A stochastic variance-reduced accelerated primal-dual method for finite-sum saddle-point problems

In this paper, we propose a variance-reduced primal-dual algorithm with Bregman distance functions for solving convex-concave saddle-point problems finite-sum structure and nonbilinear coupling function. This type of problem typically arises in machine learning game theory. Based on some standard assumptions, the is proved to converge oracle complexities $${\mathcal {O}}(\frac{\sqrt{n}}{\epsilon })$$ {O}}(\frac{n}{\sqrt{\epsilon }}+\frac{1}{\epsilon ^{1.5}})$$ using constant non-constant parameters, respectively where n number function components. Compared existing methods, our framework yields significant improvement over required gradient samples achieve $$\epsilon $$ -accuracy gap. We also present numerical experiments showcase superior performance method compared state-of-the-art methods.