Weighted Regret Metric for Online Multiple Testing

A new paper on arXiv introduces Weighted Regret as a unified metric for evaluating Online Multiple Testing (OMT), addressing the asymmetric costs of false positives and false negatives. The authors prove the Duality of Regret Conservation, showing that deterministic procedures with strict FDR control incur an Ω(T) linear regret penalty due to threshold depletion during signal-sparse cold starts. They propose Decoupled-OMT (DOMT), a meta-wrapper that uses history-decoupled, non-negative random perturbations to rescue deterministic baselines from severe threshold depletion while preserving exact asymptotic safety.