PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees
Jonas Rothfuss, Vincent Fortuin, Martin Josifoski, Andreas Krause
Abstract
Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well.When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.
BibTeX
@InProceedings{pmlr-v139-rothfuss21a,
title = {PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees},
author = {Rothfuss, Jonas and Fortuin, Vincent and Josifoski, Martin and Krause, Andreas},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {9116--9126},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/rothfuss21a/rothfuss21a.pdf},
url = {https://proceedings.mlr.press/v139/rothfuss21a.html},
abstract = {Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well.When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.}
}