One of the most complex tasks of decision making and planning is to gather information. This task becomes even more complex when the state is high-dimensional and its belief cannot be expressed with a parametric distribution. Although the state is high-dimensional, in many problems only a small fraction of it might be involved in transitioning the state and generating observations. We exploit this fact to calculate an information-theoretic expected reward, mutual information (MI), over a much lower-dimensional subset of the state, to improve efficiency and without sacrificing accuracy. A similar approach was used in previous works, yet specifically for Gaussian distributions, and we here extend it for general distributions. Moreover, we apply the dimensionality reduction for cases in which the new states are augmented to the previous, yet again without sacrificing accuracy. We then continue by developing an estimator for the MI which works in a Sequential Monte Carlo (SMC) manner, and avoids the reconstruction of future belief's surfaces. Finally, we show how this work is applied to the informative planning optimization problem. This work is then evaluated in a simulation of an active SLAM problem, where the improvement in both accuracy and timing is demonstrated.

本文提出一种计算信息论预期奖励的方法，运用信息量(mutual information)进行降维，开发出一个Sequential Monte Carlo (SMC)估计器，以避免未来信仰表面的重建，并将此方法应用于信息规划优化问题，最后在活动 SLAM问题的模拟中评估该方法。

高维非参数信念的信息化规划