  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 a rotation aligning the trust region with the weighted principal
components 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.
