Efficient Byzantine Sequential Change Detection

In multichannel sequential change detection, multiple sensors monitor an environment and communicate their data to a fusion center; the latter is responsible for detecting, as soon as possible, an abrupt change that affects the observations in an unknown subset of sensors. In the Byzantine version of this problem, which is the focus of this paper, this task is further complicated by the fact that an unknown subset of sensors is compromised, in the sense that their data, both before and after the change, are controlled by an adversary. In this adversarial framework, we propose three robust, scalable, multichannel sequential change-detection rules. The proposed procedures impose different communication requirements and make different assumptions regarding knowledge of the number of compromised and affected sensors. We characterize their first-order asymptotic performance under a modification of Lorden's criterion, in which conditional expected detection delay and expected time to false alarm are both evaluated with respect to the worst-case scenario for the data in the compromised sensors. Our theoretical findings are also corroborated by a simulation study.