On the Global Optimality of Model-Agnostic Meta-Learning

Lingxiao Wang, Qi Cai, Zhuoran Yang, Zhaoran Wang
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:9837-9846, 2020.

Abstract

Model-agnostic meta-learning (MAML) formulates meta-learning as a bilevel optimization problem, where the inner level solves each subtask based on a shared prior, while the outer level searches for the optimal shared prior by optimizing its aggregated performance over all the subtasks. Despite its empirical success, MAML remains less understood in theory, especially in terms of its global optimality, due to the nonconvexity of the meta-objective (the outer-level objective). To bridge such a gap between theory and practice, we characterize the optimality gap of the stationary points attained by MAML for both reinforcement learning and supervised learning, where the inner-level and outer-level problems are solved via first-order optimization methods. In particular, our characterization connects the optimality gap of such stationary points with (i) the functional geometry of inner-level objectives and (ii) the representation power of function approximators, including linear models and neural networks. To the best of our knowledge, our analysis establishes the global optimality of MAML with nonconvex meta-objectives for the first time.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-wang20b, title = {On the Global Optimality of Model-Agnostic Meta-Learning}, author = {Wang, Lingxiao and Cai, Qi and Yang, Zhuoran and Wang, Zhaoran}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {9837--9846}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/wang20b/wang20b.pdf}, url = {https://proceedings.mlr.press/v119/wang20b.html}, abstract = {Model-agnostic meta-learning (MAML) formulates meta-learning as a bilevel optimization problem, where the inner level solves each subtask based on a shared prior, while the outer level searches for the optimal shared prior by optimizing its aggregated performance over all the subtasks. Despite its empirical success, MAML remains less understood in theory, especially in terms of its global optimality, due to the nonconvexity of the meta-objective (the outer-level objective). To bridge such a gap between theory and practice, we characterize the optimality gap of the stationary points attained by MAML for both reinforcement learning and supervised learning, where the inner-level and outer-level problems are solved via first-order optimization methods. In particular, our characterization connects the optimality gap of such stationary points with (i) the functional geometry of inner-level objectives and (ii) the representation power of function approximators, including linear models and neural networks. To the best of our knowledge, our analysis establishes the global optimality of MAML with nonconvex meta-objectives for the first time.} }
Endnote
%0 Conference Paper %T On the Global Optimality of Model-Agnostic Meta-Learning %A Lingxiao Wang %A Qi Cai %A Zhuoran Yang %A Zhaoran Wang %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-wang20b %I PMLR %P 9837--9846 %U https://proceedings.mlr.press/v119/wang20b.html %V 119 %X Model-agnostic meta-learning (MAML) formulates meta-learning as a bilevel optimization problem, where the inner level solves each subtask based on a shared prior, while the outer level searches for the optimal shared prior by optimizing its aggregated performance over all the subtasks. Despite its empirical success, MAML remains less understood in theory, especially in terms of its global optimality, due to the nonconvexity of the meta-objective (the outer-level objective). To bridge such a gap between theory and practice, we characterize the optimality gap of the stationary points attained by MAML for both reinforcement learning and supervised learning, where the inner-level and outer-level problems are solved via first-order optimization methods. In particular, our characterization connects the optimality gap of such stationary points with (i) the functional geometry of inner-level objectives and (ii) the representation power of function approximators, including linear models and neural networks. To the best of our knowledge, our analysis establishes the global optimality of MAML with nonconvex meta-objectives for the first time.
APA
Wang, L., Cai, Q., Yang, Z. & Wang, Z.. (2020). On the Global Optimality of Model-Agnostic Meta-Learning. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:9837-9846 Available from https://proceedings.mlr.press/v119/wang20b.html.

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