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Information-Theoretic Generalization Bounds for Meta-Learning and Applications.

Sharu Theresa Jose1, Osvaldo Simeone1

  • 1Department of Engineering, King's College London, London WC2R 2LS, UK.

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Summary
This summary is machine-generated.

This study introduces new information-theoretic bounds for meta-generalization gap in meta-learning algorithms. These bounds leverage mutual information to improve understanding of sample efficiency in learning to learn.

Keywords:
generalization boundsmeta-learningmutual informationnoisy iterative algorithms

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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.