Theoretical guarantees on penalized information gathering

Optimal measurement selection for inference is combinatorially complex and intractable for large scale problems. Under mild technical conditions, it has been proven that greedy heuristics combined with conditional mutual information rewards achieve performance within a factor of the optimal. Here we provide conditions under which cost-penalized mutual information may achieve similar guarantees. Specifically, if the cost of a measurement is proportional to the information it conveys, the bounds proven in [4] and [10] still apply.