  In recent years, federated minimax optimization has attracted growing
interest due to its extensive applications in various machine learning tasks.
While Smoothed Alternative Gradient Descent Ascent (Smoothed-AGDA) has proved
its success in centralized nonconvex minimax optimization, how and whether
smoothing technique could be helpful in federated setting remains unexplored.
In this paper, we propose a new algorithm termed Federated Stochastic Smoothed
Gradient Descent Ascent (FESS-GDA), which utilizes the smoothing technique for
federated minimax optimization. We prove that FESS-GDA can be uniformly used to
solve several classes of federated minimax problems and prove new or better
analytical convergence results for these settings. We showcase the practical
efficiency of FESS-GDA in practical federated learning tasks of training
generative adversarial networks (GANs) and fair classification.
