A crucial component of the BO framework is the surrogate model, an ML model which produces an estimate of the true objective function given a dataset of observations. Many ML models have been used as BO surrogates, including Bayesian neural networks, tree-based models, and kernel smoothing, but the most prevelant and well-studied choice is the Gaussian process (GP). GPs are non-parametric probabilistic ML models. They are a collection of random variables such that the joint distribution of each finite set of variables is a multivariate normal. GPs are characterized by a mean, m(x), and covariance function, k(x, x ′ ), and are written as