AI 中文总结
研究针对贝叶斯优化中核选择依赖目标未知结构的问题，提出ALAS核族，通过学习稳定性参数α适应数据，给出两种参数化，实验表明其在多样设置下性能强大且稳健。
AI 中文摘要
贝叶斯优化广泛用于昂贵的黑箱优化，但其成功通常依赖于选择与目标未知结构匹配的核。本文提出ALAS，一个由对称α-稳定谱分量构建的灵活高斯过程核族。通过学习稳定性参数α，ALAS从数据中适应其有效平滑度，捕捉平滑趋势和尖锐不规则性。给出两种参数化：ALAS（具有联合谱调制的单个平稳分量）和ALAS-Sep（一种可分离变体）。在标准基准和实际替代物上的实验证明了在不同设置下的强大且稳健的性能。
英文摘要
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.
