发表机构
Fraunhofer IOSB; Karlsruhe Institute of Technology (KIT)（弗劳恩霍夫光电、系统技术与图像处理研究所; 卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过信息几何视角分析贝叶斯优化，提出基于拉回Fisher权重的信赖域方法FITR，以解决高维梯度消失问题，并在GP基准上验证了其竞争力。
AI 中文摘要
我们通过信息几何的视角研究贝叶斯优化（BO）。将Fisher信息度量通过代理后验映射拉回，得到输入空间上的局部灵敏度张量，这导致可重参数化采集函数梯度的上界。这一观点解释了高维BO中的梯度消失行为，并为RAASP和维度缩放长度尺度等启发式方法提供了统一的解释。基于此分析，我们提出了FITR，一种基于信赖域的BO方法，该方法用局部拉回Fisher权重替代基于长度尺度的缩放。FITR不限于具有显式长度尺度的GP核。在使用SE核的GP基准测试中，实验表明FITR具有竞争力的性能。所提出的方法也容易推广到非各向同性的代理模型，尽管在该设置中收益更依赖于任务。
英文摘要
We study Bayesian optimization (BO) through the lens of information geometry. Pulling back the Fisher information metric through the surrogate posterior map yields a local sensitivity tensor on the input space, which leads to an upper bound on the gradient of reparameterizable acquisition functions. This view explains vanishing-gradient behavior in high-dimensional BO and provides a common interpretation of heuristics such as RAASP and dimension-scaled lengthscales. Building on this analysis, we propose FITR, a trust-region-based BO method that replaces lengthscale-based scaling by local pullback-Fisher weights. FITR is not restricted to GP kernels with explicit lengthscales. On GP benchmarks with an SE kernel, experiments show competitive performance using FITR. The proposed method also easily generalizes to non-isotropic surrogates, although the gains are more task-dependent in that setting.
CommentsAccepted at NeurIPS 2026
