Bayesian Optimization (BO) is typically used to optimize an unknown function $f$ that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Although provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open research problem, often tackled by assuming an additive structure for $f$. However, such algorithms introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. In this paper, we relax the restrictive assumptions on the additive structure of $f$, at the expense of weakening the maximization guarantees of the acquisition function, and we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of $f$ does not exist or comprises high-dimensional factors.

翻译：贝叶斯优化通常用于优化一个未知函数$f$，该函数存在噪声且评估成本高昂，通过利用在每个优化步骤中必须最大化的采集函数来实现。虽然理论上渐近最优的贝叶斯优化算法在优化低维函数方面高效，但将其扩展到高维空间仍是一个开放的研究问题，常通过假设$f$具有可加结构来解决。然而，此类算法对可加结构引入了额外的限制性假设，从而缩小了其适用范围。在本文中，我们以弱化采集函数最大化保证为代价，放宽了关于$f$可加结构的限制性假设，并解决了去中心化贝叶斯优化算法的过度探索问题。为此，我们提出了DuMBO，一种渐近最优的去中心化贝叶斯优化算法，在与最先进的贝叶斯优化算法相比时取得了极具竞争力的性能，特别是在$f$不存在可加结构或包含高维因子时。