Computationally efficient decision making under uncertainty in high-dimensional state spaces

We develop a novel approach for decision making under uncertainty in high-dimensional state spaces, considering both active unfocused and focused inference, where in the latter case reducing the uncertainty of only a subset of variables is of interest. State of the art approaches typically first calculate the posterior information (or covariance) matrix, followed by its determinant calculation, and do so separately for each candidate action. In contrast, using the generalized matrix determinant lemma, we avoid calculating these posteriors and determinants of large matrices. Furthermore, as our key contribution we introduce the concept of calculation re-use, performing a onetime computation that depends on state dimensionality and system sparsity, after which evaluating the impact of each candidate action no longer depends on state dimensionality. Such a concept is derived for both active focused and unfocused inference, leading to general, non-myopic and exact approaches that are faster by orders of magnitude compared to the state of the art. We verify our approach experimentally in two scenarios, sensor deployment (focused and unfocused) and measurement selection in visual SLAM, and show its superiority over standard techniques.