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.

翻译：贝叶斯优化算法在求解低维昂贵优化问题中非常流行。将贝叶斯优化扩展到高维是一项有意义但具有挑战性的任务。主要挑战之一在于，由于采集函数本身也是高维的，因此难以找到优质填充解。本文针对高维贝叶斯优化提出了期望坐标改进准则。该准则通过衡量沿单一坐标移动当前最优解所能获得的潜在改进量，在每次迭代中选择具有最高期望坐标改进值的坐标进行细化，并通过逐步迭代覆盖所有坐标。与标准贝叶斯优化算法相比，所提期望坐标改进贝叶斯优化算法的最大优势在于，其填充解选择问题始终是一维问题，从而易于求解。数值实验表明，该算法能取得显著优于标准贝叶斯优化的结果，且与五种前沿高维贝叶斯优化方法相比具有竞争力。本文为高维贝叶斯优化提供了一种简单而高效的解决途径。