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This paper introduces $L^0$ Manifold Optimization (L0MO), a novel approach to Functional Bayesian Optimization that operates within infinite-dimensional Reproducing Kernel Hilbert Spaces by enforcing sparsity in kernel representations. The authors provide a unifying theoretical framework and extensive benchmarks demonstrating that their method outperforms existing state-of-the-art techniques for optimizing function spaces derived from discretized relationships. This work advances the mathematical foundations of hyperparameter tuning and black-box optimization, offering significant potential for improving efficiency in complex machine learning workflows.
Bayesian Optimization on Function Spaces via Sparse RKHS Manifolds
arXiv:2610.07417v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.07417 [stat.ML]
(or arXiv:2610.07417v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.07417 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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