Asymptotic Optimality in Byzantine Distributed Quickest Change Detection

The Byzantine distributed quickest change detection (BDQCD) is studied, where a fusion center monitors the occurrence of an abrupt event through bunch sensors that may be compromised. We first consider binary hypothesis case there only one post-change and prove novel converse to first-order asymptotic delay in large mean time false alarm regime. This tight it coincides with currently best achievability shown by Fellouris et al.; hence, optimal performance BDQCD characterized. An important implication this result that, even compromised sensors, 1-bit link between each sensor suffices achieve optimality. To accommodate multiple hypotheses, we then formulate multi-hypothesis problem again investigate under different bandwidth constraints. A obtained extending our from BDQCD. Two families stopping rules, namely simultaneous d-th multi-shot alarm, are proposed. Under sufficient bandwidth, d being set number honest can derived bound; asymptotically Moreover, although for some special cases, much more bandwidth-efficient energy-efficient than alarm. Built upon above success characterizing optimality BDQCD, corresponding leader-follower Stackelberg game formulated its solution found.