PAC-Bayes Bounds for Meta-learning with Data-Dependent Prior
This work provides theoretical generalization guarantees for meta-learning algorithms, which is important for researchers and practitioners who want to understand the reliability and performance of these methods.
This paper tackles the problem of understanding the generalization properties of meta-learning algorithms. It derives three novel PAC-Bayes generalization error bounds for meta-learning and extends one with a data-dependent prior, showing competitive generalization performance and rapid convergence.
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.