Asymptotic efficiency analysis on the modified Paulson's procedure with a PAC guarantee

While solving large-scale ranking-and-selection (R&S) problems, the statistical validities of many existing fully-sequential R&S procedures may no longer hold. With a few modifications on a classical fully-sequential procedure, Paulson's procedure, it can provide the probably approximately correct (PAC) guarantee which is a good fit for large-scale R&S problems. To provide the PAC guarantee, the modified procedure loses some efficiency on the total sample size. In this paper, we show, both theoretically and numerically, that the efficiency loss is tolerable.