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

• URL: http://arxiv.org/abs/2111.01460v2
• Date: Sat, 18 Mar 2023 02:19:29 GMT
• Title: Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat\'ern Kernels
• Authors: No\'emie Jaquier, Viacheslav Borovitskiy, Andrei Smolensky, Alexander Terenin, Tamim Asfour, Leonel Rozo
• Abstract summary: We show how to implement geometry-aware kernels for Bayesian optimization. This technique can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics.
• Score: 64.62221198500467
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian optimization is a data-efficient technique which can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics. Many of these problems require optimization of functions defined on non-Euclidean domains like spheres, rotation groups, or spaces of positive-definite matrices. To do so, one must place a Gaussian process prior, or equivalently define a kernel, on the space of interest. Effective kernels typically reflect the geometry of the spaces they are defined on, but designing them is generally non-trivial. Recent work on the Riemannian Mat\'ern kernels, based on stochastic partial differential equations and spectral theory of the Laplace-Beltrami operator, offers promising avenues towards constructing such geometry-aware kernels. In this paper, we study techniques for implementing these kernels on manifolds of interest in robotics, demonstrate their performance on a set of artificial benchmark functions, and illustrate geometry-aware Bayesian optimization for a variety of robotic applications, covering orientation control, manipulability optimization, and motion planning, while showing its improved performance.

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