  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.
