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By leveraging experience from previous tasks, meta-learning algorithms canachieve effective fast adaptation ability when encountering new tasks. Howeverit is unclear how the generalization property applies to new tasks. Probablyapproximately correct (PAC) Bayes bound theory provides a theoretical frameworkto analyze the generalization performance for meta-learning. We derive threenovel generalisation error bounds for meta-learning based on PAC-Bayes relativeentropy 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 formeta-learning guarantee a competitive generalization performance guarantee, andthe extended PAC-Bayes bound with data-dependent prior can achieve rapidconvergence ability.

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