  Generalization error bounds are critical to understanding the performance of
machine learning models. In this work, building upon a new bound of the
expected value of an arbitrary function of the population and empirical risk of
a learning algorithm, we offer a more refined analysis of the generalization
behaviour of a machine learning models based on a characterization of (bounds)
to their generalization error moments. We discuss how the proposed bounds --
which also encompass new bounds to the expected generalization error -- relate
to existing bounds in the literature. We also discuss how the proposed
generalization error moment bounds can be used to construct new generalization
error high-probability bounds.
