mlsanityData to 7 Oct 2026

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

arXiv 2111.01460 ↗First posted 2 Nov 2021cs.RO cs.LGcited by 24

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Abstract (arXiv)

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.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 20 of its 56 references that are in the map. First posted on arXiv 2 Nov 2021.

Builds on

20 of 56 references.

References · 20

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  2. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
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  4. 2020Efficiently Sampling Functions from Gaussian Process Posteriorscited by 125
  5. 2016Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiationcited by 93
  6. 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
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8 more
  1. 2019Bayesian Optimization Meets Riemannian Manifolds in Robot Learningcited by 23
  2. 2017Bayesian Optimization Using Domain Knowledge on the ATRIAS Bipedcited by 17
  3. 2020High-Dimensional Bayesian Optimization via Nested Riemannian Manifoldscited by 17
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 9; 2023: 6; 2024: 6; 2025: 2; 2026: 1.

24 papers.

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  1. 2022Recent Advances in Bayesian Optimizationcited by 74
  2. 2022Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact casecited by 25
  3. 2023A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifoldcited by 21
  4. 2022Learning Riemannian Stable Dynamical Systems via Diffeomorphismscited by 17
  5. 2023Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spacescited by 15
  6. 2024MANTRA: The Manifold Triangulations Assemblagecited by 12
  7. 2024The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphscited by 10
  8. 2022Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifoldscited by 9
  9. 2023Alignment of Density Maps in Wasserstein Distancecited by 8
  10. 2022Isotropic Gaussian Processes on Finite Spaces of Graphscited by 7
  11. 2023Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifoldscited by 6
  12. 2023Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learningcited by 6
12 more
  1. 2022Optimization on Manifolds via Graph Gaussian Processescited by 4
  2. 2024Sample-efficient Bayesian Optimisation Using Known Invariancescited by 4
  3. 2024Residual Deep Gaussian Processes on Manifoldscited by 2
  4. 2024High-Dimensional Bayesian Optimization via Random Projection of Manifold Subspacescited by 2
  5. 2022Visualizing Riemannian data with Rie-SNEcited by 1
  6. 2024On Probabilistic Pullback Metrics for Latent Hyperbolic Manifoldscited by 1
  7. 2022On power sum kernels on symmetric groupscited by 0
  8. 2022Extrinsic Bayesian Optimizations on Manifoldscited by 0
  9. 2023Non-parametric regression for robot learning on manifoldscited by 0
  10. 2025Efficient Sliced Wasserstein Distance Computation via Adaptive Bayesian Optimizationcited by 0
  11. 2025Taxonomy-aware Dynamic Motion Generation on Hyperbolic Manifoldscited by 0
  12. 2026Information Theoretic Bayesian Optimization over the Probability Simplexcited by 0