基于信息几何的贝叶斯优化方法，提升概率单纯形上的优化效率。
Information Theoretic Bayesian Optimization over the Probability Simplex
- 利用信息几何构建符合概率单纯形结构的核函数与优化器。
- 在混合组件、分类器及机器人控制任务中性能优于传统方法。
- 适合需在概率分布空间高效寻优的机器学习与控制场景。
贝叶斯优化是一种数据高效的黑箱函数优化技术，广泛应用于高成本、噪声干扰的场景。许多实际问题涉及概率分布或混合物的优化，其定义域为概率单纯形——一个非负且和为1的约束非欧几里得空间。本文提出α-GaBO，一种基于信息几何的贝叶斯优化新方法。该方法利用黎曼几何中的度量与联络结构，在单纯形上构造反映其几何特性的Matérn核函数，并设计了一族单参数的几何型采集函数优化器。在基准函数及真实应用（包括成分混合、分类器混合与机器人控制任务）中验证表明，该方法显著优于传统的受限欧氏空间优化方法。
原文摘要 · Abstract (English)
Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions. Many applications involve optimizing probabilities and mixtures which naturally belong to the probability simplex, a constrained non-Euclidean domain defined by non-negative entries summing to one. This paper introduces $α$-GaBO, a novel family of Bayesian optimization algorithms over the probability simplex. Our approach is grounded in information geometry, a branch of Riemannian geometry which endows the simplex with a Riemannian metric and a class of connections. Based on information geometry theory, we construct Matérn kernels that reflect the geometry of the probability simplex, as well as a one-parameter family of geometric optimizers for the acquisition function. We validate our method on benchmark functions and on a variety of real-world applications including mixtures of components, mixtures of classifiers, and a robotic control task, showing its increased performance compared to constrained Euclidean approaches.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。