where β is a trade-off hyperparameter (sometimes denoted as the confidence parameter), which controls the balance between exploitation and exploration. For the purposes of this paper, we fix this hyperparameter to 0.2. The final acquisition function considered in this paper, is a numerically stable variant of the logarithm of the expected improvement (logEI), which was recently introduced to alleviate the vanishing gradient problems sometimes encountered in the classical version of EI and is defined as