Change Acceleration and Detection

TL;DR

This paper introduces a new sequential change detection framework that not only detects changes but also accelerates their occurrence by optimizing treatment assignments, with solutions applicable to Markovian and non-Markovian models.

Contribution

It proposes a novel change acceleration and detection method, providing optimal solutions under Markovian models and a computationally simple alternative applicable to broader scenarios.

Findings

Proposed method achieves asymptotic optimality in a wide class of models.

Simulation results show performance comparable to the optimal method.

The approach effectively accelerates change detection while controlling false alarms.

Abstract

A novel sequential change detection problem is proposed, in which the goal is to not only detect but also accelerate the change. Specifically, it is assumed that the sequentially collected observations are responses to treatments selected in real time. The assigned treatments determine the pre-change and post-change distributions of the responses and also influence when the change happens. The goal is to find a treatment assignment rule and a stopping rule that minimize the expected total number of observations subject to a user-specified bound on the false alarm probability. The optimal solution is obtained under a general Markovian change-point model. Moreover, an alternative procedure is proposed, whose applicability is not restricted to Markovian change-point models and whose design requires minimal computation. For a large class of change-point models, the proposed procedure is shown to achieve the optimal performance in an asymptotic sense. Finally, its performance is found in simulation studies to be comparable to the optimal, uniformly with respect to the error probability.