  Bayesian optimization (BO) algorithm is very popular for solving
low-dimensional expensive optimization problems. Extending Bayesian
optimization to high dimension is a meaningful but challenging task. One of the
major challenges is that it is difficult to find good infill solutions as the
acquisition functions are also high-dimensional. In this work, we propose the
expected coordinate improvement (ECI) criterion for high-dimensional Bayesian
optimization. The proposed ECI criterion measures the potential improvement we
can get by moving the current best solution along one coordinate. The proposed
approach selects the coordinate with the highest ECI value to refine in each
iteration and covers all the coordinates gradually by iterating over the
coordinates. The greatest advantage of the proposed ECI-BO (expected coordinate
improvement based Bayesian optimization) algorithm over the standard BO
algorithm is that the infill selection problem of the proposed algorithm is
always a one-dimensional problem thus can be easily solved. Numerical
experiments show that the proposed algorithm can achieve significantly better
results than the standard BO algorithm and competitive results when compared
with five state-of-the-art high-dimensional BOs. This work provides a simple
but efficient approach for high-dimensional Bayesian optimization.
