# Robust Sequential Change-Point Detection by Convex Optimization

## TL;DR

This paper introduces a convex optimization-based method for robust sequential change-point detection in multi-dimensional Gaussian settings with unknown parameters, addressing computational challenges and demonstrating strong theoretical and numerical performance.

## Contribution

It proposes a novel convex optimization approach to find robust detection procedures for multi-dimensional Gaussian distributions with uncertain parameters, improving computational feasibility.

## Key findings

- Method effectively finds robust detection procedures.
- Theoretical properties of the procedures are established.
- Numerical examples show good performance.

## Abstract

We address the computational challenge of finding the robust sequential change-point detection procedures when the pre- and post-change distributions are not completely specified. Earlier works [veeravalli 1994] and [Unnikrishnan 2011] establish the general conditions for robust procedures which include finding a pair of least favorable distributions (LFDs). However, in the multi-dimensional setting, it is hard to find such LFDs computationally. We present a method based on convex optimization that addresses this issue when the distributions are Gaussian with unknown parameters from pre-specified uncertainty sets. We also establish theoretical properties of our robust procedures, and numerical examples demonstrate their good performance.