PAC-Bayes Bounds for Meta-learning with Data-Dependent Prior

TL;DR

This paper develops new PAC-Bayes generalization bounds for meta-learning, including data-dependent priors, demonstrating their effectiveness through experiments in guaranteeing rapid convergence and performance.

Contribution

It introduces three novel PAC-Bayes bounds for meta-learning and extends the framework to include data-dependent priors, enhancing theoretical understanding.

Findings

Proposed bounds guarantee competitive generalization performance.

Extended bounds with data-dependent priors achieve rapid convergence.

Experimental results validate the theoretical guarantees.

Abstract

By leveraging experience from previous tasks, meta-learning algorithms can achieve effective fast adaptation ability when encountering new tasks. However it is unclear how the generalization property applies to new tasks. Probably approximately correct (PAC) Bayes bound theory provides a theoretical framework to analyze the generalization performance for meta-learning. We derive three novel generalisation error bounds for meta-learning based on PAC-Bayes relative entropy bound. Furthermore, using the empirical risk minimization (ERM) method, a PAC-Bayes bound for meta-learning with data-dependent prior is developed. Experiments illustrate that the proposed three PAC-Bayes bounds for meta-learning guarantee a competitive generalization performance guarantee, and the extended PAC-Bayes bound with data-dependent prior can achieve rapid convergence ability.