  We introduce a new PAC-Bayes oracle bound for unbounded losses. This result
can be understood as a PAC-Bayesian version of the Cram\'er-Chernoff bound. The
proof technique relies on controlling the tails of certain random variables
involving the Cram\'er transform of the loss. We highlight several applications
of the main theorem. First, we show that our result naturally allows exact
optimization of the free parameter on many PAC-Bayes bounds. Second, we recover
and generalize previous results. Finally, we show that our approach allows
working with richer assumptions that result in more informative and potentially
tighter bounds. In this direction, we provide a general bound under a new
``model-dependent bounded CGF" assumption from which we obtain bounds based on
parameter norms and log-Sobolev inequalities. All these bounds can be minimized
to obtain novel posteriors.
