This repository contains the source code to perform Geometry-aware Bayesian Optimization with Riemannian Matérn kernels.

This code runs with Python>=3.7. It requires the following packages:

• numpy
• scipy
• matplotlib
• pymanopt
• torch
• gpytorch
• botorch
• sympy

To install it, first clone the repository and install the related packages, as explained below.

pip install -r requirements.txt

The following example are available:

These examples show the computation of various Riemannian and Euclidean kernels on different manifolds.

• kernels_euclidean.py
• kernels_sphere.py
• kernels_spd.py
• kernels_hyperbolic.py
• kernels_so.py
• kernels_torus.py

These examples show the use of Bayesian optimization on various manifolds to optimize benchmark functions. For each example, the type of BO, the type of kernel and acquisition function, the dimension of the manifold, and the benchmark function can be selected by the user.

• bo_manifold_sphere.py
• bo_manifold_spd.py
• bo_manifold_hyperbolic.py
• bo_manifold_so.py
• bo_manifold_torus.py

If you found this code useful, we would be grateful if you cite the following reference:

[ 1 ] N. Jaquier*, V. Borovitskiy*, A. Smolensky, A. Terenin, T. Asfour, and L. Rozo (2021). Geometry-aware Bayesian Optimization in Robotics using Riemannian Matérn Kernels. In Conference on Robot Learning (CoRL).

You can find the video accompanying the paper here.

@inproceedings{Jaquier21MaternGaBO,
	author="Jaquier, N. and Borovitskiy, V. and Smolensky, A. and Terenin, A. and Asfour, T. and Rozo, L.", 
	title="Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat\'ern Kernels",
	booktitle="Conference on Robot Learning (CoRL)",
	year="2021",
	pages=""
}