Geometry-aware Bayesian Optimization in Robotics using Riemannian Matérn Kernels

Noémie Jaquier, Viacheslav Borovitskiy, Andrei Smolensky, Alexander Terenin, Tamim Asfour, Leonel Rozo
Proceedings of the 5th Conference on Robot Learning, PMLR 164:794-805, 2022.

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 Matérn 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v164-jaquier22a, title = {Geometry-aware Bayesian Optimization in Robotics using Riemannian Matérn Kernels}, author = {Jaquier, No\'emie and Borovitskiy, Viacheslav and Smolensky, Andrei and Terenin, Alexander and Asfour, Tamim and Rozo, Leonel}, booktitle = {Proceedings of the 5th Conference on Robot Learning}, pages = {794--805}, year = {2022}, editor = {Faust, Aleksandra and Hsu, David and Neumann, Gerhard}, volume = {164}, series = {Proceedings of Machine Learning Research}, month = {08--11 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v164/jaquier22a/jaquier22a.pdf}, url = {https://proceedings.mlr.press/v164/jaquier22a.html}, 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 Matérn 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.} }
Endnote
%0 Conference Paper %T Geometry-aware Bayesian Optimization in Robotics using Riemannian Matérn Kernels %A Noémie Jaquier %A Viacheslav Borovitskiy %A Andrei Smolensky %A Alexander Terenin %A Tamim Asfour %A Leonel Rozo %B Proceedings of the 5th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2022 %E Aleksandra Faust %E David Hsu %E Gerhard Neumann %F pmlr-v164-jaquier22a %I PMLR %P 794--805 %U https://proceedings.mlr.press/v164/jaquier22a.html %V 164 %X 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 Matérn 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.
APA
Jaquier, N., Borovitskiy, V., Smolensky, A., Terenin, A., Asfour, T. & Rozo, L.. (2022). Geometry-aware Bayesian Optimization in Robotics using Riemannian Matérn Kernels. Proceedings of the 5th Conference on Robot Learning, in Proceedings of Machine Learning Research 164:794-805 Available from https://proceedings.mlr.press/v164/jaquier22a.html.

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