  We derive a novel information-theoretic analysis of the generalization
property of meta-learning algorithms. Concretely, our analysis proposes a
generic understanding of both the conventional learning-to-learn framework and
the modern model-agnostic meta-learning (MAML) algorithms. Moreover, we provide
a data-dependent generalization bound for a stochastic variant of MAML, which
is non-vacuous for deep few-shot learning. As compared to previous bounds that
depend on the square norm of gradients, empirical validations on both simulated
data and a well-known few-shot benchmark show that our bound is orders of
magnitude tighter in most situations.
