  This paper considers stochastic first-order algorithms for convex-concave
minimax problems of the form $\min_{\bf x}\max_{\bf y}f(\bf x, \bf y)$, where
$f$ can be presented by the average of $n$ individual components which are
$L$-average smooth. For $\mu_x$-strongly-convex-$\mu_y$-strongly-concave
setting, we propose a new method which could find a $\varepsilon$-saddle point
of the problem in $\tilde{\mathcal O}
\big(\sqrt{n(\sqrt{n}+\kappa_x)(\sqrt{n}+\kappa_y)}\log(1/\varepsilon)\big)$
stochastic first-order complexity, where $\kappa_x\triangleq L/\mu_x$ and
$\kappa_y\triangleq L/\mu_y$. This upper bound is near optimal with respect to
$\varepsilon$, $n$, $\kappa_x$ and $\kappa_y$ simultaneously. In addition, the
algorithm is easily implemented and works well in practical. Our methods can be
extended to solve more general unbalanced convex-concave minimax problems and
the corresponding upper complexity bounds are also near optimal.
