  In this paper, we propose a variance-reduced primal-dual algorithm for
solving convex-concave saddle-point problems with finite-sum structure and
nonbilinear coupling function. This type of problems typically arises in
machine learning and game theory. Based on some standard assumptions, the
algorithm is proved to converge with oracle complexity of $O\left(\frac{\sqrt
n}{\epsilon}\right)$ and $O\left(\frac{n}{\sqrt
\epsilon}+\frac{1}{\epsilon^{1.5}}\right)$ using constant and non-constant
parameters, respectively where n is the number of function components. Compared
with existing methods, our framework yields a significant improvement over the
number of required primal-dual gradient samples to achieve $\epsilon$-accuracy
of the primal-dual gap. We tested our method for solving distributionally
robust optimization problem to show the effectiveness of the algorithm.
