Active Quickest Detection When Monitoring Multi-streams with Two Affected Streams

We study the multi-stream quickest detection problem under the active learning setup, It is assumed that there are p local streams in a system and s ≤ p unknown local streams are affected by an undesired event at some unknown time, but one is only able to take observations from r of these p local streams at each time instant. The objective is how to adaptively sample from these p local streams and how to use the observed data to raise a correct global alarm as quickly as possible. In this paper, we develop the first asymptotic optimality theory in the active quickest detection literature for the case when s = r = 2. To be more concrete, we propose to combine three ideas to develop efficient active quickest detection algorithms: (1) win-stay, lose-switch sampling strategy; (2) local CUSUM statistics for local monitoring; and (3) the SUM-Shrinkage technique to fuse local statistics into a global decision. We show that our proposed algorithms are asymptotically optimal in the sense of minimizing detection delay up to the second order subject to the false alarm constraint. Numerical studies are conducted to validate our theoretical results.