论文标题

内核和采集功能的组成,用于高维贝叶斯优化

Composition of kernel and acquisition functions for High Dimensional Bayesian Optimization

论文作者

Candelieri, Antonio, Giordani, Ilaria, Perego, Riccardo, Archetti, Francesco

论文摘要

贝叶斯优化已成为黑匣子全球优化,昂贵且可能是嘈杂功能的参考方法。贝叶斯运算式化学习了一个有关目标函数(通常是高斯过程)的概率模型,并根据其平均值和方差构建,这是一种采集函数,其优化器可产生新的评估点,从而更新了概率替代模型。尽管具有样品效率,但随着问题的尺寸,贝叶斯优化效果并不能很好地扩展。获取函数的优化受到了较少的关注,因为与OBJEC-TIVE功能的评估相比,通常认为其计算成本可以忽略不计。多个极值通常会抑制其有效的优化,尤其是在高射线范围的问题中。在本文中,我们利用目标函数的加法性来映射贝叶斯优化在较低维子空间中的内核和采集函数。此AP洞穴使概率替代模型的学习/更新更有效,并允许对采集功能进行有效的优化。实验结果是用于现实生活中的实验结果,即对城市水分配系统中的泵的控制。

Bayesian Optimization has become the reference method for the global optimization of black box, expensive and possibly noisy functions. Bayesian Op-timization learns a probabilistic model about the objective function, usually a Gaussian Process, and builds, depending on its mean and variance, an acquisition function whose optimizer yields the new evaluation point, leading to update the probabilistic surrogate model. Despite its sample efficiency, Bayesian Optimiza-tion does not scale well with the dimensions of the problem. The optimization of the acquisition function has received less attention because its computational cost is usually considered negligible compared to that of the evaluation of the objec-tive function. Its efficient optimization is often inhibited, particularly in high di-mensional problems, by multiple extrema. In this paper we leverage the addition-ality of the objective function into mapping both the kernel and the acquisition function of the Bayesian Optimization in lower dimensional subspaces. This ap-proach makes more efficient the learning/updating of the probabilistic surrogate model and allows an efficient optimization of the acquisition function. Experi-mental results are presented for real-life application, that is the control of pumps in urban water distribution systems.

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