Extrinsic Bayesian Optimization on Manifolds

We propose an extrinsic Bayesian optimization (eBO) framework for general problems on manifolds. algorithms build a surrogate of the objective function by employing Gaussian processes and utilizing uncertainty in that deriving acquisition function. This represents probability improvement based kernel process, which guides search process. The critical challenge designing manifolds lies difficulty constructing valid covariance kernels Our approach is to employ first embedding manifold onto some higher dimensional Euclidean space via equivariant embeddings then image after embedding. leads efficient scalable over complex Simulation study real data analyses are carried out demonstrate utilities our eBO applying various such as sphere, Grassmannian, positive definite matrices.