  Meta-learning aims at optimizing the hyperparameters of a model class or
training algorithm from the observation of data from a number of related tasks.
Following the setting of Baxter [1], the tasks are assumed to belong to the
same task environment, which is defined by a distribution over the space of
tasks and by per-task data distributions. The statistical properties of the
task environment thus dictate the similarity of the tasks. The goal of the
meta-learner is to ensure that the hyperparameters obtain a small loss when
applied for training of a new task sampled from the task environment. The
difference between the resulting average loss, known as meta-population loss,
and the corresponding empirical loss measured on the available data from
related tasks, known as meta-generalization gap, is a measure of the
generalization capability of the meta-learner. In this paper, we present novel
information-theoretic bounds on the average absolute value of the
meta-generalization gap. Unlike prior work [2], our bounds explicitly capture
the impact of task relatedness, the number of tasks, and the number of data
samples per task on the meta-generalization gap. Task similarity is gauged via
the Kullback-Leibler (KL) and Jensen-Shannon (JS) divergences. We illustrate
the proposed bounds on the example of ridge regression with meta-learned bias.
