Minimax Robust Quickest Change Detection using Wasserstein Ambiguity Sets

TL;DR

This paper develops a minimax robust quickest change detection method using Wasserstein ambiguity sets, providing a data-driven, nonparametric approach that is computationally feasible and asymptotically optimal.

Contribution

It introduces a novel Wasserstein-distance-based ambiguity set for robust change detection and constructs a tractable, asymptotically optimal minimax test.

Findings

The proposed Wasserstein-based robust test outperforms existing methods.

The test is computationally tractable and asymptotically optimal.

It effectively handles distributional uncertainties without parametric assumptions.

Abstract

We study the robust quickest change detection under unknown pre- and post-change distributions. To deal with uncertainties in the data-generating distributions, we formulate two data-driven ambiguity sets based on the Wasserstein distance, without any parametric assumptions. The minimax robust test is constructed as the CUSUM test under least favorable distributions, a representative pair of distributions in the ambiguity sets. We show that the minimax robust test can be obtained in a tractable way and is asymptotically optimal. We investigate the effectiveness of the proposed robust test over existing methods, including the generalized likelihood ratio test and the robust test under KL divergence based ambiguity sets.