The reparameterization trick for acquisition functions

James T. Wilson; Riccardo Moriconi; Frank Hutter; Marc Peter Deisenroth

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arXiv · 1712.00424

The reparameterization trick for acquisition functions

James T. Wilson·Riccardo Moriconi·Frank Hutter·Marc Peter Deisenroth

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Abstract

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.

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BibTeX RIS

James T. Wilson, Riccardo Moriconi, Frank Hutter, Marc Peter Deisenroth. 2017-12-01. The reparameterization trick for acquisition functions. https://arxiv.org/abs/1712.00424

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