Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory

TL;DR

This paper introduces a PAC-Bayes-based framework for meta-learning that constructs experience-dependent priors to improve generalization across tasks, demonstrated with neural networks.

Contribution

It extends PAC-Bayes bounds to meta-learning, enabling the construction of adaptive priors based on observed tasks for better transfer learning.

Findings

Improved generalization performance with meta-learning.

Effective neural network training using the proposed bounds.

Clear visualization of prior influence at different network levels.

Abstract

In meta-learning an agent extracts knowledge from observed tasks, aiming to facilitate learning of novel future tasks. Under the assumption that future tasks are 'related' to previous tasks, the accumulated knowledge should be learned in a way which captures the common structure across learned tasks, while allowing the learner sufficient flexibility to adapt to novel aspects of new tasks. We present a framework for meta-learning that is based on generalization error bounds, allowing us to extend various PAC-Bayes bounds to meta-learning. Learning takes place through the construction of a distribution over hypotheses based on the observed tasks, and its utilization for learning a new task. Thus, prior knowledge is incorporated through setting an experience-dependent prior for novel tasks. We develop a gradient-based algorithm which minimizes an objective function derived from the bounds and demonstrate its effectiveness numerically with deep neural networks. In addition to establishing the improved performance available through meta-learning, we demonstrate the intuitive way by which prior information is manifested at different levels of the network.