2020/10/21 by Noémie Jaquier, Jaquier, Noémie, Leonel Rozo +1 · 2 citations
Computer Science · #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning and Data Classification #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2010.10904
openalex publication_date 2020/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.