How Does the Task Landscape Affect MAML Performance?

Liam Collins, Aryan Mokhtari, Sanjay Shakkottai
Proceedings of The 1st Conference on Lifelong Learning Agents, PMLR 199:23-59, 2022.

Abstract

Model-Agnostic Meta-Learning (MAML) has become increasingly popular for training models that can quickly adapt to new tasks via one or few stochastic gradient descent steps. However, the MAML objective is significantly more difficult to optimize compared to standard non-adaptive learning (NAL), and little is understood about how much MAML improves over NAL in terms of the fast adaptability of their solutions in various scenarios. We analytically address this issue in a linear regression setting consisting of a mixture of easy and hard tasks, where hardness is related to the rate that gradient descent converges on the task. Specifically, we prove that in order for MAML to achieve substantial gain over NAL, (i) there must be some discrepancy in hardness among the tasks, and (ii) the optimal solutions of the hard tasks must be closely packed with the center far from the center of the easy tasks optimal solutions. We also give numerical and analytical results suggesting that these insights apply to two-layer neural networks. Finally, we provide few-shot image classification experiments that support our insights for when MAML should be used and emphasize the importance of training MAML on hard tasks in practice.

Cite this Paper

BibTeX
@InProceedings{pmlr-v199-collins22a, title = {How Does the Task Landscape Affect MAML Performance?}, author = {Collins, Liam and Mokhtari, Aryan and Shakkottai, Sanjay}, booktitle = {Proceedings of The 1st Conference on Lifelong Learning Agents}, pages = {23--59}, year = {2022}, editor = {Chandar, Sarath and Pascanu, Razvan and Precup, Doina}, volume = {199}, series = {Proceedings of Machine Learning Research}, month = {22--24 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v199/collins22a/collins22a.pdf}, url = {https://proceedings.mlr.press/v199/collins22a.html}, abstract = {Model-Agnostic Meta-Learning (MAML) has become increasingly popular for training models that can quickly adapt to new tasks via one or few stochastic gradient descent steps. However, the MAML objective is significantly more difficult to optimize compared to standard non-adaptive learning (NAL), and little is understood about how much MAML improves over NAL in terms of the fast adaptability of their solutions in various scenarios. We analytically address this issue in a linear regression setting consisting of a mixture of easy and hard tasks, where hardness is related to the rate that gradient descent converges on the task. Specifically, we prove that in order for MAML to achieve substantial gain over NAL, (i) there must be some discrepancy in hardness among the tasks, and (ii) the optimal solutions of the hard tasks must be closely packed with the center far from the center of the easy tasks optimal solutions. We also give numerical and analytical results suggesting that these insights apply to two-layer neural networks. Finally, we provide few-shot image classification experiments that support our insights for when MAML should be used and emphasize the importance of training MAML on hard tasks in practice.} }
Endnote
%0 Conference Paper %T How Does the Task Landscape Affect MAML Performance? %A Liam Collins %A Aryan Mokhtari %A Sanjay Shakkottai %B Proceedings of The 1st Conference on Lifelong Learning Agents %C Proceedings of Machine Learning Research %D 2022 %E Sarath Chandar %E Razvan Pascanu %E Doina Precup %F pmlr-v199-collins22a %I PMLR %P 23--59 %U https://proceedings.mlr.press/v199/collins22a.html %V 199 %X Model-Agnostic Meta-Learning (MAML) has become increasingly popular for training models that can quickly adapt to new tasks via one or few stochastic gradient descent steps. However, the MAML objective is significantly more difficult to optimize compared to standard non-adaptive learning (NAL), and little is understood about how much MAML improves over NAL in terms of the fast adaptability of their solutions in various scenarios. We analytically address this issue in a linear regression setting consisting of a mixture of easy and hard tasks, where hardness is related to the rate that gradient descent converges on the task. Specifically, we prove that in order for MAML to achieve substantial gain over NAL, (i) there must be some discrepancy in hardness among the tasks, and (ii) the optimal solutions of the hard tasks must be closely packed with the center far from the center of the easy tasks optimal solutions. We also give numerical and analytical results suggesting that these insights apply to two-layer neural networks. Finally, we provide few-shot image classification experiments that support our insights for when MAML should be used and emphasize the importance of training MAML on hard tasks in practice.
APA
Collins, L., Mokhtari, A. & Shakkottai, S.. (2022). How Does the Task Landscape Affect MAML Performance?. Proceedings of The 1st Conference on Lifelong Learning Agents, in Proceedings of Machine Learning Research 199:23-59 Available from https://proceedings.mlr.press/v199/collins22a.html.

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