Provable Generalization of Overparameterized Meta-learning Trained with SGD

• URL: http://arxiv.org/abs/2206.09136v1
• Date: Sat, 18 Jun 2022 07:22:57 GMT
• Title: Provable Generalization of Overparameterized Meta-learning Trained with SGD
• Authors: Yu Huang and Yingbin Liang and Longbo Huang
• Abstract summary: We study the generalization of a widely used meta-learning approach, Model-Agnostic Meta-Learning (MAML) We provide both upper and lower bounds for the excess risk of MAML, which captures how SGD dynamics affect these generalization bounds. Our theoretical findings are further validated by experiments.
• Score: 62.892930625034374
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Despite the superior empirical success of deep meta-learning, theoretical understanding of overparameterized meta-learning is still limited. This paper studies the generalization of a widely used meta-learning approach, Model-Agnostic Meta-Learning (MAML), which aims to find a good initialization for fast adaptation to new tasks. Under a mixed linear regression model, we analyze the generalization properties of MAML trained with SGD in the overparameterized regime. We provide both upper and lower bounds for the excess risk of MAML, which captures how SGD dynamics affect these generalization bounds. With such sharp characterizations, we further explore how various learning parameters impact the generalization capability of overparameterized MAML, including explicitly identifying typical data and task distributions that can achieve diminishing generalization error with overparameterization, and characterizing the impact of adaptation learning rate on both excess risk and the early stopping time. Our theoretical findings are further validated by experiments.

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