发表机构
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对函数空间上的贝叶斯优化问题，提出L0MO方法，在RKHS中搜索核稀疏表示的函数并优化核位置与系数，实验证明其在多个基准上性能优越。
AI 中文摘要
贝叶斯优化（BO）已成为最小化向量输入黑箱函数的成熟方法。然而，该参数向量往往源于对固有函数关系的离散化。近期多篇文章考虑了函数贝叶斯优化（FBO）设置，其中待优化变量不属于有限维向量空间，而是无限维函数空间。在本工作中，我们提出$L^0$流形优化（L0MO），一种简单的FBO方法，它搜索再生核希尔伯特空间（RKHS）中由核函数稀疏表示的函数子集，同时优化核位置及其系数。我们详细讨论了所提方法与现有方法之间的关系，为审视先前工作提供了统一视角。为评估所提方法相较于最先进技术的性能，我们进行了广泛的计算研究，并在此过程中开发了一组新颖的基准测试函数，将标准有限维函数移植到无限维域。实验表明，总体而言，所提方法在广泛的测试基准上实现了优越性能。
英文摘要
Bayesian Optimization (BO) has become an established methodology for minimizing black-box functions of a vector input. Often, however, this parameter vector arises from the discretization of an inherently functional relationship. Several recent articles have considered the Functional Bayesian Optimization (FBO) setting, in which the variable to be optimized is not a member of a finite dimensional vector space, but rather an infinite dimensional function space. In this work, we propose $L^0$ Manifold Optimization (L0MO), a simple approach to FBO which searches the subset of a Reproducing Kernel Hilbert Space (RKHS) consisting of functions with a sparse representation in the kernel functions, optimizing both the kernel locations and their coefficients. We discuss in detail the relationship between our method and existing ones, providing a unifying lens through which to view prior works. To assess our method against the state of the art, we conduct an extensive computational study, and along the way develop a novel set of benchmark test functions which port standard finite-dimensional ones to the infinite dimensional domain. Our experiments demonstrate that, on balance, the proposed method achieves superior performance across a wide range of test benchmarks.
