Quickest Change Detection in the Presence of Covert Adversaries

This paper investigates the damage that an adversary can effect while remaining covert in the presence of the Cumulative Sum (CuSum) procedure. An adversary is covert if the time to detection is on the same order as the time to false alarm. Damage is given as an increasing function of the KL-divergence of the adversarial actions and the normal distribution prior to the adversarial attack. By analyzing the problem with a focus on the growth function g(n), which measures the cumulative expected log-likelihood ratio after n time slots following the change, we establish conditions under which the adversary remains covert and provide an analysis of the impact of different adversarial strategies on damage.