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Bayesian optimization is a data-efficient technique which can be used forcontrol parameter tuning, parametric policy adaptation, and structure design inrobotics. Many of these problems require optimization of functions defined onnon-Euclidean domains like spheres, rotation groups, or spaces ofpositive-definite matrices. To do so, one must place a Gaussian process prior,or equivalently define a kernel, on the space of interest. Effective kernelstypically reflect the geometry of the spaces they are defined on, but designingthem is generally non-trivial. Recent work on the Riemannian Mat\'ern kernels,based on stochastic partial differential equations and spectral theory of theLaplace-Beltrami operator, offers promising avenues towards constructing suchgeometry-aware kernels. In this paper, we study techniques for implementingthese kernels on manifolds of interest in robotics, demonstrate theirperformance on a set of artificial benchmark functions, and illustrategeometry-aware Bayesian optimization for a variety of robotic applications,covering orientation control, manipulability optimization, and motion planning,while showing its improved performance.

Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat\'ern Kernels