  Minimax optimization problems have attracted significant attention in recent
years due to their widespread application in numerous machine learning models.
To solve the minimax problem, a wide variety of stochastic optimization methods
have been proposed. However, most of them ignore the distributed setting where
the training data is distributed on multiple workers. In this paper, we
developed a novel decentralized stochastic gradient descent ascent method for
the finite-sum minimax problem. In particular, by employing the
variance-reduced gradient, our method can achieve
$O(\frac{\sqrt{n}\kappa^3}{(1-\lambda)^2\epsilon^2})$ sample complexity and
$O(\frac{\kappa^3}{(1-\lambda)^2\epsilon^2})$ communication complexity for the
nonconvex-strongly-concave minimax problem. As far as we know, our work is the
first one to achieve such theoretical complexities for this kind of minimax
problem. At last, we apply our method to AUC maximization, and the experimental
results confirm the effectiveness of our method.
