  This paper addresses the problem of unsupervised domain adaption from
theoretical and algorithmic perspectives. Existing domain adaptation theories
naturally imply minimax optimization algorithms, which connect well with the
domain adaptation methods based on adversarial learning. However, several
disconnections still exist and form the gap between theory and algorithm. We
extend previous theories (Mansour et al., 2009c; Ben-David et al., 2010) to
multiclass classification in domain adaptation, where classifiers based on the
scoring functions and margin loss are standard choices in algorithm design. We
introduce Margin Disparity Discrepancy, a novel measurement with rigorous
generalization bounds, tailored to the distribution comparison with the
asymmetric margin loss, and to the minimax optimization for easier training.
Our theory can be seamlessly transformed into an adversarial learning algorithm
for domain adaptation, successfully bridging the gap between theory and
algorithm. A series of empirical studies show that our algorithm achieves the
state of the art accuracies on challenging domain adaptation tasks.
