Controlled Sensing for Multi-hypothesis Testing with Co-dependent Actions

Multi-hypothesis testing, which is widely used in many domains for discerning the true model governing the data, is often studied in a fixed sample-size setting. In such settings, the data-acquisition and decision-making processes are decoupled and the data-acquisition policies are pre-specified. Motivated by the advantages of sequential sampling, this paper treats the inherently coupled problems of data-acquisition and decision-making for multi-hypothesis testing, where data-acquisition can be abstracted as selecting one possible sensing action from a finite set. It aims to devise the quickest detection strategy by characterizing the minimum number of samples required to make a reliable decision as well as designing the dynamic attendant decision rules for selecting the best actions. The setting in which the available control actions are co-dependent is considered, which is a major distinction from the existing literature. Specifically, the existing data-adaptive approaches lose their optimality guarantees for this problem as they fail to account for such dependence. A novel sampling strategy that incorporates the dependence of the control actions into its decision rules is proposed, and its optimality properties are established.