# Asymptotically optimal sequential change detection for bounded means

arXiv: https://arxiv.org/abs/2602.05272 · HTML: https://mlsanity.com/paper/2602.05272/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 4 of 4)

- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)
- [A composite generalization of Ville's martingale theorem using e-processes](https://mlsanity.com/paper/2203.04485/) (2022)

## Built on by (most cited first, 4 of 4)

- [The optimal betting wealth growth rate](https://mlsanity.com/paper/2604.25280/) (2026)
- [Non-partitioned e-detectors for nonparametric sequential change detection](https://mlsanity.com/paper/2607.28322/) (2026)
- [A complete characterization of sequential testability and change detectability in i.i.d. models](https://mlsanity.com/paper/2609.05752/) (2026)
- [Optimal sequential tests yield log-optimal e-processes](https://mlsanity.com/paper/2605.12720/) (2026)

## Abstract (arXiv)

We consider the problem of quickest changepoint detection under the Average Run Length (ARL) constraint where the pre-change and post-change laws lie in composite families mathscrP and mathscrQ respectively. In such a problem, a massive challenge is characterizing the best possible detection delay when the "hardest" pre-change law in mathscrP depends on the unknown post-change law Q∈mathscrQ. And typical simple-hypothesis likelihood-ratio arguments for Page-CUSUM and Shiryaev-Roberts do not at all apply here. To that end, we derive a universal sharp lower bound in full generality for any ARL-calibrated changepoint detector in the low type-I error (γ→∞ regime) of the order log(γ)/KLinf(Q,mathscrP). We show achievability of this universal lower bound by proving a tight matching upper bound (with the same sharp logγ constant) in the important bounded mean detection setting. In addition, for separated mean shifts, we also we derive a uniform minimax guarantee of this achievability over the alternatives.