Covert Bayesian Quickest Change Detection

2026-05-15

AI Summary

This study addresses the problem of covert and rapid detection of abrupt state changes in discrete memoryless channels over an infinite time horizon within a Bayesian framework, where the goal is to enable fast detection through active probing while ensuring the probing actions remain undetectable to an adversary. The work introduces the expected covert budget (ECB) as an analytically tractable measure of covertness and, for the first time, establishes a second-order asymptotic converse bound on the average detection delay under joint constraints on both the probability of false alarm (PFA) and ECB. This bound reveals a maximal square-root-order gain achievable through covert-aware design. A Shiryaev-type constant probing strategy is proposed that attains this theoretical lower bound in the second-order asymptotic regime, with numerical experiments confirming its superior performance.

Abstract

We investigate the problem of covert quickest change detection in a Bayesian and infinite-horizon setting. A legitimate entity seeks to detect a change in the state of a discrete memoryless channel as quickly as possible by actively probing it. Simultaneously, the entity must ensure its probing remains covert from an adversary monitoring the channel for active sensing. We introduce the expected covertness budget (ECB) as an analytically tractable covertness metric that bounds from above the relative entropy between the observation sequences induced by active and passive sensing. Under constraints on both the probability of false alarm (PFA) and the ECB, we establish a second-order asymptotic converse bound on the average detection delay as the PFA constraint approaches zero, for any positive ECB constraint, explicitly quantifying the maximum square-root-order covert sensing gain possible. Furthermore, we propose an achievability scheme utilizing a constant-sensing-probability Shiryaev-type policy and show that it matches the second-order asymptotic converse. We illustrate our result with a numerical example.

Problem

• covert sensing
• quickest change detection
• Bayesian detection
• covertness constraint
• discrete memoryless channel

Innovation

• covert sensing
• quickest change detection
• expected covertness budget
• second-order asymptotics
• Shiryaev policy