On the expected runtime of multiple testing algorithms with bounded error

Consider testing multiple hypotheses in the setting where the p-values of all hypotheses are unknown and thus have to be approximated using Monte Carlo simulations. One class of algorithms published in the literature for this scenario provides guarantees on the correctness of their testing result through the computation of confidence statements on all approximated p-values. This article focuses on the expected runtime of such algorithms and derives a variety of finite and infinite expected runtime results.