Description

This repository contains the processing code used in the experiments of the paper "Heteroscedastic Gaussian Processes and Random Features: Scalable Motion Primitives with Guarantees" (Edoardo Caldarelli, Antoine Chatalic, Adrià Colomé, Lorenzo Rosasco, Carme Torras), published in the 7th Conference on Robot Learning (CoRL), Atlanta, GA, USA, 2023.

Sources

The data of the trajectories are taken from [https://codeocean.com/capsule/9688212/tree/v2]. The implementation of the heteroscedastic Gaussian process (HGP) with random features (RFs) is based on the gpflow Python package [https://www.gpflow.org/].

Installation

The required packages can be installed by running the following command:

pip install -r requirements.txt

Offline processing of trajectories

In order to process the trajectories of the three experiments offline, run the script process_trajs.py. In this case, all the human demonstrations are merged and form a unique dataset, for each task. The results can be found in the experiments' directories, e.g., proof-of-concept.

Online processing of trajectories

In order to process the trajectories online, run the script process_trajs_online.py. In this case, the posterior distribution of the HGP is subject to low-rank updates as soon as a new trajectory is processed. The experiments are run with RFs and with the Nyström method. Note that the exact GP needs to be fitted to the data via process_trajs.py prior to running this script.

Utilitites

The script MLHGP_RFFs.py contains the implementation of the EM algorithm used for training the RF-HGP and the exact HGP. The script MLHGP_variational.py contains the EM algorithm adapted to the sparse variationl Gaussian process (SVGP) by Hensman et al. (2013). The script gp_utilities.py contains the implementation of the RF-based kernel, as well as the Nyström approximation used in our online processing experiments.

Plotting code

This repository further contains the code that can be used to generate our plots. This code can be found in plot_metrics_with_rate.py (plotting the oracle experiments and the theoretical rates), plot_metrics_online.py, plotting the results of the incremental learning experiments, and plot_metrics_w_variational.py, plotting the results of our heuristic experiments.