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In this paper, we propose a variance-reduced primal-dual algorithm withBregman distance for solving convex-concave saddle-point problems withfinite-sum structure and nonbilinear coupling function. This type of problemstypically arises in machine learning and game theory. Based on some standardassumptions, 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-constantparameters, respectively where $n$ is the number of function components.Compared with existing methods, our framework yields a significant improvementover the number of required primal-dual gradient samples to achieve$\epsilon$-accuracy of the primal-dual gap. We tested our method for solving adistributionally robust optimization problem to show the effectiveness of thealgorithm.

A Stochastic Variance-reduced Accelerated Primal-dual Method for Finite-sum Saddle-point Problems