Expected improvement is equivalent to OCBA

This paper summarizes new theoretical results on the asymptotic sampling rates of expected improvement (EI) methods in fully sequential ranking and selection (R&S). These methods have been widely observed to perform well in practice, and often have asymptotic consistency properties, but rate results are generally difficult to obtain when observations are subject to stochastic noise. We find that, in one general R&S problem, variants of EI produce simulation allocations that are virtually identical to the rate-optimal allocations calculated by the optimal computing budget allocation (OCBA) methodology. This result provides new insight into the good empirical performance of EI under normality assumptions.