ALAS: Additive Learnable Alpha-Stable Kernels for Flexible Bayesian Optimization

Abstract:Bayesian Optimization is widely used for expensive black-box optimization, yet its success often depends on choosing a kernel that matches the objective's unknown structure. In this work, we propose ALAS, a flexible Gaussian Process kernel family built from symmetric $\alpha$-stable spectral components. By learning the stability parameter $\alpha$, ALAS adapts its effective smoothness from data, capturing both smooth trends and sharp irregularities. We present two parameterizations: ALAS, a single stationary component with joint spectral modulation, and ALAS-Sep, a separable variant that learns dimension-wise tail behavior to improve robustness on approximately decomposable objectives. Experiments on standard benchmarks and real-world surrogates demonstrate strong and robust performance across diverse settings.

Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2607.18282 [cs.LG]

(or arXiv:2607.18282v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.18282 Focus to learn more arXiv-issued DOI via DataCite

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