  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.
