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）通常用于优化一个带有噪声且评估代价高昂的未知函数 $f$，其核心思想是在每一步优化中最大化某个采集函数。尽管理论上渐进最优的BO算法在低维函数优化中表现出色，但将其扩展到高维空间仍是一个开放性问题，现有方法通常假设 $f$ 具有可加性结构。然而，这种假设往往伴随额外的限制性约束，削弱了算法的适用范围。本文有两项主要贡献：(i) 在不削弱采集函数最大化保证的前提下，放宽了对 $f$ 可加性结构的限制性假设；(ii) 解决了去中心化BO算法的过度探索问题。为此，我们提出DuMBO算法——一种渐进最优的去中心化BO算法，在与最先进的BO算法对比中展现出极具竞争力的性能，尤其当 $f$ 的可加性结构包含高维因子时表现突出。