The overall predictive uncertainty of a trained predictor can be decomposed\ninto separate contributions due to epistemic and aleatoric uncertainty. Under a\nBayesian formulation, assuming a well-specified model, the two contributions\ncan be exactly expressed (for the log-loss) or bounded (for more general\nlosses) in terms of information-theoretic quantities (Xu and Raginsky, 2020).\nThis paper addresses the study of epistemic uncertainty within an\ninformation-theoretic framework in the broader setting of Bayesian\nmeta-learning. A general hierarchical Bayesian model is assumed in which\nhyperparameters determine the per-task priors of the model parameters. Exact\ncharacterizations (for the log-loss) and bounds (for more general losses) are\nderived for the epistemic uncertainty -quantified by the minimum excess\nmeta-risk (MEMR)- of optimal meta-learning rules. This characterization is\nleveraged to bring insights into the dependence of the epistemic uncertainty on\nthe number of tasks and on the amount of per-task training data. Experiments\nare presented that use the proposed information-theoretic bounds, evaluated via\nneural mutual information estimators, to compare the performance of\nconventional learning and meta-learning as the number of meta-learning tasks\nincreases.\n