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

arXiv: https://arxiv.org/abs/2607.18282 · HTML: https://mlsanity.com/paper/2607.18282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 14 of 14)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Non-Stationary Spectral Kernels](https://mlsanity.com/paper/1705.08736/) (2017)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Band-Limited Gaussian Processes: The Sinc Kernel](https://mlsanity.com/paper/1909.07279/) (2019)
- [Scalable L'evy Process Priors for Spectral Kernel Learning](https://mlsanity.com/paper/1802.00530/) (2018)
- [Posterior Inference on Shallow Infinitely Wide Bayesian Neural Networks under Weights with Unbounded Variance](https://mlsanity.com/paper/2305.10664/) (2023)

## Abstract (arXiv)

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 α-stable spectral components. By learning the stability parameter α, 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.