A uniform improvement to conformal risk control via a generalization of e-closure

The paper extends the e‑closure principle for multiple testing to general state and action spaces and to arbitrarily indexed risk families. It introduces a recertification method that reallocates unused risk budget, enlarging certifying e‑values while preserving validity and yielding less conservative decisions. Applications include improved conformal risk control and enhanced false discovery rate procedures, with empirical gains shown on CIFAR‑100 and simulations.

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