Safe Bayesian Optimization for Uncertain Correlations in Linear Models of Coregionalization

Reference implementation for “Safe Bayesian Optimization for Uncertain Correlations Matrices in Linear Models of Co-Regionalization” by Jannis O. Lübsen and Annika Eichler. The code compares intrinsic and linear models of coregionalization (ICM/LMC) for safe multi-task Bayesian optimization under uncertain inter-task correlations.

Read the preprint on arXiv

Repository layout

Path	Purpose
rkhs_opt.py	Multi-task safe Bayesian optimization with an LMC or ICM model
rkhs_opt_ST.py	Single-task comparison experiment
bo/	Safe Bayesian optimization loop and acquisition logic
model/, cov/	LMC/ICM GP models, task covariance modules, and kernels
utils/	Synthetic RKHS functions, robust bounds, MCMC, and optimization helpers
data/x_init_dim4/	Reproducible initial conditions for the published seeds
data/RKHS/, data/RKHS_ST/	Serialized multi-task and single-task results
plot_scripts/generate_plots.ipynb	Recreates the paper figures
plots/	Publication figures included with the repository

Requirements

The code was developed with Python 3.12.8 on Ubuntu 24.04.2 LTS.

python3.12 -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install -r requirements.txt

Reproducing the experiments

Run all commands from the repository root.

Multi-task LMC/ICM experiment

Select the model in rkhs_opt.py by setting function_name to "LMC" or "ICM", then run:

python rkhs_opt.py

The default is the LMC experiment. Results are written to data/RKHS/<model>_dim4_3.obj.

Single-task comparison

python rkhs_opt_ST.py

Results are written to data/RKHS_ST/Single_Task_dim4_3.obj.

Both runners execute 100 optimization iterations for each of 20 predefined random seeds. Missing initial-condition files are generated automatically. Adjust seeds, nruns, and the model configuration near the top of each script for shorter exploratory runs.

Figures

Open the plotting notebook and run all cells to recreate the manuscript figures from the bundled result files:

python -m pip install jupyterlab
python -m jupyter lab plot_scripts/generate_plots.ipynb

Citation

@article{lubsen2026safe,
  title   = {Safe Bayesian Optimization for Uncertain Correlations Matrices in Linear Models of Co-Regionalization},
  author  = {L\"{u}bsen, Jannis O. and Eichler, Annika},
  journal = {arXiv preprint arXiv:2605.13302},
  year    = {2026},
  url     = {https://arxiv.org/abs/2605.13302}
}

License

This project is licensed under the MIT License. See LICENSE.