We consider the problem of finding an informative path through a graph, given initial and terminal nodes and a given maximum path length. We assume that a linear noise corrupted measurement is taken at each node of an underlying unknown vector that we wish to estimate. The informativeness is measured by the reduction in uncertainty in our estimate, evaluated using several metrics. We present a convex relaxation for this informative path planning problem, which we can readily solve to obtain a bound on the possible performance. We develop an approximate sequential method where the path is constructed segment by segment through dynamic programming. This involves solving an orienteering problem, with the node reward acting as a surrogate for informativeness, taking the first step, and then repeating the process. The method scales to very large problem instances and achieves performance not too far from the bound produced by the convex relaxation. We also demonstrate our method's ability to handle adaptive objectives, multimodal sensing, and multi-agent variations of the informative path planning problem.

翻译：我们考虑在给定初始节点、终止节点以及最大路径长度的条件下，在图中寻找一条信息性路径的问题。假设在底层未知向量的每个节点处进行线性噪声污染测量，我们希望通过这些测量估计该向量。信息性通过估计不确定性的减少量来度量，并采用多种指标进行评估。针对该信息路径规划问题，我们提出一种凸松弛方法，可便捷求解以获得性能上界。我们开发了一种近似序贯方法，通过动态规划逐段构建路径。该方法需解决一个定向问题，其中节点奖励作为信息性的代理指标，执行第一步后重复此过程。该方法可扩展至超大规模问题实例，且其性能与凸松弛产生的上界相差不大。我们还展示了该方法处理信息路径规划问题中自适应目标、多模态感知及多智能体变体的能力。