  PAC-Bayesian learning bounds are of the utmost interest to the learning
community. Their role is to connect the generalization ability of an
aggregation distribution $\rho$ to its empirical risk and to its
Kullback-Leibler divergence with respect to some prior distribution $\pi$.
Unfortunately, most of the available bounds typically rely on heavy assumptions
such as boundedness and independence of the observations. This paper aims at
relaxing these constraints and provides PAC-Bayesian learning bounds that hold
for dependent, heavy-tailed observations (hereafter referred to as
\emph{hostile data}). In these bounds the Kullack-Leibler divergence is
replaced with a general version of Csisz\'ar's $f$-divergence. We prove a
general PAC-Bayesian bound, and show how to use it in various hostile settings.
