Information-Theoretic Generalization Bounds for Meta-Learning and Applications

Area of Science:

• Machine Learning
• Artificial Intelligence
• Information Theory

Background:

• Meta-learning, or 'learning to learn', aims to enhance sample efficiency for new tasks by inferring inductive biases from related tasks.
• The meta-generalization gap, a key performance metric, measures the difference between meta-training and new task performance.

Purpose of the Study:

• To derive novel information-theoretic upper bounds on the meta-generalization gap for meta-learning algorithms.
• To analyze bounds for algorithms with separate (e.g., MAML) and joint (e.g., Reptile) within-task training and test sets.

Main Methods:

• Developed information-theoretic upper bounds on the meta-generalization gap.
• Extended conventional learning bounds using mutual information (MI) between algorithm output and meta-training data.
• Incorporated additional MI for joint training sets to capture within-task uncertainty.
• Introduced novel individual task MI (ITMI) bounds for tighter estimations.

Main Results:

• Derived MI-dependent upper bounds for meta-learning algorithms with separate within-task data splits.
• Established bounds for algorithms with joint within-task data splits, including within-task uncertainty.
• Achieved tighter bounds using individual task mutual information (ITMI) metrics.

Conclusions:

• The derived bounds offer a theoretical framework for analyzing meta-generalization in diverse meta-learning settings.
• The findings are applicable to a range of meta-learning algorithms, including noisy iterative methods.
• This work advances the understanding of generalization in meta-learning through an information-theoretic lens.