Expected improvement is equivalent to OCBA

Abstract

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.

The Local Time Method for Targeting and Selection

“…Their characterization can be found by exploiting the structural similarities between the LTM and EI formulas. Ryzhov (2015bRyzhov ( , 2016 derives the sampling ratios for EI in R&S, and a straightforward modification of this analysis (using the target c as the "reference value" in the EI formula) yields the following result.…”