  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.
