Expected Coordinate Improvement for High-Dimensional Bayesian Optimization
This provides an efficient approach for high-dimensional Bayesian optimization, addressing a bottleneck in optimization tasks, though it is incremental as it builds on existing BO frameworks.
The authors tackled the challenge of extending Bayesian optimization to high-dimensional problems by proposing the Expected Coordinate Improvement (ECI) criterion, which simplifies infill selection to one-dimensional problems, and numerical experiments showed it achieves significantly better results than standard BO and competitive results against five state-of-the-art methods.
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.