  Many machine learning problems can be formulated as minimax problems such as
Generative Adversarial Networks (GANs), AUC maximization and robust estimation,
to mention but a few. A substantial amount of studies are devoted to studying
the convergence behavior of their stochastic gradient-type algorithms. In
contrast, there is relatively little work on their generalization, i.e., how
the learning models built from training examples would behave on test examples.
In this paper, we provide a comprehensive generalization analysis of stochastic
gradient methods for minimax problems under both convex-concave and
nonconvex-nonconcave cases through the lens of algorithmic stability. We
establish a quantitative connection between stability and several
generalization measures both in expectation and with high probability. For the
convex-concave setting, our stability analysis shows that stochastic gradient
descent ascent attains optimal generalization bounds for both smooth and
nonsmooth minimax problems. We also establish generalization bounds for both
weakly-convex-weakly-concave and gradient-dominated problems.
