This paper describes a general-purpose extension of max-value entropy search,
a popular approach for Bayesian Optimisation (BO). A novel approximation is
proposed for the information gain -- an information-theoretic quantity central
to solving a range of BO problems, including noisy, multi-fidelity and batch
optimisations across both continuous and highly-structured discrete spaces.
Previously, these problems have been tackled separately within
information-theoretic BO, each requiring a different sophisticated
approximation scheme, except for batch BO, for which no
computationally-lightweight information-theoretic approach has previously been
proposed. GIBBON (General-purpose Information-Based Bayesian OptimisatioN)
provides a single principled framework suitable for all the above,
out-performing existing approaches whilst incurring substantially lower
computational overheads. In addition, GIBBON does not require the problem's
search space to be Euclidean and so is the first high-performance yet
computationally light-weight acquisition function that supports batch BO over
general highly structured input spaces like molecular search and gene design.
Moreover, our principled derivation of GIBBON yields a natural interpretation
of a popular batch BO heuristic based on determinantal point processes.
Finally, we analyse GIBBON across a suite of synthetic benchmark tasks, a
molecular search loop, and as part of a challenging batch multi-fidelity
framework for problems with controllable experimental noise.

本文介绍了 GIBBON 作为一种通用的贝叶斯优化方法，它提供了一种新的信息增益近似方法，可解决包括噪声、多保真度和批量优化在内的一系列 BO 问题，并且是目前支持非欧氏空间的高性能但计算量轻的批量 BO 获取函数，同时在各种综合测试中表现优异。

GIBBON: 通用信息为基础的贝叶斯优化

GIBBON: General-purpose Information-Based Bayesian OptimisatioN

In this work, we investigate black-box optimization from the perspective of
frequentist kernel methods. We propose a novel batch optimization algorithm,
which jointly maximizes the acquisition function and select points from a whole
batch in a holistic way. Theoretically, we derive regret bounds for both the
noise-free and perturbation settings irrespective of the choice of kernel.
Moreover, we analyze the property of the adversarial regret that is required by
a robust initialization for Bayesian Optimization (BO). We prove that the
adversarial regret bounds decrease with the decrease of covering radius, which
provides a criterion for generating a point set to minimize the bound. We then
propose fast searching algorithms to generate a point set with a small covering
radius for the robust initialization. Experimental results on both synthetic
benchmark problems and real-world problems show the effectiveness of the
proposed algorithms.

本研究从基于频率的核方法角度探讨黑盒优化，提出了一种新的批处理优化算法，可以同时优化收购函数并从整个批次中选择点，理论上为无噪声和扰动设置导出了遗憾界限，同时分析了对贝叶斯优化的鲁棒初始化所需的敌对遗憾的性质。