Data-Efficient Minimax Quickest Change Detection with Composite Post-Change Distribution

TL;DR

This paper introduces a data-efficient minimax quickest change detection method that employs on-off observation control and generalized likelihood ratio techniques, achieving asymptotic optimality for composite post-change distributions.

Contribution

It proposes a novel minimax change detection algorithm that handles composite post-change distributions with observation cost constraints, and proves its asymptotic optimality under specific conditions.

Findings

Algorithm is asymptotically optimal for finite post-change families.

Method effectively balances observation cost and detection delay.

Proven optimality for exponential family distributions.

Abstract

The problem of quickest change detection is studied, where there is an additional constraint on the cost of observations used before the change point and where the post-change distribution is composite. Minimax formulations are proposed for this problem. It is assumed that the post-change family of distributions has a member which is least favorable in some sense. An algorithm is proposed in which on-off observation control is employed using the least favorable distribution, and a generalized likelihood ratio based approach is used for change detection. Under the additional condition that either the post-change family of distributions is finite, or both the pre- and post-change distributions belong to a one parameter exponential family, it is shown that the proposed algorithm is asymptotically optimal, uniformly for all possible post-change distributions.