LABCAT: Locally adaptive Bayesian optimization using principal
  component-aligned trust regions
E. Visser C. E. van Daalen J. C. Schoeman
Bayesian optimization (BO) is a popular method for optimizing expensive
black-box functions. BO has several well-documented shortcomings, including
computational slowdown with longer optimization runs, poor suitability for
non-stationary or ill-conditioned objective functions, and poor convergence
characteristics. Several algorithms have been proposed that incorporate local
strategies, such as trust regions, into BO to mitigate these limitations;
however, none address all of them satisfactorily. To address these
shortcomings, we propose the LABCAT algorithm, which extends trust-region-based
BO by adding principal-component-aligned rotation and an adaptive rescaling
strategy based on the length-scales of a local Gaussian process surrogate model
with automatic relevance determination. Through extensive numerical experiments
using a set of synthetic test functions and the well-known COCO benchmarking
software, we show that the LABCAT algorithm outperforms several
state-of-the-art BO and other black-box optimization algorithms.