Quick Change Detection in Discrete-Time in Presence of a Covert Adversary

2026-01-27

AI Summary

This study addresses the problem of quickest change detection in discrete-time sequences under a stealthy adversary who knows the false alarm constraint parameter γ and seeks to maximize the time until detection by selecting a posterior distribution that remains close to the pre-change prior. Building upon the CuSum framework and leveraging Kullback–Leibler divergence analysis, the work characterizes the asymptotic behavior of adversarial perturbations under Gaussian and exponential models, deriving precise asymptotic expressions for both average detection delay and mean time to false alarm. The key contribution lies in revealing that, under stealthy adversarial attacks, the average detection delay degrades from the classical O(log γ) to Θ(γ). The paper further establishes sufficient conditions for the adversary to maintain stealthiness and quantifies the interplay among detection performance, distributional divergence, and the false alarm parameter γ.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Adversarial Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study the problem of covert quickest change detection in a discrete-time setting, where a sequence of observations undergoes a distributional change at an unknown time. Unlike classical formulations, we consider a covert adversary who has knowledge of the detector's false alarm constraint parameter $\gamma$ and selects a stationary post-change distribution that depends on it, seeking to remain undetected for as long as possible. Building on the theoretical foundations of the CuSum procedure, we rigorously characterize the asymptotic behavior of the average detection delay (ADD) and the average time to false alarm (AT2FA) when the post-change distribution converges to the pre-change distribution as $\gamma \to \infty$. Our analysis establishes exact asymptotic expressions for these quantities, extending and refining classical results that no longer hold in this regime. We identify the critical scaling laws governing covert behavior and derive explicit conditions under which an adversary can maintain covertness, defined by ADD = $\Theta(\gamma)$, whereas in the classical setting, ADD grows only as $\mathcal{O}(\log \gamma)$. In particular, for Gaussian and Exponential models under adversarial perturbations of their respective parameters, we asymptotically characterize ADD as a function of the Kullback--Leibler divergence between the pre- and post-change distributions and $\gamma$.

Problem

• covert adversary
• quickest change detection
• false alarm constraint
• average detection delay
• discrete-time

Innovation

• covert adversary
• quickest change detection
• asymptotic analysis
• CuSum procedure
• Kullback-Leibler divergence