  Optimization of product and system characteristics is required in many
fields, including design and control. Bayesian optimization (BO) is often used
when there are high observing costs, because BO theoretically guarantees an
upper bound on regret. However, computational costs increase exponentially with
the number of parameters to be optimized, decreasing search efficiency. We
propose a BO that limits the search region to lower dimensions and utilizes
local Gaussian process regression (LGPR) to scale the BO to higher dimensions.
LGPR treats the low-dimensional search region as "local," improving prediction
accuracies there. The LGPR model is trained on a local subset of data specific
to that region. This improves prediction accuracy and search efficiency and
reduces the time complexity of matrix inversion in the Gaussian process
regression. In evaluations with 20D Ackley and Rosenbrock functions, search
efficiencies are equal to or higher than those of the compared methods,
improved by about 69% and 40% from the case without LGPR. We apply our method
to an automatic design task for a power semiconductor device. We successfully
reduce the specific on-resistance to 25% better than a conventional method and
3.4% better than without LGPR.
