Selecting the selector: Comparison of update rules for discrete global optimization

We compare some well-known Bayesian global optimization methods in four distinct regimes, corresponding to high and low levels of measurement noise and to high and low levels of "quenched noise" which term we use to describe the roughness of the function we are trying to optimize. We isolate the two stages of this optimization in terms of a "regressor," which fits a model to the data measured so far, and a "selector," which identifies the next point to be measured. The focus of this paper is to investigate the choice of selector when the regressor is well matched to the data.