  Federated learning is a popular distributed and privacy-preserving learning
paradigm in machine learning. Recently, some federated learning algorithms have
been proposed to solve the distributed minimax problems. However, these
federated minimax algorithms still suffer from high gradient or communication
complexity. Meanwhile, few algorithm focuses on using adaptive learning rate to
accelerate these algorithms. To fill this gap, in the paper, we study a class
of nonconvex minimax optimization, and propose an efficient adaptive federated
minimax optimization algorithm (i.e., AdaFGDA) to solve these distributed
minimax problems. Specifically, our AdaFGDA builds on the momentum-based
variance reduced and local-SGD techniques, and it can flexibly incorporate
various adaptive learning rates by using the unified adaptive matrices.
Theoretically, we provide a solid convergence analysis framework for our
AdaFGDA algorithm under non-i.i.d. setting. Moreover, we prove our AdaFGDA
algorithm obtains a lower gradient (i.e., stochastic first-order oracle, SFO)
complexity of $\tilde{O}(\epsilon^{-3})$ with lower communication complexity of
$\tilde{O}(\epsilon^{-2})$ in finding $\epsilon$-stationary point of the
nonconvex minimax problems. Experimentally, we conduct some experiments on the
deep AUC maximization and robust neural network training tasks to verify
efficiency of our algorithms.
