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We study the success probability for a variant of the secretary problem, withnoisy observations and multiple offline selection. Our formulation emulates,and is motivated by, problems involving noisy selection arising in thedisciplines of stochastic simulation and simulation-based optimisation. Inaddition, we employ the philosophy of ordinal optimisation - involving anordinal selection rule, and a percentile notion of goal softening for thesuccess probability. As a result, it is shown that the success probability onlydepends on the underlying copula of the problem. Other general properties forthe success probability are also presented. Specialising to the case ofGaussian copulas, we also derive an analytic lower bound for the successprobability, which may then be inverted to find sufficiently large sample sizesthat guarantee a high success probability arbitrarily close to one.

Ordinal Optimisation and the Offline Multiple Noisy Secretary Problem