Rate-optimality of the complete expected improvement criterion

Expected improvement (EI) is a leading algorithmic approach to simulation-based optimization. However, it was recently proved that, in the context of ranking and selection, some of the most well-known EI-type methods cause the probability of incorrect selection to converge at suboptimal rates. We investigate a more recent variant of EI (known as “complete EI”) that was proposed by Salemi, Nelson, and Staum (2014), and summarize results showing that, with some minor modifications, complete EI can be made to achieve the optimal convergence rate in ranking and selection with independent Gaussian noise. This is the strongest theoretical guarantee available for any EI-type method.