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

arXiv: https://arxiv.org/abs/2012.13456 · HTML: https://mlsanity.com/paper/2012.13456/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [Variance Reduced Halpern Iteration for Finite-Sum Monotone Inclusions](https://mlsanity.com/paper/2310.02987/) (2023)
- [Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyond](https://mlsanity.com/paper/2403.03562/) (2024)
- [Coordinate Linear Variance Reduction for Generalized Linear Programming](https://mlsanity.com/paper/2111.01842/) (2021)
- [Cyclic Coordinate Dual Averaging with Extrapolation](https://mlsanity.com/paper/2102.13244/) (2021)
- [SOREL: A Stochastic Algorithm for Spectral Risks Minimization](https://mlsanity.com/paper/2407.14618/) (2024)

## Abstract (arXiv)

In this paper, we propose a variance-reduced primal-dual algorithm with Bregman distance 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 Oleft(frac√ nεright) and Oleft(fracn√ ε+frac1ε1.5right) 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 ε-accuracy of the primal-dual gap. We tested our method for solving a distributionally robust optimization problem to show the effectiveness of the algorithm.