Researchers Derive Scaling Laws for Covert Quickest Change Detection

Global: Researchers Derive Scaling Laws for Covert Quickest Change Detection

A recent arXiv preprint investigates covert quickest change detection in discrete time, focusing on scenarios where an adversary knows the detector’s false‑alarm constraint parameter (gamma) and selects a stationary post‑change distribution to remain hidden. The study rigorously characterizes the asymptotic behavior of the average detection delay (ADD) and the average time to false alarm (AT2FA) as (gamma) grows without bound, providing exact expressions that differ from classical results.

Background on Quickest Change Detection

Quickest change detection traditionally relies on procedures such as CuSum, which guarantee that the ADD scales on the order of (mathcal{O}(log gamma)) while satisfying a prescribed false‑alarm rate. These classical formulations assume that the post‑change distribution is fixed and independent of the detector’s parameters.

Covert Adversary Model

The paper introduces a covert adversary who adapts the post‑change distribution based on the known false‑alarm constraint (gamma). By allowing the post‑change distribution to converge toward the pre‑change distribution as (gamma) increases, the adversary seeks to maximize the detection delay while keeping the false‑alarm rate within the prescribed bound.

Key Theoretical Findings

Under the covert model, the authors derive asymptotic expressions for both ADD and AT2FA. They identify critical scaling laws that dictate when covertness is achievable, defining covertness as the condition where ADD grows proportionally to (Theta(gamma)). This linear scaling contrasts sharply with the logarithmic growth observed in non‑covert settings.

Model‑Specific Results

For Gaussian and Exponential observation models, the analysis links the ADD to the Kullback–Leibler (KL) divergence between the pre‑change and post‑change distributions and to (gamma). The results show that, as the KL divergence diminishes with increasing (gamma), the detection delay can be forced to follow the linear (Theta(gamma)) regime.

Implications for Detection Systems

The findings suggest that adversaries capable of tailoring post‑change statistics can substantially degrade the performance of conventional CuSum‑based detectors. Systems that rely on fixed post‑change assumptions may need to incorporate adaptive strategies or additional safeguards to mitigate covert manipulation.

Future Directions

The authors propose extending the framework to non‑stationary adversarial strategies and to multi‑sensor networks, where coordinated attacks could further challenge detection robustness. Continued exploration of covert detection limits may inform the design of more resilient monitoring algorithms.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.