  In this work, we introduce several expected generalization error bounds based
on the Wasserstein distance. More precisely, we present full-dataset,
single-letter, and random-subset bounds on both the standard setting and the
randomized-subsample setting from Steinke and Zakynthinou [2020]. Moreover, we
show that, when the loss function is bounded, these bounds recover from below
(and thus are tighter than) current bounds based on the relative entropy and,
for the standard setting, generate new, non-vacuous bounds also based on the
relative entropy. Then, we show how similar bounds featuring the backward
channel can be derived with the proposed proof techniques. Finally, we show how
various new bounds based on different information measures (e.g., the lautum
information or several $f$-divergences) can be derived from the presented
bounds.
