Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

Noémie Jaquier, Leonel Rozo, Sylvain Calinon, Mathias Bürger
Proceedings of the Conference on Robot Learning, PMLR 100:233-246, 2020.

Abstract

Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromised when the parameter space is high-dimensional. A way to tackle this problem is to introduce domain knowledge into the BO framework. We propose to exploit the geometry of non-Euclidean parameter spaces, which often arise in robotics (e.g. orientation, stiffness matrix). Our approach, built on Riemannian manifold theory, allows BO to properly measure similarities in the parameter space through geometry-aware kernel functions and to optimize the acquisition function on the manifold as an unconstrained problem. We test our approach in several benchmark artificial landscapes and using a 7-DOF simulated robot to learn orientation and impedance parameters for manipulation skills.

Cite this Paper

BibTeX
@InProceedings{pmlr-v100-jaquier20a, title = {Bayesian Optimization Meets Riemannian Manifolds in Robot Learning}, author = {Jaquier, No\'emie and Rozo, Leonel and Calinon, Sylvain and B\"urger, Mathias}, booktitle = {Proceedings of the Conference on Robot Learning}, pages = {233--246}, year = {2020}, editor = {Kaelbling, Leslie Pack and Kragic, Danica and Sugiura, Komei}, volume = {100}, series = {Proceedings of Machine Learning Research}, month = {30 Oct--01 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v100/jaquier20a/jaquier20a.pdf}, url = {https://proceedings.mlr.press/v100/jaquier20a.html}, abstract = {Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromised when the parameter space is high-dimensional. A way to tackle this problem is to introduce domain knowledge into the BO framework. We propose to exploit the geometry of non-Euclidean parameter spaces, which often arise in robotics (e.g. orientation, stiffness matrix). Our approach, built on Riemannian manifold theory, allows BO to properly measure similarities in the parameter space through geometry-aware kernel functions and to optimize the acquisition function on the manifold as an unconstrained problem. We test our approach in several benchmark artificial landscapes and using a 7-DOF simulated robot to learn orientation and impedance parameters for manipulation skills.} }
Endnote
%0 Conference Paper %T Bayesian Optimization Meets Riemannian Manifolds in Robot Learning %A Noémie Jaquier %A Leonel Rozo %A Sylvain Calinon %A Mathias Bürger %B Proceedings of the Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2020 %E Leslie Pack Kaelbling %E Danica Kragic %E Komei Sugiura %F pmlr-v100-jaquier20a %I PMLR %P 233--246 %U https://proceedings.mlr.press/v100/jaquier20a.html %V 100 %X Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be seriously compromised when the parameter space is high-dimensional. A way to tackle this problem is to introduce domain knowledge into the BO framework. We propose to exploit the geometry of non-Euclidean parameter spaces, which often arise in robotics (e.g. orientation, stiffness matrix). Our approach, built on Riemannian manifold theory, allows BO to properly measure similarities in the parameter space through geometry-aware kernel functions and to optimize the acquisition function on the manifold as an unconstrained problem. We test our approach in several benchmark artificial landscapes and using a 7-DOF simulated robot to learn orientation and impedance parameters for manipulation skills.
APA
Jaquier, N., Rozo, L., Calinon, S. & Bürger, M.. (2020). Bayesian Optimization Meets Riemannian Manifolds in Robot Learning. Proceedings of the Conference on Robot Learning, in Proceedings of Machine Learning Research 100:233-246 Available from https://proceedings.mlr.press/v100/jaquier20a.html.

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