Fast-Rate PAC-Bayesian Generalization Bounds for Meta-Learning

Jiechao Guan, Zhiwu Lu
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:7930-7948, 2022.

Abstract

PAC-Bayesian error bounds provide a theoretical guarantee on the generalization abilities of meta-learning from training tasks to unseen tasks. However, it is still unclear how tight PAC-Bayesian bounds we can achieve for meta-learning. In this work, we propose a general PAC-Bayesian framework to cope with single-task learning and meta-learning uniformly. With this framework, we generalize the two tightest PAC-Bayesian bounds (i.e., kl-bound and Catoni-bound) from single-task learning to standard meta-learning, resulting in fast convergence rates for PAC-Bayesian meta-learners. By minimizing the derived two bounds, we develop two meta-learning algorithms for classification problems with deep neural networks. For regression problems, by setting Gibbs optimal posterior for each training task, we obtain the closed-form formula of the minimizer of our Catoni-bound, leading to an efficient Gibbs meta-learning algorithm. Although minimizing our kl-bound can not yield a closed-form solution, we show that it can be extended for analyzing the more challenging meta-learning setting where samples from different training tasks exhibit interdependencies. Experiments empirically show that our proposed meta-learning algorithms achieve competitive results with respect to latest works.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-guan22b, title = {Fast-Rate {PAC}-{B}ayesian Generalization Bounds for Meta-Learning}, author = {Guan, Jiechao and Lu, Zhiwu}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {7930--7948}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/guan22b/guan22b.pdf}, url = {https://proceedings.mlr.press/v162/guan22b.html}, abstract = {PAC-Bayesian error bounds provide a theoretical guarantee on the generalization abilities of meta-learning from training tasks to unseen tasks. However, it is still unclear how tight PAC-Bayesian bounds we can achieve for meta-learning. In this work, we propose a general PAC-Bayesian framework to cope with single-task learning and meta-learning uniformly. With this framework, we generalize the two tightest PAC-Bayesian bounds (i.e., kl-bound and Catoni-bound) from single-task learning to standard meta-learning, resulting in fast convergence rates for PAC-Bayesian meta-learners. By minimizing the derived two bounds, we develop two meta-learning algorithms for classification problems with deep neural networks. For regression problems, by setting Gibbs optimal posterior for each training task, we obtain the closed-form formula of the minimizer of our Catoni-bound, leading to an efficient Gibbs meta-learning algorithm. Although minimizing our kl-bound can not yield a closed-form solution, we show that it can be extended for analyzing the more challenging meta-learning setting where samples from different training tasks exhibit interdependencies. Experiments empirically show that our proposed meta-learning algorithms achieve competitive results with respect to latest works.} }
Endnote
%0 Conference Paper %T Fast-Rate PAC-Bayesian Generalization Bounds for Meta-Learning %A Jiechao Guan %A Zhiwu Lu %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-guan22b %I PMLR %P 7930--7948 %U https://proceedings.mlr.press/v162/guan22b.html %V 162 %X PAC-Bayesian error bounds provide a theoretical guarantee on the generalization abilities of meta-learning from training tasks to unseen tasks. However, it is still unclear how tight PAC-Bayesian bounds we can achieve for meta-learning. In this work, we propose a general PAC-Bayesian framework to cope with single-task learning and meta-learning uniformly. With this framework, we generalize the two tightest PAC-Bayesian bounds (i.e., kl-bound and Catoni-bound) from single-task learning to standard meta-learning, resulting in fast convergence rates for PAC-Bayesian meta-learners. By minimizing the derived two bounds, we develop two meta-learning algorithms for classification problems with deep neural networks. For regression problems, by setting Gibbs optimal posterior for each training task, we obtain the closed-form formula of the minimizer of our Catoni-bound, leading to an efficient Gibbs meta-learning algorithm. Although minimizing our kl-bound can not yield a closed-form solution, we show that it can be extended for analyzing the more challenging meta-learning setting where samples from different training tasks exhibit interdependencies. Experiments empirically show that our proposed meta-learning algorithms achieve competitive results with respect to latest works.
APA
Guan, J. & Lu, Z.. (2022). Fast-Rate PAC-Bayesian Generalization Bounds for Meta-Learning. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:7930-7948 Available from https://proceedings.mlr.press/v162/guan22b.html.

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