  In this paper, we study the generalization properties of Model-Agnostic
Meta-Learning (MAML) algorithms for supervised learning problems. We focus on
the setting in which we train the MAML model over $m$ tasks, each with $n$ data
points, and characterize its generalization error from two points of view:
First, we assume the new task at test time is one of the training tasks, and we
show that, for strongly convex objective functions, the expected excess
population loss is bounded by $\mathcal{O}(1/mn)$. Second, we consider the MAML
algorithm's generalization to an unseen task and show that the resulting
generalization error depends on the total variation distance between the
underlying distributions of the new task and the tasks observed during the
training process. Our proof techniques rely on the connections between
algorithmic stability and generalization bounds of algorithms. In particular,
we propose a new definition of stability for meta-learning algorithms, which
allows us to capture the role of both the number of tasks $m$ and number of
samples per task $n$ on the generalization error of MAML.
