On the "near-universal proxy" argument for theoretical justification of information-driven sensor management

In sensor management applications, sometimes it may be difficult to find a goal function that meaningfully represents the desired qualities of the estimate, such as when we do not have a clear performance metric or when the computation cost of the goal function is prohibitive. An alternative is to use goal functions based on information theory, such as the Rényi divergence (also called $\alpha$-divergence). One strong argument in favor of information-driven sensor management is that the Rényi divergence is a "near-universal" proxy for arbitrary task-driven risk functions, implying that these could be replaced by a Rényi divergence-based criterion, and this would usually result in satisfactory performance. In this paper, we present a rebuttal to that argument, which implies that finding theoretical justification for information-driven sensor management still seems to be an open problem.