Active Hypothesis Testing for Quickest Anomaly Detection

TL;DR

This paper develops an active hypothesis testing strategy for quickest anomaly detection among multiple processes, demonstrating that a simple deterministic test outperforms the Chernoff test in finite regimes and extends to multiple anomalies with known bounds.

Contribution

It introduces a deterministic testing approach for quickest anomaly detection that is asymptotically optimal and performs better in finite cases, extending to multiple anomalies with known bounds.

Findings

Deterministic test achieves asymptotic optimality.

Proposed method outperforms Chernoff test in finite regimes.

Extension to multiple anomalies with known upper bounds.

Abstract

The problem of quickest detection of an anomalous process among M processes is considered. At each time, a subset of the processes can be observed, and the observations from each chosen process follow two different distributions, depending on whether the process is normal or abnormal. The objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint. This problem can be considered as a special case of active hypothesis testing first considered by Chernoff in 1959 where a randomized strategy, referred to as the Chernoff test, was proposed and shown to be asymptotically (as the error probability approaches zero) optimal. For the special case considered in this paper, we show that a simple deterministic test achieves asymptotic optimality and offers better performance in the finite regime. We further extend the problem to the case where multiple anomalous processes are present. In particular, we examine the case where only an upper bound on the number of anomalous processes is known.