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.

本文提出了一种松弛针对 $f$ 的加性结构限制的去中心化贝叶斯优化算法 DuMBO，并针对过度探索问题进行调节，是一种在高维环境下实现成本高昂的优化的良好选择。

去除去中心化无懊悔高维贝叶斯优化中的可加性约束

Relaxing the Additivity Constraints in Decentralized No-Regret  High-Dimensional Bayesian Optimization

Gaussian Process (GP) models are a class of flexible non-parametric models
that have rich representational power. By using a Gaussian process with
additive structure, complex responses can be modelled whilst retaining
interpretability. Previous work showed that additive Gaussian process models
require high-dimensional interaction terms. We propose the orthogonal additive
kernel (OAK), which imposes an orthogonality constraint on the additive
functions, enabling an identifiable, low-dimensional representation of the
functional relationship. We connect the OAK kernel to functional ANOVA
decomposition, and show improved convergence rates for sparse computation
methods. With only a small number of additive low-dimensional terms, we
demonstrate the OAK model achieves similar or better predictive performance
compared to black-box models, while retaining interpretability.

提出了正交加性核（OAK）来代替传统高维交互项的加性高斯过程（GP）模型，能够实现可识别、低维度表示的功能关系，并展示了其在稀疏计算方法中的改进收敛速度和优越的预测性能。

加法高斯过程再审视

Additive Gaussian Processes Revisited

Bayesian Optimisation (BO) is a technique used in optimising a
$D$-dimensional function which is typically expensive to evaluate. While there
have been many successes for BO in low dimensions, scaling it to high
dimensions has been notoriously difficult. Existing literature on the topic are
under very restrictive settings. In this paper, we identify two key challenges
in this endeavour. We tackle these challenges by assuming an additive structure
for the function. This setting is substantially more expressive and contains a
richer class of functions than previous work. We prove that, for additive
functions the regret has only linear dependence on $D$ even though the function
depends on all $D$ dimensions. We also demonstrate several other statistical
and computational benefits in our framework. Via synthetic examples, a
scientific simulation and a face detection problem we demonstrate that our
method outperforms naive BO on additive functions and on several examples where
the function is not additive.

本文提出在具有加性结构的情形下，基于贝叶斯优化算法优化高维函数具有更好的表达性和计算优势，并且证明该方法在加性函数下的误差仅与维数呈线性关系。此外，通过各种实验表明，我们的算法在加性函数和非加性函数情形下的效果显著优于 naive BO。