自适应学习稳定参数，让贝叶斯优化更灵活地捕捉复杂函数形态。
ALAS: Additive Learnable Alpha-Stable Kernels for Flexible Bayesian Optimization
- 通过可学习的α-稳定谱成分构建核函数，动态调整平滑性。
- 在标准测试与真实代理模型上均表现稳健，优于传统核函数。
- 适合处理具有尖锐不规则性的高维黑箱优化问题。
贝叶斯优化广泛用于昂贵的黑箱优化，但其性能常依赖于与目标函数结构匹配的核函数。本文提出ALAS，一种由对称α-稳定谱成分构成的灵活高斯过程核族。通过学习稳定性参数α，ALAS能从数据中自适应调整有效平滑度，同时捕捉平滑趋势与尖锐不规则性。我们提出了两种参数化：ALAS（单个平稳分量，联合谱调制）和ALAS-Sep（可分离变体，学习各维度尾部行为），以提升在近似可分解目标上的鲁棒性。在标准基准和真实世界代理模型上的实验表明，ALAS在多种场景下均表现出色且稳健。
原文摘要 · Abstract (English)
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.
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