Asymptotic Optimality Theory for Active Quickest Detection with Unknown PostChange Parameters

The active quickest detection problem with unknown post-change parameters is studied under the sampling control constraint, where there are p local streams in a system but one is only able to take observations from one and only one of these p local streams at each time instant. The objective is to raise a correct alarm as quickly as possible once the change occurs subject to both false alarm and sampling control constraints. Here we assume that exactly one of the p local streams is affected, and the post-change distribution involves unknown parameters. In this context, we propose an efficient greedy-cyclic-sampling-based quickest detection algorithm, and show that our proposed algorithm is asymptotically optimal in the sense of minimizing the detection delay under both false alarm and sampling control constraints. Numerical studies are conducted to show the effectiveness and applicability of the proposed algorithm.