  In this paper, we provide two main contributions in PAC-Bayesian theory for
domain adaptation where the objective is to learn, from a source distribution,
a well-performing majority vote on a different target distribution. On the one
hand, we propose an improvement of the previous approach proposed by Germain et
al. (2013), that relies on a novel distribution pseudodistance based on a
disagreement averaging, allowing us to derive a new tighter PAC-Bayesian domain
adaptation bound for the stochastic Gibbs classifier. We specialize it to
linear classifiers, and design a learning algorithm which shows interesting
results on a synthetic problem and on a popular sentiment annotation task. On
the other hand, we generalize these results to multisource domain adaptation
allowing us to take into account different source domains. This study opens the
door to tackle domain adaptation tasks by making use of all the PAC-Bayesian
tools.
