  In this work, we examine the problem of online decision making under
uncertainty, which we formulate as planning in the belief space. Maintaining
beliefs (i.e., distributions) over high-dimensional states (e.g., entire
trajectories) was not only shown to significantly improve accuracy, but also
allows planning with information-theoretic objectives, as required for the
tasks of active SLAM and information gathering. Nonetheless, planning under
this "smoothing" paradigm holds a high computational complexity, which makes it
challenging for online solution. Thus, we suggest the following idea: before
planning, perform a standalone state variable reordering procedure on the
initial belief, and "push forwards" all the predicted loop closing variables.
Since the initial variable order determines which subset of them would be
affected by incoming updates, such reordering allows us to minimize the total
number of affected variables, and reduce the computational complexity of
candidate evaluation during planning. We call this approach PIVOT: Predictive
Incremental Variable Ordering Tactic. Applying this tactic can also improve the
state inference efficiency; if we maintain the PIVOT order after the planning
session, then we should similarly reduce the cost of loop closures, when they
actually occur. To demonstrate its effectiveness, we applied PIVOT in a
realistic active SLAM simulation, where we managed to significantly reduce the
computation time of both the planning and inference sessions. The approach is
applicable to general distributions, and induces no loss in accuracy.
