  Bayesian optimization (BO) has been widely used in machine learning and
simulation optimization. With the increase in computational resources and
storage capacities in these fields, high-dimensional and large-scale problems
are becoming increasingly common. In this study, we propose a model aggregation
method in the Bayesian optimization (MamBO) algorithm for efficiently solving
high-dimensional large-scale optimization problems. MamBO uses a combination of
subsampling and subspace embeddings to collectively address high dimensionality
and large-scale issues; in addition, a model aggregation method is employed to
address the surrogate model uncertainty issue that arises when embedding is
applied. This surrogate model uncertainty issue is largely ignored in the
embedding literature and practice, and it is exacerbated when the problem is
high-dimensional and data are limited. Our proposed model aggregation method
reduces these lower-dimensional surrogate model risks and improves the
robustness of the BO algorithm. We derive an asymptotic bound for the proposed
aggregated surrogate model and prove the convergence of MamBO. Benchmark
numerical experiments indicate that our algorithm achieves superior or
comparable performance to other commonly used high-dimensional BO algorithms.
Moreover, we apply MamBO to a cascade classifier of a machine learning
algorithm for face detection, and the results reveal that MamBO finds settings
that achieve higher classification accuracy than the benchmark settings and is
computationally faster than other high-dimensional BO algorithms.
