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.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Sartor, D., Huber, M. E., Kim, D., & Wycoff, N. (2026). Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds. https://omanscience.com/en/articles/bayesian-optimization-on-function-spaces-via-sparse-rkhs-manifolds
MLA 9
Sartor, Davide, et al. "Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds." https://omanscience.com/en/articles/bayesian-optimization-on-function-spaces-via-sparse-rkhs-manifolds.
Chicago (author–date)
Sartor, Davide, Meghan E. Huber, Donghyun Kim, and Nathan Wycoff. 2026. "Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds." https://omanscience.com/en/articles/bayesian-optimization-on-function-spaces-via-sparse-rkhs-manifolds.
Harvard
Sartor, D., Huber, M. E., Kim, D. and Wycoff, N. (2026) 'Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds', Available at: https://omanscience.com/en/articles/bayesian-optimization-on-function-spaces-via-sparse-rkhs-manifolds.
Vancouver
Sartor D, Huber ME, Kim D, Wycoff N. Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds. https://omanscience.com/en/articles/bayesian-optimization-on-function-spaces-via-sparse-rkhs-manifolds
IEEE
D. Sartor, M. E. Huber, D. Kim, and N. Wycoff, "Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds," https://omanscience.com/en/articles/bayesian-optimization-on-function-spaces-via-sparse-rkhs-manifolds.