A Regret Perspective on Online Multiple Testing
arXiv:2605.13916v1 Announce Type: new Abstract: Online Multiple Testing (OMT), a fundamental pillar of sequential statistical inference, traditionally evaluates the False Discovery Rate (FDR) and statistical power in isolation, obscuring the highly asymmetric costs of false positives and false negatives in modern automated pipelines. To unify this evaluation, we introduce $textit{Weighted Regret}$. Under this metric, we prove the $textit{Duality of Regret Conservation}$: purely deterministic procedures ensuring strict FDR control inevitably incur an $Omega(T)$ linear regret penalty, as threshold depletion […]