Transfer Meta-Learning: Information- Theoretic Bounds and Information Meta-Risk Minimization

Sharu Theresa Jose, Osvaldo Simeone, Giuseppe Durisi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Meta-learning automatically infers an inductive bias by observing data from a number of related tasks. The inductive bias is encoded by hyperparameters that determine aspects of the model class or training algorithm, such as initialization or learning rate. Meta-learning assumes that the learning tasks belong to a task environment, and that tasks are drawn from the same task environment both during meta-training and meta-testing. This, however, may not hold true in practice. In this paper, we introduce the problem of transfer meta-learning, in which tasks are drawn from a target task environment during meta-testing that may differ from the source task environment observed during meta-training. Novel information-theoretic upper bounds are obtained on the transfer meta-generalization gap, which measures the difference between the meta-training loss, available at the meta-learner, and the average loss on meta-test data from a new, randomly selected, task in the target task environment. The first bound, on the average transfer meta-generalization gap, captures the meta-environment shift between source and target task environments via the KL divergence between source and target data distributions. The second, PAC-Bayesian bound, and the third, single-draw bound, account for this shift via the log-likelihood ratio between source and target task distributions. Furthermore, two transfer meta-learning solutions are introduced. For the first, termed Empirical Meta-Risk Minimization (EMRM), we derive bounds on the average optimality gap. The second, referred to as Information Meta-Risk Minimization (IMRM), is obtained by minimizing the PAC-Bayesian bound. IMRM is shown via experiments to potentially outperform EMRM.

Original languageEnglish (US)
Pages (from-to)474-501
Number of pages28
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 1 2022

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • PAC-Bayesian bounds
  • Transfer meta-learning
  • information risk minimization
  • information-theoretic generalization bounds
  • single-draw bounds


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