AI 中文总结
针对标准贝叶斯优化对异常值敏感的问题，提出q-ED-BO方法，采用q-指数分布代理模型，在保持闭式解的同时增强鲁棒性，实验证明其在噪声环境下性能优于现有基线。
AI 中文摘要
贝叶斯优化（BO）是一种广泛用于优化昂贵黑箱目标函数的框架，但标准BO方法通常使用高斯过程（GP）代理模型，其高斯假设对异常值和重尾噪声敏感。我们提出了q-ED-BO，一种鲁棒BO方法，其代理模型遵循单变量q-指数（q-ED）分布，保留了GP-BO的闭式后验均值和方差，同时形状参数q控制尾部行为，在q=2时恢复GP，随着q减小，尾部变重，置信界变宽。这种可处理性产生了具有亚线性遗憾的闭式q-上置信界（q-UCB），以及精确的闭式q-期望改进（q-EI），将EI推广到重尾预测，在q=2时恢复经典EI。在具有脉冲异常值的波束成形器和自适应滤波器调谐实验表明，q-ED-BO在干净数据上匹配或超过现有基线，在数据损坏下，输出信干噪比（SINR）比最强基线提高约0.7 dB，失配减少提高1.1至1.2 dB。
英文摘要
Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box objectives, but standard BO methods often use Gaussian process (GP) surrogates whose Gaussian assumption is sensitive to outliers and heavy-tailed noise. We introduce q-ED-BO, a robust BO method whose surrogate follows a univariate q-exponential (q-ED) distribution, preserving GP-BO's closed-form posterior mean and variance while a shape parameter q controls the tail behavior, recovering the GP at q = 2 and growing heavier-tailed with wider confidence bounds as q decreases. This tractability yields a closed-form q-upper confidence bound (q-UCB) with sublinear regret, and an exact closed-form q-expected improvement (q-EI) that generalizes EI to the heavy-tailed predictive, recovering classical EI at q = 2. Experiments on beamformer and adaptive filter tuning with impulsive outliers show that q-ED-BO matches or exceeds existing baselines on clean data, and under corruption, improves the strongest baseline by approximately 0.7 dB in output SINR and 1.1 to 1.2 dB in misalignment reduction.
CommentsSubmitted to ICASSP 2027
