Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible for many online systems. This paper introduces a novel approach to efficient decision-making, by partitioning the high-dimensional observation space. Using the partitioned observation space, we formulate analytical bounds on the expected information-theoretic reward, for general belief distributions. These bounds are then used to plan efficiently while keeping performance guarantees. We show that the bounds are adaptive, computationally efficient, and that they converge to the original solution. We extend the partitioning paradigm and present a hierarchy of partitioned spaces that allows greater efficiency in planning. We then propose a specific variant of these bounds for Gaussian beliefs and show a theoretical performance improvement of at least a factor of 4. Finally, we compare our novel method to other state of the art algorithms in active SLAM scenarios, in simulation and in real experiments. In both cases we show a significant speed-up in planning with performance guarantees.

翻译：在信息不完美条件下进行决策是任何自主系统的核心问题。解决该决策问题的成本在动作空间和观测空间上呈指数增长，因此对许多在线系统而言难以实现。本文提出了一种通过划分高维观测空间来实现高效决策的新方法。利用划分后的观测空间，我们为一般信念分布推导了期望信息论奖励的解析边界。这些边界随后被用于在保持性能保证的前提下进行高效规划。我们证明这些边界具有自适应性、计算高效性，且能收敛到原始解。我们扩展了划分范式，提出了一种允许更高规划效率的层次化划分空间结构。随后针对高斯信念分布提出了这些边界的一个特定变体，并证明了至少4倍的理论性能提升。最后，我们将新方法与主动SLAM场景中的其他先进算法进行了比较，包括仿真实验和真实实验。两种情况下均显示出在保持性能保证前提下规划速度的显著提升。