# Bayesian Optimization Meets Riemannian Manifolds in Robot Learning

arXiv: https://arxiv.org/abs/1910.04998 · HTML: https://mlsanity.com/paper/1910.04998/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2019.

## Built on by (most cited first, 23 of 23)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case](https://mlsanity.com/paper/2208.14960/) (2022)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [Learning Riemannian Manifolds for Geodesic Motion Skills](https://mlsanity.com/paper/2106.04315/) (2021)
- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces](https://mlsanity.com/paper/2301.13088/) (2023)
- [Orientation Probabilistic Movement Primitives on Riemannian Manifolds](https://mlsanity.com/paper/2110.15036/) (2021)
- [Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policies](https://mlsanity.com/paper/2305.10411/) (2023)
- [Reactive Motion Generation on Learned Riemannian Manifolds](https://mlsanity.com/paper/2203.07761/) (2022)
- [Optimization on Manifolds via Graph Gaussian Processes](https://mlsanity.com/paper/2210.10962/) (2022)
- [Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning](https://mlsanity.com/paper/2310.07902/) (2023)
- [Efficient Hyperparameter Optimization for Physics-based Character Animation](https://mlsanity.com/paper/2104.12365/) (2021)
- [Adversarial Attacks on Gaussian Process Bandits](https://mlsanity.com/paper/2110.08449/) (2021)
- [ODBO: Bayesian Optimization with Search Space Prescreening for Directed Protein Evolution](https://mlsanity.com/paper/2205.09548/) (2022)
- [The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circle](https://mlsanity.com/paper/2302.10623/) (2023)
- [Gaussian Process regression over discrete probability measures: on the non-stationarity relation between Euclidean and Wasserstein Squared Exponential Kernels](https://mlsanity.com/paper/2212.01310/) (2022)
- [High-Dimensional Bayesian Optimization via Random Projection of Manifold Subspaces](https://mlsanity.com/paper/2412.16554/) (2024)
- [Causal-PIK: Causality-based Physical Reasoning with a Physics-Informed Kernel](https://mlsanity.com/paper/2505.22861/) (2025)
- [Convergence and Complexity Guarantee for Inexact First-order Riemannian Optimization Algorithms](https://mlsanity.com/paper/2405.03073/) (2024)
- [Riemannian Bilevel Optimization](https://mlsanity.com/paper/2405.15816/) (2024)
- [TamedPUMA: safe and stable imitation learning with geometric fabrics](https://mlsanity.com/paper/2503.17432/) (2025)
- [Information Theoretic Bayesian Optimization over the Probability Simplex](https://mlsanity.com/paper/2603.09793/) (2026)
- [Bayesian Optimization with Fisher Information Geometry: Gradient Bounds and Trust-Region Methods](https://mlsanity.com/paper/2609.31107/) (2026)

## Abstract (arXiv)

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.