arXiv cs.AI· Saksham Kiroriwal, Julius Pfrommer, J\"urgen Beyerer·· 14 小时前AI 评分20
基于 Fisher 信息几何的贝叶斯优化：梯度界与信赖域方法
Bayesian Optimization with Fisher Information Geometry: Gradient Bounds and Trust-Region Methods
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研究从信息几何视角分析贝叶斯优化，通过代理后验映射拉回 Fisher 信息度量，在输入空间得到局部敏感度张量，从而给出可重参数化采集函数梯度的上界，解释了高维 BO 中的梯度消失现象，并为 RAASP 和维度缩放长度尺度等启发式方法提供统一解释。
正文 · 原文
Abstract: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.
| Comments: | Accepted at NeurIPS 2026 (Camera Ready Version) |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Information Theory (cs.IT) |
| Cite as: | arXiv:2609.31107 [cs.LG] |
| (or arXiv:2609.31107v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.31107 arXiv-issued DOI via DataCite |
Submission history
From: Saksham Kiroriwal [view email]
[v1]
Fri, 25 Sep 2026 10:52:30 UTC (2,358 KB)
[v2]
Mon, 26 Oct 2026 16:03:35 UTC (2,165 KB)
来源：arXiv cs.AI · arxiv.org