🤖 AI Summary
This study addresses sequential multi-stream detection under the constraint that only one data stream can be observed at each time step, with the goal of simultaneously controlling global false alarm and missed detection probabilities while minimizing detection delay. To this end, the work introduces a novel optimality criterion based on the expected order statistics of detection times and proposes an active sampling strategy—dubbed “follow-the-leader”—that integrates exploration and exploitation mechanisms. Theoretical analysis demonstrates that the proposed strategy achieves asymptotic optimality for all such criteria as error probabilities vanish. Numerical experiments further confirm its superior finite-sample performance compared to existing methods and show that it closely approaches the performance of an ideal oracle policy that has full knowledge of the anomalous streams.
📝 Abstract
This work considers the problem of detecting signals from multiple sequentially observed data streams, where only one stream can be observed at every time instant. The goal is to detect signals as quickly as possible while controlling the global probabilities of false alarm and missed detection. In this active sampling setup, it is impossible to minimize the expected detection time simultaneously for every signal, so we formulate a novel set of performance criteria that aim to minimize the expectations of the order statistics of the detection times. A novel procedure is proposed, which incorporates an exploration mechanism to a "follow-the-leader" procedure, and is shown to optimize all the criteria asymptotically as the global error probabilities go to zero. Its finite-sample performance is compared with existing and oracle procedures in simulation studies.