Two acquisition functions are considered in this work. The expected improvement (EI) acquisition function is a commonly used function in the Bayesian optimization literature. Given a black-box function f to be optimized, let f ′ be the best value of this function observed so far. EI proposes to evaluate f at the parameter point at which we expect to improve on f ′ the most. The utility of a parameter point x is then max (0, f ′ -f (x)), and the EI acquisition function is the expectation value of this utility,