereby the incremental benefit of a specific measurement is higher when the set of other available measures is smaller. Metrics which exhibit this property can be optimized using efficient greedy approaches, with certain guarantees on the near-optimality of the results. In this paper, we examine the issue of submodularity related to the optimization of sensor monitoring schemes using the value of information metric. We illustrate how greedy optimization approaches using value of information can lead to sub-optimal solutions for sensing in certain situations. We also examine how one potential heuristic approach involving a submodular surrogate metric (e.g. the conditional entropy) might be used to avoid some of these shortcomings.