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PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees

This repository provides source code corresponding the paper PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees. In particular, the meta_learn package holds implementations of the following meta-learning algorithms:


Additionaly, an implementation of MAML as well as Neural Processes (NPs), based on third party code is comprised in the the meta_learn package.

The experiments directory holds code for synthetic task-environments and provides the necessary scripts to reproduce the experimental results reported in the paper.

Compute framework

The code in this repository builds on PyTorch. A similar implementation of PACOH-GP in JAX can be found in the pacoh-jax repository of Nicolas Emmenegger.


To install the minimal dependencies needed to use the meta-learning algorithms, run in the main directory of this repository

pip install .

For full support of all scripts in the repository, for instance to reproduce the experiments, further dependencies need to be installed. To do so, please run in the main directory of this repository

pip install -r requirements.txt


The following code snippet demonstrates the core functionality of the meta-learners provided in this repository. In addition, we refer to and demo.ipynb for a code example.

""" A) generate meta-training and meta-testing data """
from experiments.data_sim import SinusoidDataset
task_environment = SinusoidDataset()
meta_train_data = task_environment.generate_meta_train_data(n_tasks=20, n_samples=5)
meta_test_data = task_environment.generate_meta_test_data(n_tasks=20, n_samples_context=5, n_samples_test=50)

""" B) Meta-Learning with PACOH-MAP """
from meta_learn import GPRegressionMetaLearned
meta_gp = GPRegressionMetaLearned(meta_train_data, weight_decay=0.2)
meta_gp.meta_fit(meta_test_data, log_period=1000)

"""  C) Meta-Testing with PACOH-MAP """
x_context, y_context, x_test, y_test = meta_test_data[0]

# target training in (x_ontext, y_context) & predictions for x_test
pred_mean, pred_std = meta_gp.predict(x_context, y_context, x_test)

# confidence intervals predictions in x_test 
ucb, lcb = meta_gp.confidence_intervals(x_context, y_context, x_test, confidence=0.9)

# compute evaluation metrics on one target task
log_likelihood, rmse, calib_error = meta_gp.eval(x_context, y_context, x_test, y_test)

# compute evaluation metrics for multiple tasks / test datasets
log_likelihood, rmse, calib_error = meta_gp.eval_datasets(meta_test_data)

Reproducing the experiments

Below we point to the experiment scripts that were used to generate the results reported in the paper. Note that all of the experiment scripts use multiprocessing and were written for machines / high-performance clusters designed heavy workloads. Please take this into consideration, before launching any of the experiment scripts.

Meta-overfitting experiments

To run the experiments:

python experiments/meta_overfitting_v2/
python experiments/meta_overfitting_v2/

To generate the plots in the paper:

python experiments/meta_overfitting_v2/

Hyper-Parameter Search for PACOH and MLAP

The following command will launch multiple hyper-parameter tuning session with ray tune, based on hyperopt.

python experiments/hyperparam_search/

Reproducing the baselines

python experiments/baselines/


Meta-learning Gaussian process (GP) priors via PAC-Bayes bounds







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