论文标题
高维贝叶斯通过树结构添加剂模型优化
High-Dimensional Bayesian Optimization via Tree-Structured Additive Models
论文作者
论文摘要
贝叶斯优化（BO）在解决昂贵的低维黑盒优化问题方面表现出了巨大的成功。许多感兴趣的优化问题是高维的，而将BO扩展到此类环境仍然是一个重要的挑战。在本文中，我们考虑了一般的加性模型，其中具有变量重叠子集的低维函数构成了高维目标函数的建模。我们的目标是降低所需的计算资源，并通过降低模型复杂性，同时保留现有方法的样本效率来促进更快的模型学习。具体而言，我们将基本依赖图限制为树结构，以促进采集功能的结构学习和优化。对于前者，我们提出了一种基于吉布斯采样和突变的混合图学习算法。此外，我们提出了一种基于缩放的新型算法，该算法允许在连续域的情况下更有效地采用广义的加性模型。我们通过一系列有关合成功能和现实数据集的实验来证明和讨论方法的功效。
Bayesian Optimization (BO) has shown significant success in tackling expensive low-dimensional black-box optimization problems. Many optimization problems of interest are high-dimensional, and scaling BO to such settings remains an important challenge. In this paper, we consider generalized additive models in which low-dimensional functions with overlapping subsets of variables are composed to model a high-dimensional target function. Our goal is to lower the computational resources required and facilitate faster model learning by reducing the model complexity while retaining the sample-efficiency of existing methods. Specifically, we constrain the underlying dependency graphs to tree structures in order to facilitate both the structure learning and optimization of the acquisition function. For the former, we propose a hybrid graph learning algorithm based on Gibbs sampling and mutation. In addition, we propose a novel zooming-based algorithm that permits generalized additive models to be employed more efficiently in the case of continuous domains. We demonstrate and discuss the efficacy of our approach via a range of experiments on synthetic functions and real-world datasets.
