Bridging the Gap Between Practice and PAC-Bayes Theory in Few-Shot Meta-Learning
This work addresses a theoretical limitation for researchers in meta-learning, providing a bridge to explain practical performance in few-shot settings, though it is incremental as it builds on existing theories and algorithms.
The paper tackles the gap between PAC-Bayesian theory and practice in few-shot meta-learning by relaxing an unrealistic assumption about task distributions, developing tailored bounds that derive existing algorithms like MAML and Reptile, and introducing a new PACMAML algorithm that outperforms others on benchmark datasets with concrete performance improvements.
Despite recent advances in its theoretical understanding, there still remains a significant gap in the ability of existing PAC-Bayesian theories on meta-learning to explain performance improvements in the few-shot learning setting, where the number of training examples in the target tasks is severely limited. This gap originates from an assumption in the existing theories which supposes that the number of training examples in the observed tasks and the number of training examples in the target tasks follow the same distribution, an assumption that rarely holds in practice. By relaxing this assumption, we develop two PAC-Bayesian bounds tailored for the few-shot learning setting and show that two existing meta-learning algorithms (MAML and Reptile) can be derived from our bounds, thereby bridging the gap between practice and PAC-Bayesian theories. Furthermore, we derive a new computationally-efficient PACMAML algorithm, and show it outperforms existing meta-learning algorithms on several few-shot benchmark datasets.