  Bayesian optimization (BO) with Gaussian processes is a powerful methodology
to optimize an expensive black-box function with as few function evaluations as
possible. The expected improvement (EI) and probability of improvement (PI) are
among the most widely used schemes for BO. There is a plethora of other schemes
that outperform EI and PI, but most of them are numerically far more expensive
than EI and PI. In this work, we propose a new one-parameter family of
acquisition functions for BO that unifies EI and PI. The proposed method is
numerically inexpensive, is easy to implement, can be easily parallelized, and
on benchmark tasks shows a performance superior to EI and GP-UCB. Its
generalization to BO with Student-t processes is also presented.

Machine Learning