Provable Meta-Learning of Linear Representations

Nilesh Tripuraneni, Chi Jin, Michael Jordan
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:10434-10443, 2021.

Abstract

Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning—a key tool for performing meta-learning—learns a data representation that can transfer knowledge across multiple tasks, which is essential in regimes where data is scarce. Despite a recent surge of interest in the practice of meta-learning, the theoretical underpinnings of meta-learning algorithms are lacking, especially in the context of learning transferable representations. In this paper, we focus on the problem of multi-task linear regression—in which multiple linear regression models share a common, low-dimensional linear representation. Here, we provide provably fast, sample-efficient algorithms to address the dual challenges of (1) learning a common set of features from multiple, related tasks, and (2) transferring this knowledge to new, unseen tasks. Both are central to the general problem of meta-learning. Finally, we complement these results by providing information-theoretic lower bounds on the sample complexity of learning these linear features.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-tripuraneni21a, title = {Provable Meta-Learning of Linear Representations}, author = {Tripuraneni, Nilesh and Jin, Chi and Jordan, Michael}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {10434--10443}, 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/tripuraneni21a/tripuraneni21a.pdf}, url = {https://proceedings.mlr.press/v139/tripuraneni21a.html}, abstract = {Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning—a key tool for performing meta-learning—learns a data representation that can transfer knowledge across multiple tasks, which is essential in regimes where data is scarce. Despite a recent surge of interest in the practice of meta-learning, the theoretical underpinnings of meta-learning algorithms are lacking, especially in the context of learning transferable representations. In this paper, we focus on the problem of multi-task linear regression—in which multiple linear regression models share a common, low-dimensional linear representation. Here, we provide provably fast, sample-efficient algorithms to address the dual challenges of (1) learning a common set of features from multiple, related tasks, and (2) transferring this knowledge to new, unseen tasks. Both are central to the general problem of meta-learning. Finally, we complement these results by providing information-theoretic lower bounds on the sample complexity of learning these linear features.} }
Endnote
%0 Conference Paper %T Provable Meta-Learning of Linear Representations %A Nilesh Tripuraneni %A Chi Jin %A Michael Jordan %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-tripuraneni21a %I PMLR %P 10434--10443 %U https://proceedings.mlr.press/v139/tripuraneni21a.html %V 139 %X Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning—a key tool for performing meta-learning—learns a data representation that can transfer knowledge across multiple tasks, which is essential in regimes where data is scarce. Despite a recent surge of interest in the practice of meta-learning, the theoretical underpinnings of meta-learning algorithms are lacking, especially in the context of learning transferable representations. In this paper, we focus on the problem of multi-task linear regression—in which multiple linear regression models share a common, low-dimensional linear representation. Here, we provide provably fast, sample-efficient algorithms to address the dual challenges of (1) learning a common set of features from multiple, related tasks, and (2) transferring this knowledge to new, unseen tasks. Both are central to the general problem of meta-learning. Finally, we complement these results by providing information-theoretic lower bounds on the sample complexity of learning these linear features.
APA
Tripuraneni, N., Jin, C. & Jordan, M.. (2021). Provable Meta-Learning of Linear Representations. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:10434-10443 Available from https://proceedings.mlr.press/v139/tripuraneni21a.html.

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