Sequential Optimization of Multiple Stopping Times with Spatial Subset Selection

Abstract In this paper, we present a sequential decision-making problem with spatial and temporal components. We consider a sequential decision problem involving both temporal and spatial decisions. The temporal component is formulated as a multiple stopping problem, while the spatial component consists of selecting subsets of locations at each intervention time. This leads to a multivariate sequential decision problem combining optimal stopping and spatial action selection. We propose a solution based on backward induction, which is a baseline tool to overcome optimal stopping problems, in which we encapsulate a method called Cross Entropy Method to tackle the combinatorial complexity of the spatial optimization. To study the proposed sequential procedure, numerical simulations on both simulated and real dataset have been conducted. In particular, we illustrate the applicability of the method for the mitigation of the pollution impact on health by considering 5 States in the United States of America and by focusing on the pollutant PM2.5. The results clearly highlight the benefits of such a method for decision makers.