Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.

翻译：学习昂贵黑箱函数的分解方法有望将贝叶斯优化扩展到高维问题。然而，此类技术的成功取决于能否找到准确表征黑箱函数的适当分解。不同于先前基于数据学习分解的工作，本文研究数据无关的分解采样规则。我们首先发现，数据驱动的分解学习器容易被误导至仅在局部成立、而非全局适用的分解模式。随后我们从理论上证明，基于随机树的分解采样器具有优越的理论保证，能有效权衡最大信息增益与分解导致的真实黑箱函数及其代理模型之间的函数失配。这些理论成果催生了随机分解上置信界算法（RDUCB），该算法实现简便（近乎即插即用），且令人惊讶地在全面基准测试中相较于先前最优方法取得显著实证提升。我们通过将所提模块与HEBO框架集成，进一步验证了即插即用的特性，在Bayesmark最高维任务中展现出改进的实际效能。