A General framework for PAC-Bayes Bounds for Meta-Learning
This work addresses the theoretical understanding of generalization in meta-learning, which is incremental as it builds on existing PAC-Bayes frameworks to provide tighter bounds for practitioners in machine learning.
The paper tackles the problem of bounding the meta-generalization gap in meta-learning, which arises from finite tasks and data per task, by deriving new PAC-Bayes bounds through convex function upper bounds and developing algorithms that show improved performance over prior methods in numerical examples.
Meta learning automatically infers an inductive bias, that includes the hyperparameter of the base-learning algorithm, by observing data from a finite number of related tasks. This paper studies PAC-Bayes bounds on meta generalization gap. The meta-generalization gap comprises two sources of generalization gaps: the environment-level and task-level gaps resulting from observation of a finite number of tasks and data samples per task, respectively. In this paper, by upper bounding arbitrary convex functions, which link the expected and empirical losses at the environment and also per-task levels, we obtain new PAC-Bayes bounds. Using these bounds, we develop new PAC-Bayes meta-learning algorithms. Numerical examples demonstrate the merits of the proposed novel bounds and algorithm in comparison to prior PAC-Bayes bounds for meta-learning.