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High-Dimensional Bayesian Optimization via Nested Riemannian Manifolds
Noémie Jaquier · Leonel Rozo

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #1051

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-manifolds 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.

Author Information

Noémie Jaquier (Karlsruhe Institute of Technology)
Leonel Rozo (Bosch Center for Artificial Intelligence)