Towards information-theoretic decision making in a conservative information space

We propose the conceptual idea of resorting to conservative information fusion techniques for information-theoretic decision making, aiming to address challenges involved with decision making over a high-dimensional, possibly highly-correlated, information space. Our key observation is that in certain cases, the impact of any two actions (or controls) on an appropriate utility measure, such as entropy, has the same trend regardless if using the original probability distribution function (pdf) or a conservative approximation of thereof. This observation suggests that in these cases, decision making can be performed over a conservative pdf, instead of the original pdf, without sacrificing performance. We introduce and prove this concept for the basic one-dimensional case assuming Gaussian probability distributions, and then consider its extension to a high-dimensional state space. In particular, we consider a specific conservative pdf that decouples the random variables in the joint pdf, admitting extremely efficient entropy computation. We then present our progress in identifying classes of problems in which information-theoretic decision making over this conservative and original pdfs produce identical results. The concept is illustrated in the context of choosing informative image observations in an aerial visual simultaneous localization and mapping scenario.