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We consider the indifference-zone (IZ) formulation of the ranking andselection problem in which the goal is to choose an alternative with thelargest mean with guaranteed probability, as long as the difference betweenthis mean and the second largest exceeds a threshold. Conservatism leadsclassical IZ procedures to take too many samples in problems with manyalternatives. The Bayes-inspired Indifference Zone (BIZ) procedure, proposed inFrazier (2014), is less conservative than previous procedures, but its proof ofvalidity requires strong assumptions, specifically that samples are normal, andvariances are known with an integer multiple structure. In this paper, we showasymptotic validity of a slight modification of the original BIZ procedure asthe difference between the best alternative and the second best goes tozero,when the variances are known and finite, and samples are independent andidentically distributed, but not necessarily normal.

Asymptotic Validity of the Bayes-Inspired Indifference Zone Procedure: The Non-Normal Known Variance Case