On the Convergence Rates of Expected Improvement Methods

We consider a ranking and selection problem with independent normal observations, and analyze the asymptotic sampling rates of expected improvement (EI) methods in this setting. Such methods often perform well in practice, but a tractable analysis of their convergence rates is difficult due to the nonlinearity and nonconvexity of the functions used in the EI calculations. We present new results indicating that variants of EI produce simulation allocations that are essentially identical (for both known and unknown sampling variance) to those chosen by the optimal computing budget allocation (OCBA) methodology, which is known to yield nearoptimal asymptotic performance in R&S. This is the first general equivalence result between EI and OCBA, and provides insight into the good practical performance of EI.