  PAC-Bayesian bounds are known to be tight and informative when studying the
generalization ability of randomized classifiers. However, when applied to some
family of deterministic models such as neural networks, they require a loose
and costly derandomization step. As an alternative to this step, we introduce
three new PAC-Bayesian generalization bounds that have the originality to be
pointwise, meaning that they provide guarantees over one single hypothesis
instead of the usual averaged analysis. Our bounds are rather general,
potentially parameterizable, and provide novel insights for various machine
learning settings that rely on randomized algorithms. We illustrate the
interest of our theoretical result for the analysis of neural network training.
