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Bayesian optimization has risen over the last few years as a very attractive method to optimize expensive to evaluate, black box, derivative-free and possibly noisy functions This framework uses surrogate models, such as the likes of a Gaussian Process (Rasmussen and Williams 2004) which describe a prior belief over the possible objective functions in order to approximate them. The procedure itself is inherently sequential: our function is first evaluated a few times, a surrogate model is then fit with this information, which will later suggest the next point to be evaluated according to a predefined acquisition function. These strategies typically aim to balance exploitation and exploration, that is, areas where the posterior mean or variance of our surrogate model are high respectively.
Jiménez-Luna et al. (Thu,) studied this question.