The Behavior and Convergence of Local Bayesian Optimization

Kaiwen Wu, Kyurae Kim, Roman Garnett, Jacob R. Gardner

Keywords: Bayesian optimization, convergence rates

TL;DR: We provide the first convergence rate for a local Bayesian optimization algorithm in both the noisy and noiseless settings.

Abstract: A recent development in Bayesian optimization is the use of local optimization strategies, which can deliver strong empirical performance on high-dimensional problems compared to traditional global strategies. The "folk wisdom" in the literature is that the focus on local optimization sidesteps the curse of dimensionality; however, little is known concretely about the expected behavior or convergence of Bayesian local optimization routines. We first study the behavior of the local approach, and find that the statistics of individual local solutions of Gaussian process sample paths are surprisingly good compared to what we would expect to recover from global methods. We then present the first rigorous analysis of such a Bayesian local optimization algorithm recently proposed by Müller et al. (2021), and derive convergence rates in both the noisy and noiseless settings.

Submission Number: 8715