Asymptotically optimal sequential change detection for bounded means

arXiv:2602.05272v1 Announce Type: cross
Abstract: 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 $mathscr{P}$ and $mathscr{Q}$ respectively. In such a problem, a massive challenge is characterizing the best possible detection delay when the “hardest” pre-change law in $mathscr{P}$ depends on the unknown post-change law $Qinmathscr{Q}$. 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 ($gammatoinfty$ regime) of the order $log(gamma)/mathrm{KL}_{mathrm{inf}}(Q,mathscr{P})$. We show achievability of this universal lower bound by proving a tight matching upper bound (with the same sharp $loggamma$ 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.