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