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

2025-11-16

AI Summary

This paper investigates the fundamental trade-off between detection delay and false alarm probability in quickest change detection (QCD) over a finite time horizon. Addressing change detection in non-stationary environments, we derive a universal lower bound on performance—characterized by prescribed false alarm rate and delay tolerance—and construct a class of order-optimal detectors applicable uniformly to both parametric and nonparametric settings. Methodologically, we model pre- and post-change distributions as sub-Gaussian, leveraging probabilistic upper bounds and finite-horizon optimization to achieve theoretically guaranteed delay minimization. We prove that the proposed detector attains the derived lower bound’s order optimality. Simulation results confirm that it significantly reduces average detection delay while strictly controlling the false alarm rate, offering a QCD solution that is both theoretically sound and practically viable for resource-constrained applications.

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

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.

Problem

• Detecting distribution changes in non-stationary environments with finite horizons
• Minimizing detection latency while controlling false alarm probability
• Developing optimal change detectors for known and unknown distributions

Innovation

• Finite-horizon quickest change detection balancing latency
• Universal lower bound derived for latency under constraints
• Order-optimal change detectors developed for known distributions