Bayesian Optimization over Hybrid Spaces
Bayesian Optimization over Hybrid Spaces
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发表时间：
2021-06
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通讯作者：
Aryan Deshwal;Syrine Belakaria;J. Doppa
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作者：
Aryan Deshwal;Syrine Belakaria;J. Doppa
我们考虑通过昂贵的黑盒函数评估优化混合结构（离散和连续输入变量的混合）的问题。这个问题出现在许多实际应用程序中。例如，在通过实验室实验进行的材料设计优化中，离散变量和连续变量分别对应原始元素的存在/不存在及其相对浓度。关键的挑战是如何准确地模拟离散变量和连续变量之间复杂的相互作用。在本文中，我们提出了一种新的方法，称为混合贝叶斯优化（HyBO），利用扩散核，这是自然定义在连续和离散变量。我们开发了一种利用可加性核公式在混合空间上构造扩散核的原则方法，该方法允许以可处理的方式进行所有阶的可加性相互作用。从理论上分析了加性混合核的建模强度，证明了它具有普适性。我们在合成和六个不同的现实世界基准上的实验表明，HyBO明显优于最先进的方法。
We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design optimization via lab experiments, discrete and continuous variables correspond to the presence/absence of primitive elements and their relative concentrations respectively. The key challenge is to accurately model the complex interactions between discrete and continuous variables. In this paper, we propose a novel approach referred as Hybrid Bayesian Optimization (HyBO) by utilizing diffusion kernels, which are naturally defined over continuous and discrete variables. We develop a principled approach for constructing diffusion kernels over hybrid spaces by utilizing the additive kernel formulation, which allows additive interactions of all orders in a tractable manner. We theoretically analyze the modeling strength of additive hybrid kernels and prove that it has the universal approximation property. Our experiments on synthetic and six diverse real-world benchmarks show that HyBO significantly outperforms the state-of-the-art methods.