arXiv：cs.LG· Davide Sartor, Meghan E. Huber, Donghyun Kim, Nathan Wycoff·· 4 小时前AI 评分28
L0MO：基于稀疏 RKHS 流形的函数空间贝叶斯优化
Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds
AI 导读
研究者提出 L0MO，一种在 RKHS 中仅由稀疏核函数表示构成子集上进行搜索的函数空间贝叶斯优化（FBO）方法，同时优化核位置与系数。该方法统一了既有 FBO 工作的视角，并配套构建了将标准有限维测试函数迁移到无限维域的新基准。实验显示其在广泛测试基准上总体性能优于现有方法。
正文
Abstract: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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.07417 [stat.ML] |
| (or arXiv:2610.07417v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.07417 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Davide Sartor [view email]
[v1]
Mon, 5 Oct 2026 21:28:26 UTC (1,002 KB)
来源：arXiv：cs.LG · arxiv.org