# The reparameterization trick for acquisition functions

arXiv: https://arxiv.org/abs/1712.00424 · HTML: https://mlsanity.com/paper/1712.00424/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2017.

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## Abstract (arXiv)

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.