When it comes to expensive black-box optimization problems, Bayesian Optimization (BO) is a well-known and powerful solution. Many real-world applications involve a large number of dimensions, hence scaling BO to high dimension is of much interest. However, state-of-the-art high-dimensional BO methods still suffer from the curse of dimensionality, highlighting the need for further improvements. In this work, we introduce BOIDS, a novel high-dimensional BO algorithm that guides optimization by a sequence of one-dimensional direction lines using a novel tailored line-based optimization procedure. To improve the efficiency, we also propose an adaptive selection technique to identify most optimal lines for each round of line-based optimization. Additionally, we incorporate a subspace embedding technique for better scaling to high-dimensional spaces. We further provide theoretical analysis of our proposed method to analyze its convergence property. Our extensive experimental results show that BOIDS outperforms state-of-the-art baselines on various synthetic and real-world benchmark problems.

翻译：针对昂贵黑盒优化问题，贝叶斯优化（BO）是一种广为人知且强大的解决方案。众多现实应用涉及高维参数空间，因此将BO扩展至高维场景具有重要意义。然而，当前最先进的高维BO方法仍受维度灾难的困扰，这表明该领域仍需进一步改进。本研究提出BOIDS算法——一种新颖的高维贝叶斯优化方法，其通过采用新型定制化线优化流程，沿一系列一维方向线引导优化过程。为提升效率，我们同时提出自适应选择技术以确定每轮线优化中的最优方向线。此外，算法引入子空间嵌入技术以增强对高维空间的适应能力。我们进一步通过理论分析验证了所提方法的收敛特性。大量实验结果表明，BOIDS在多种合成与真实世界基准问题上均优于当前最先进的基线方法。