Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds
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 L0 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.
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BibTeX
@misc{sartor2026bayesian,
title = {{Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds}},
author = {Davide Sartor and Meghan E. Huber and Donghyun Kim and Nathan Wycoff},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07417},
eprint = {2610.07417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07417},
}
RIS
TY - UNPB
TI - Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds
AU - Davide Sartor
AU - Meghan E. Huber
AU - Donghyun Kim
AU - Nathan Wycoff
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07417
UR - https://arxiv.org/abs/2610.07417
AB - 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.
ER -