Information-theoretic generalization bounds for meta-learning and applications

Sharu Theresa Jose, Osvaldo Simeone

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Meta-learning, or “learning to learn”, refers to techniques that infer an inductive bias from data corresponding to multiple related tasks with the goal of improving the sample efficiency for new, previously unobserved, tasks. A key performance measure for meta-learning is the meta-generalization gap, that is, the difference between the average loss measured on the meta-training data and on a new, randomly selected task. This paper presents novel information-theoretic upper bounds on the meta-generalization gap. Two broad classes of meta-learning algorithms are considered that use either separate within-task training and test sets, like model agnostic meta-learning (MAML), or joint within-task training and test sets, like reptile. Extending the existing work for conventional learning, an upper bound on the meta-generalization gap is derived for the former class that depends on the mutual information (MI) between the output of the meta-learning algorithm and its input meta-training data. For the latter, the derived bound includes an additional MI between the output of the per-task learning procedure and corresponding data set to capture within-task uncertainty. Tighter bounds are then developed for the two classes via novel individual task MI (ITMI) bounds. Applications of the derived bounds are finally discussed, including a broad class of noisy iterative algorithms for meta-learning.

Original languageEnglish (US)
Article number126
Pages (from-to)1-28
Number of pages28
Issue number1
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Electrical and Electronic Engineering
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)


  • Generalization bounds
  • Meta-learning
  • Mutual information
  • Noisy iterative algorithms


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