Generalization Bounds for Meta-Learning via PAC-Bayes and Uniform Stability

TL;DR

This paper develops new PAC-Bayes and stability-based generalization bounds for gradient-based meta-learning, providing tighter guarantees especially when the base learner adapts quickly, and demonstrates their effectiveness on toy and real tasks.

Contribution

It introduces a novel PAC bound for meta-learning that combines stability and PAC-Bayes frameworks, improving over existing bounds and guiding practical regularization.

Findings

Tighter generalization bounds for meta-learning with fast-adapting base learners.

Empirical validation on toy and text classification tasks showing improved guarantees.

A practical regularization scheme inspired by the bounds enhances performance.

Abstract

We are motivated by the problem of providing strong generalization guarantees in the context of meta-learning. Existing generalization bounds are either challenging to evaluate or provide vacuous guarantees in even relatively simple settings. We derive a probably approximately correct (PAC) bound for gradient-based meta-learning using two different generalization frameworks in order to deal with the qualitatively different challenges of generalization at the "base" and "meta" levels. We employ bounds for uniformly stable algorithms at the base level and bounds from the PAC-Bayes framework at the meta level. The result of this approach is a novel PAC bound that is tighter when the base learner adapts quickly, which is precisely the goal of meta-learning. We show that our bound provides a tighter guarantee than other bounds on a toy non-convex problem on the unit sphere and a text-based classification example. We also present a practical regularization scheme motivated by the bound in settings where the bound is loose and demonstrate improved performance over baseline techniques.