Finite-Horizon Quickest Change Detection Balancing Latency with False Alarm Probability

A finite-horizon variant of the quickest change detection (QCD) problem that is of relevance to learning in non-stationary environments is studied. The metric characterizing false alarms is the probability of a false alarm occurring before the horizon ends. The metric that characterizes the delay is \emph{latency}, which is the smallest value such that the probability that detection delay exceeds this value is upper bounded to a predetermined latency level. The objective is to minimize the latency (at a given latency level), while maintaining a low false alarm probability. Under the pre-specified latency and false alarm levels, a universal lower bound on the latency, which any change detection procedure needs to satisfy, is derived. Change detectors are then developed, which are order-optimal in terms of the horizon. The case where the pre- and post-change distributions are known is considered first, and then the results are generalized to the non-parametric case when they are unknown except that they are sub-Gaussian with different means. Simulations are provided to validate the theoretical results.