Recent advances have extended the scope of Bayesian optimization (BO) to expensive-to-evaluate black-box functions with dozens of dimensions, aspiring to unlock impactful applications, for example, in the life sciences, neural architecture search, and robotics. However, a closer examination reveals that the state-of-the-art methods for high-dimensional Bayesian optimization (HDBO) suffer from degrading performance as the number of dimensions increases or even risk failure if certain unverifiable assumptions are not met. This paper proposes BAxUS that leverages a novel family of nested random subspaces to adapt the space it optimizes over to the problem. This ensures high performance while removing the risk of failure, which we assert via theoretical guarantees. A comprehensive evaluation demonstrates that BAxUS achieves better results than the state-of-the-art methods for a broad set of applications.

翻译：近期研究进展将贝叶斯优化（BO）的适用范围扩展到数十维度、评估代价高昂的黑盒函数，有望推动生命科学、神经架构搜索与机器人技术等领域的重要应用。然而更深入的分析表明，当前高维贝叶斯优化（HDBO）的最优方法存在两个问题：随着维度增加其性能逐渐下降，若某些不可验证的假设不成立则存在失败风险。本文提出BAxUS方法，通过利用新型嵌套随机子空间族，使优化空间自适应适应问题特性。这既保证了高性能表现，又消除了失败风险——我们通过理论证明对此加以确认。全面评估表明，BAxUS在广泛的应用场景中均取得了优于现有最优方法的效果。