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.

@inproceedings{rothfuss21pacoh,
	author = {Jonas Rothfuss and Vincent Fortuin and Martin Josifoski and Andreas Krause},
	booktitle = {Proc. International Conference on Machine Learning (ICML)},
	eprint = {2002.05551},
	month = {July},
	title = {PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees},
	year = {2021}}