No Correlations Involved: Decision Making Under Uncertainty in a Conservative Sparse Information Space

This letter is concerned with decision making under uncertainty in problems involving high dimensional state spaces. Inspired by conservative information fusion techniques, we propose a novel paradigm where decision making is performed over a conservative rather than the original information space. The key idea is that regardless of the sparsity pattern of the latter, one can always calculate a sparse conservative information space, which admits computationally efficient decision making. In this letter, we take this concept to the extreme and consider a conservative approximation that decouples the state variables, leading to a conservative diagonal information matrix. As a result, the computational complexity involved with evaluating impact of a candidate action is reduced to O(n), for an n-dimensional state, as the calculations do not involve any correlations. Importantly, we show that for measurement observation models involving arbitrary single state variables, this concept yields exactly the same results compared to using the original information matrix. We demonstrate applicability of this concept to a sensor deployment problem.