  Off-policy learning (OPL) aims at finding improved policies from logged
bandit data, often by minimizing the inverse propensity scoring (IPS) estimator
of the risk. In this work, we investigate a smooth regularization for IPS, for
which we derive a two-sided PAC-Bayes generalization bound. The bound is
tractable, scalable, interpretable and provides learning certificates. In
particular, it is also valid for standard IPS without making the assumption
that the importance weights are bounded. We demonstrate the relevance of our
approach and its favorable performance through a set of learning tasks. Since
our bound holds for standard IPS, we are able to provide insight into when
regularizing IPS is useful. Namely, we identify cases where regularization
might not be needed. This goes against the belief that, in practice, clipped
IPS often enjoys favorable performance than standard IPS in OPL.
