  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.
