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.

翻译：我们研究了贝叶斯且无限时域下的隐蔽快速变化检测问题。合法实体通过主动探测离散无记忆信道，力求尽快检测到信道状态的变化。同时，该实体必须确保其探测行为对监控信道的对手保持隐蔽，以避免主动感知被察觉。我们引入期望隐蔽预算（ECB）作为一种可解析处理的隐蔽性度量，该度量从上限约束了由主动感知与被动感知所诱导的观测序列之间的相对熵。在虚警概率（PFA）与ECB的双重约束下，当PFA约束趋近于零时，对于任意正的ECB约束，我们建立了平均检测延迟的二阶渐近逆界，明确量化了最大平方根阶隐蔽感知增益的可能性。此外，我们提出了一种采用恒定感知概率的Shiryaev类型策略的可实现方案，并证明其与二阶渐近逆界相匹配。最后通过数值实例对结果进行了说明。