  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.
