In high-dimensional settings, Bayesian optimization (BO) can be expensive and infeasible. The random embedding Bayesian optimization algorithm is commonly used to address high-dimensional BO challenges. However, this method relies on the effective subspace assumption on the optimization problem's objective function, which limits its applicability. In this paper, we introduce Condensing-Expansion Projection Bayesian optimization (CEPBO), a novel random projection-based approach for high-dimensional BO that does not reply on the effective subspace assumption. The approach is both simple to implement and highly practical. We present two algorithms based on different random projection matrices: the Gaussian projection matrix and the hashing projection matrix. Experimental results demonstrate that both algorithms outperform existing random embedding-based algorithms in most cases, achieving superior performance on high-dimensional BO problems. The code is available in \url{https://anonymous.4open.science/r/CEPBO-14429}.

本研究解决了高维贝叶斯优化中的高昂和不可行性问题。提出了一种新颖的凝聚-扩展投影贝叶斯优化方法（CEPBO），该方法不依赖于有效子空间假设，同时在实现上也较为简单。实验结果显示，此方法在大多数情况下优于现有的随机嵌入算法，对高维优化问题具有更好的性能。

高维贝叶斯优化通过凝聚-扩展投影