  The purpose of this paper is to discuss empirical risk minimization when the
losses are not necessarily bounded and may have a distribution with heavy
tails. In such situations, usual empirical averages may fail to provide
reliable estimates and empirical risk minimization may provide large excess
risk. However, some robust mean estimators proposed in the literature may be
used to replace empirical means. In this paper, we investigate empirical risk
minimization based on a robust estimate proposed by Catoni. We develop
performance bounds based on chaining arguments tailored to Catoni's mean
estimator.
