Minimax Robust Quickest Change Detection

TL;DR

This paper develops a minimax robust quickest change detection method that identifies least favorable distributions within uncertainty classes, providing a practical and improved alternative to existing GLR-based tests under distributional uncertainty.

Contribution

It introduces a robust change detection procedure based on least favorable distributions, simplifying implementation and outperforming GLR tests in certain scenarios.

Findings

The proposed test is easier to implement than GLR-based methods.

It provides an asymptotic upper bound on detection delay under robustness.

Simulation results show better performance than GLR tests for some parameters.

Abstract

The popular criteria of optimality for quickest change detection procedures are the Lorden criterion, the Shiryaev-Roberts-Pollak criterion, and the Bayesian criterion. In this paper a robust version of these quickest change detection problems is considered when the pre-change and post-change distributions are not known exactly but belong to known uncertainty classes of distributions. For uncertainty classes that satisfy a specific condition, it is shown that one can identify least favorable distributions (LFDs) from the uncertainty classes, such that the detection rule designed for the LFDs is optimal for the robust problem in a minimax sense. The condition is similar to that required for the identification of LFDs for the robust hypothesis testing problem originally studied by Huber. An upper bound on the delay incurred by the robust test is also obtained in the asymptotic setting under the Lorden criterion of optimality. This bound quantifies the delay penalty incurred to guarantee robustness. When the LFDs can be identified, the proposed test is easier to implement than the CUSUM test based on the Generalized Likelihood Ratio (GLR) statistic which is a popular approach for such robust change detection problems. The proposed test is also shown to give better performance than the GLR test in simulations for some parameter values.