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Meta-learning can successfully acquire useful inductive biases from data, especially when a large number of meta-tasks are available. Yet, its generalization properties to unseen tasks are poorly understood. Particularly if the number of meta-tasks is small, this raises concerns for potential overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning with unbounded loss functions and Bayesian base learners. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-regularization. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes as base learners, the resulting approach consistently outperforms several popular meta-learning methods, both in terms of predictive accuracy and the quality of its uncertainty estimates.
PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees J. Rothfuss, V. Fortuin, A. KrauseArXiv, 2020
Bibtex Entry:
	Archiveprefix = {arXiv},
	Author = {Jonas Rothfuss and Vincent Fortuin and Andreas Krause},
	Eprint = {2002.05551},
	Month = {February},
	Primaryclass = {stat.ML},
	Publisher = {ArXiv},
	Title = {PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees},
	Year = {2020}}