论文标题
高维贝叶斯通过嵌套的riemannian歧管优化
High-Dimensional Bayesian Optimization via Nested Riemannian Manifolds
论文作者
论文摘要
尽管贝叶斯优化（BO）最近在样本效率必须进行的各种应用中取得了成功，但其性能在以高维参数空间为特征的设置中可能严重损害。在此类问题中保留BO样品效率的一种解决方案是将域知识引入其制定中。在本文中，我们建议利用通常在各种域中出现的非欧几里得搜索空间的几何形状，以学习具有结构的映射，并优化在低维的潜在空间中BO的采集功能。我们的方法建立在Riemannian歧管理论的基础上，具有几何感知的高斯过程，共同学习了嵌套的manifold嵌入和潜在空间中目标函数的表示。我们在几种基准的人造景观中测试了我们的方法，并报告说，它不仅在几种环境中都超过了其他高维BO方法，而且一致地优化了目标函数，而不是几何形式 - unaware bo方法。
Despite the recent success of Bayesian optimization (BO) in a variety of applications where sample efficiency is imperative, its performance may be seriously compromised in settings characterized by high-dimensional parameter spaces. A solution to preserve the sample efficiency of BO in such problems is to introduce domain knowledge into its formulation. In this paper, we propose to exploit the geometry of non-Euclidean search spaces, which often arise in a variety of domains, to learn structure-preserving mappings and optimize the acquisition function of BO in low-dimensional latent spaces. Our approach, built on Riemannian manifolds theory, features geometry-aware Gaussian processes that jointly learn a nested-manifold embedding and a representation of the objective function in the latent space. We test our approach in several benchmark artificial landscapes and report that it not only outperforms other high-dimensional BO approaches in several settings, but consistently optimizes the objective functions, as opposed to geometry-unaware BO methods.
