# Accelerated Primal-dual Scheme for a Class of Stochastic Nonconvex-concave Saddle Point Problems

arXiv: https://arxiv.org/abs/2303.00211 · HTML: https://mlsanity.com/paper/2303.00211/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2023.

## Built on by (most cited first, 4 of 4)

- [On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximation](https://mlsanity.com/paper/2309.01753/) (2023)
- [Constrained Sampling with Primal-Dual Langevin Monte Carlo](https://mlsanity.com/paper/2411.00568/) (2024)
- [Solving Differential Equations with Constrained Learning](https://mlsanity.com/paper/2410.22796/) (2024)
- [An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problems](https://mlsanity.com/paper/2310.15448/) (2023)

## Abstract (arXiv)

Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we consider a class of nonconvex saddle point problems where the objective function satisfies the Polyak-Lojasiewicz condition with respect to the minimization variable and it is concave with respect to the maximization variable. The existing methods for solving nonconvex-concave saddle point problems often suffer from slow convergence and/or contain multiple loops. Our main contribution lies in proposing a novel single-loop accelerated primal-dual algorithm with new convergence rate results appearing for the first time in the literature, to the best of our knowledge. In particular, in the stochastic regime, we demonstrate a convergence rate of mathcal O(ε-4) to find an ε-gap solution which can be improved to mathcal O(ε-2) in deterministic setting.