  The optimization of high-dimensional black-box functions is a challenging
problem. When a low-dimensional linear embedding structure can be assumed,
existing Bayesian optimization (BO) methods often transform the original
problem into optimization in a low-dimensional space. They exploit the
low-dimensional structure and reduce the computational burden. However, we
reveal that this approach could be limited or inefficient in exploring the
high-dimensional space mainly due to the biased reconstruction of the
high-dimensional queries from the low-dimensional queries. In this paper, we
investigate a simple alternative approach: tackling the problem in the original
high-dimensional space using the information from the learned low-dimensional
structure. We provide a theoretical analysis of the exploration ability.
Furthermore, we show that our method is applicable to batch optimization
problems with thousands of dimensions without any computational difficulty. We
demonstrate the effectiveness of our method on high-dimensional benchmarks and
a real-world function.
