Generalization Bounds For Meta-Learning: An Information-Theoretic Analysis
This work provides a theoretical foundation for meta-learning generalization, which is important for researchers in machine learning, though it is incremental as it builds on existing analysis methods.
The authors tackled the problem of understanding generalization in meta-learning by deriving an information-theoretic analysis that applies to frameworks like MAML, resulting in a non-vacuous, data-dependent bound that is orders of magnitude tighter than previous bounds in most cases.
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.