We consider the informative path planning ($\mathtt{IPP}$) problem in which a robot interacts with an uncertain environment and gathers information by visiting locations. The goal is to minimize its expected travel cost to cover a given submodular function. Adaptive solutions, where the robot incorporates all available information to select the next location to visit, achieve the best objective. However, such a solution is resource-intensive as it entails recomputing after every visited location. A more practical approach is to design solutions with a small number of adaptive "rounds", where the robot recomputes only once at the start of each round. In this paper, we design an algorithm for $\mathtt{IPP}$ parameterized by the number $k$ of adaptive rounds, and prove a smooth trade-off between $k$ and the solution quality (relative to fully adaptive solutions). We validate our theoretical results by experiments on a real road network, where we observe that a few rounds of adaptivity suffice to obtain solutions of cost almost as good as fully-adaptive ones.

翻译：我们考虑信息路径规划（$\mathtt{IPP}$）问题，其中机器人与不确定环境交互并通过访问位置收集信息。目标是最小化其预期旅行成本以覆盖给定的子模函数。自适应解决方案（即机器人利用所有可用信息选择下一个访问位置）能实现最优目标。然而，这种方案资源消耗大，因为每次访问位置后都需要重新计算。一种更实用的方法是设计具有少量自适应"轮次"的解决方案，其中机器人仅在每轮开始时重新计算一次。本文设计了一种以自适应轮次数$k$为参数的$\mathtt{IPP}$算法，并证明了$k$与解决方案质量（相对于完全自适应方案）之间的平滑权衡。我们通过在真实道路网络上的实验验证了理论结果，观察到仅需少量自适应轮次即可获得成本几乎与完全自适应方案相当的解决方案。