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. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for $f$. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of $f$ without weakening the maximization guarantees of the acquisition function, and (ii) 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 $f$ comprises high-dimensional factors.

翻译：贝叶斯优化（BO）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，其方法是通过在每个优化步骤中最大化某个采集函数来实现。尽管可证明渐近最优的BO算法在优化低维函数时高效，但将其扩展到高维空间仍是一个开放性问题，通常通过假设$f$具有可加结构来解决。然而，BO算法在这样做时往往会引入关于可加结构的额外限制性假设，从而缩小了其应用范围。本文包含两项主要贡献：（i）我们放宽了关于$f$可加结构的限制性假设，同时不削弱采集函数的最大化保证；（ii）我们解决了去中心化BO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BO算法，该算法在$f$的可加结构包含高维因子时，能够达到与最先进BO算法极具竞争力的性能。