GaBO

This repository contains the source code to perform Geometry-aware Bayesian Optimization (GaBO) on Riemannian manifolds.

Important note:

GaBOflow depends on GPflow and GPflowOpt. However, GPflowOpt has not been updated since a while and is not compatible with the latest version of GPflow. Therefore, we created GaBOtorch, which is based on PyTorch and contains the source code of GaBO. New examples and updates will be available in GaBOtorch.

Requirements

This code was tested with Python 3.5 and 3.6. It requires the following packages:

• Numpy
• Scipy
• Matplotlib
• Tensorflow
• GPflow 0.5
• GPflowOpt
• Pymanopt

Installation

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

pip install numpy scipy matplotlib pymanopt

To install GPflowOpt and its dependencies (e.g. tensorflow and gpflow) follow the instructions given in GPflowOpt repository.

Finally, from the GaBOflow folder, run

pip install -e .

Examples

The following examples are available in GaBOflow:

Kernels

Sphere manifold
sphere_kernels	This example shows the use of different kernels for the hypershere manifold S^n , used for Gaussian process regression.
sphere_gaussian_kernel_parameters	This example shows the experimental selection of parameters for the Sphere Gaussian kernel.

SPD manifold
spd_kernels	This example shows the use of different kernels for the SPD manifold, used for Gaussian process regression
spd_gaussian_kernel_parameters	This example shows the experimental selection of parameters for the SPD Affine-Invariant Gaussian kernel.

BO on the sphere

Benchmark examples
bo_sphere_ackley_manifold	This example shows the use of Geometry-aware Bayesian optimization (GaBO) on the sphere S2 to optimize the Ackley function.
bo_sphere_ackley_eucl	This example shows the use of Euclidean Bayesian optimization on the sphere S2 to optimize the Ackley function.

Constrained benchmark examples
bo_sphere_ackley_manifold_constrained	This example shows the use of Geometry-aware Bayesian optimization (GaBO) on the sphere S2 to optimize the Ackley function. In this example, the search domain is bounded and represents a subspace of the manifold.
bo_sphere_ackley_eucl_constrained	This example shows the use of Euclidean Bayesian optimization on the sphere S2 to optimize the Ackley function. In this example, the search domain is bounded and represents a subspace of the manifold.

BO on the SPD manifold

Benchmark examples
bo_spd_ackley_manifold	This example shows the use of Geometry-aware Bayesian optimization (GaBO) on the SPD manifold S2_++ to optimize the Ackley function.
bo_spd_ackley_chol	This example shows the use of Cholesky Bayesian optimization on the SPD manifold S2_++ to optimize the Ackley function. An Euclidean BO is applied on the Cholesky decomposition of the SPD matrices.
bo_spd_ackley_eucl	This example shows the use of Euclidean Bayesian optimization on the SPD manifold S2_++ to optimize the Ackley function.

References

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

[1] N. Jaquier, L. Rozo, S. Calinon and M. Bürger (2019). Bayesian Optimization meets Riemannian Manifolds in Robot Learning. In Conference on Robot Learning (CoRL).

@inproceedings{Jaquier19GaBO,
	author="Jaquier, N and Rozo, L. and Calinon, S. and B\"urger, M.", 
	title="Bayesian Optimization meets Riemannian Manifolds in Robot Learning",
	booktitle="In Conference on Robot Learning (CoRL)",
	year="2019",
	month="October",
	address="Osaka, Japan",
	pages=""
}