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Bayesian optimization is a sample-efficient approach to solving globaloptimization problems. Along with a surrogate model, this approach relies ontheoretically motivated value heuristics (acquisition functions) to guide thesearch process. Maximizing acquisition functions yields the best performance;unfortunately, this ideal is difficult to achieve since optimizing acquisitionfunctions per se is frequently non-trivial. This statement is especially truein the parallel setting, where acquisition functions are routinely non-convex,high-dimensional, and intractable. Here, we demonstrate how many popularacquisition functions can be formulated as Gaussian integrals amenable to thereparameterization trick and, ensuingly, gradient-based optimization. Further,we use this reparameterized representation to derive an efficient Monte Carloestimator for the upper confidence bound acquisition function in the context ofparallel selection.

The reparameterization trick for acquisition functions