Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta Learning, Provably?

Lisha Chen, Tianyi Chen
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:1733-1774, 2022.

Abstract

Meta learning aims at learning a model that can quickly adapt to unseen tasks. Widely used meta learning methods include model agnostic meta learning (MAML), implicit MAML, Bayesian MAML. Thanks to its ability of modeling uncertainty, Bayesian MAML often has advantageous empirical performance. However, the theoretical understanding of Bayesian MAML is still limited, especially on questions such as if and when Bayesian MAML has provably better performance than MAML. In this paper, we aim to provide theoretical justifications for Bayesian MAML’s advantageous performance by comparing the meta test risks of MAML and Bayesian MAML. In the meta linear regression, under both the distribution agnostic and linear centroid cases, we have established that Bayesian MAML indeed has provably lower meta test risks than MAML. We verify our theoretical results through experiments, the code of which is available at https://github.com/lishachen/Bayesian-MAML-vs-MAML.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-chen22d, title = { Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta Learning, Provably? }, author = {Chen, Lisha and Chen, Tianyi}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {1733--1774}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/chen22d/chen22d.pdf}, url = {https://proceedings.mlr.press/v151/chen22d.html}, abstract = { Meta learning aims at learning a model that can quickly adapt to unseen tasks. Widely used meta learning methods include model agnostic meta learning (MAML), implicit MAML, Bayesian MAML. Thanks to its ability of modeling uncertainty, Bayesian MAML often has advantageous empirical performance. However, the theoretical understanding of Bayesian MAML is still limited, especially on questions such as if and when Bayesian MAML has provably better performance than MAML. In this paper, we aim to provide theoretical justifications for Bayesian MAML’s advantageous performance by comparing the meta test risks of MAML and Bayesian MAML. In the meta linear regression, under both the distribution agnostic and linear centroid cases, we have established that Bayesian MAML indeed has provably lower meta test risks than MAML. We verify our theoretical results through experiments, the code of which is available at https://github.com/lishachen/Bayesian-MAML-vs-MAML. } }
Endnote
%0 Conference Paper %T Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta Learning, Provably? %A Lisha Chen %A Tianyi Chen %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-chen22d %I PMLR %P 1733--1774 %U https://proceedings.mlr.press/v151/chen22d.html %V 151 %X Meta learning aims at learning a model that can quickly adapt to unseen tasks. Widely used meta learning methods include model agnostic meta learning (MAML), implicit MAML, Bayesian MAML. Thanks to its ability of modeling uncertainty, Bayesian MAML often has advantageous empirical performance. However, the theoretical understanding of Bayesian MAML is still limited, especially on questions such as if and when Bayesian MAML has provably better performance than MAML. In this paper, we aim to provide theoretical justifications for Bayesian MAML’s advantageous performance by comparing the meta test risks of MAML and Bayesian MAML. In the meta linear regression, under both the distribution agnostic and linear centroid cases, we have established that Bayesian MAML indeed has provably lower meta test risks than MAML. We verify our theoretical results through experiments, the code of which is available at https://github.com/lishachen/Bayesian-MAML-vs-MAML.
APA
Chen, L. & Chen, T.. (2022). Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta Learning, Provably? . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:1733-1774 Available from https://proceedings.mlr.press/v151/chen22d.html.

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