# Alternating proximal-gradient steps for (stochastic) nonconvex-concave minimax problems

arXiv: https://arxiv.org/abs/2007.13605 · HTML: https://mlsanity.com/paper/2007.13605/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2020.

## Built on by (most cited first, 26 of 26)

- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity](https://mlsanity.com/paper/2112.05604/) (2021)
- [The Complexity of Nonconvex-Strongly-Concave Minimax Optimization](https://mlsanity.com/paper/2103.15888/) (2021)
- [Near-optimal Local Convergence of Alternating Gradient Descent-Ascent for Minimax Optimization](https://mlsanity.com/paper/2102.09468/) (2021)
- [Proximal Gradient Descent-Ascent: Variable Convergence under KL Geometry](https://mlsanity.com/paper/2102.04653/) (2021)
- [Nest Your Adaptive Algorithm for Parameter-Agnostic Nonconvex Minimax Optimization](https://mlsanity.com/paper/2206.00743/) (2022)
- [Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization](https://mlsanity.com/paper/2408.11974/) (2024)
- [Unified Convergence Analysis for Adaptive Optimization with Moving Average Estimator](https://mlsanity.com/paper/2104.14840/) (2021)
- [Nonsmooth Nonconvex-Nonconcave Minimax Optimization: Primal-Dual Balancing and Iteration Complexity Analysis](https://mlsanity.com/paper/2209.10825/) (2022)
- [Algorithmic Foundations of Empirical X-risk Minimization](https://mlsanity.com/paper/2206.00439/) (2022)
- [TiAda: A Time-scale Adaptive Algorithm for Nonconvex Minimax Optimization](https://mlsanity.com/paper/2210.17478/) (2022)
- [Generalization Bounds of Nonconvex-(Strongly)-Concave Stochastic Minimax Optimization](https://mlsanity.com/paper/2205.14278/) (2022)
- [Deep AUC Maximization for Medical Image Classification: Challenges and Opportunities](https://mlsanity.com/paper/2111.02400/) (2021)
- [A Normal Map-Based Proximal Stochastic Gradient Method: Convergence and Identification Properties](https://mlsanity.com/paper/2305.05828/) (2023)
- [Improved Rates of Differentially Private Nonconvex-Strongly-Concave Minimax Optimization](https://mlsanity.com/paper/2503.18317/) (2025)
- [Accelerated Proximal Alternating Gradient-Descent-Ascent for Nonconvex Minimax Machine Learning](https://mlsanity.com/paper/2112.11663/) (2021)
- [Single-Loop Stochastic Algorithms for Difference of Max-Structured Weakly Convex Functions](https://mlsanity.com/paper/2405.18577/) (2024)
- [A Fully Parameter-Free Second-Order Algorithm for Convex-Concave Minimax Problems](https://mlsanity.com/paper/2407.03571/) (2024)
- [Two trust region type algorithms for solving nonconvex-strongly concave minimax problems](https://mlsanity.com/paper/2402.09807/) (2024)
- [Adaptive Algorithms with Sharp Convergence Rates for Stochastic Hierarchical Optimization](https://mlsanity.com/paper/2509.15399/) (2025)
- [An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problems](https://mlsanity.com/paper/2310.15448/) (2023)
- [Achieving Near-Optimal Convergence for Distributed Minimax Optimization with Adaptive Stepsizes](https://mlsanity.com/paper/2406.02939/) (2024)
- [Iterative Minimax Games with Coupled Linear Constraints](https://mlsanity.com/paper/2212.04672/) (2022)
- [Accelerating Distributed Optimization: A Primal-Dual Perspective on Local Steps](https://mlsanity.com/paper/2407.02689/) (2024)
- [Gradient Norm Regularization Second-Order Algorithms for Solving Nonconvex-Strongly Concave Minimax Problems](https://mlsanity.com/paper/2411.15769/) (2024)
- [Unbiased Stochastic Optimization for Gaussian Processes on Finite Dimensional RKHS](https://mlsanity.com/paper/2508.20588/) (2025)

## Abstract (arXiv)

Minimax problems of the form minx maxy Psi(x,y) have attracted increased interest largely due to advances in machine learning, in particular generative adversarial networks. These are typically trained using variants of stochastic gradient descent for the two players. Although convex-concave problems are well understood with many efficient solution methods to choose from, theoretical guarantees outside of this setting are sometimes lacking even for the simplest algorithms. In particular, this is the case for alternating gradient descent ascent, where the two agents take turns updating their strategies. To partially close this gap in the literature we prove a novel global convergence rate for the stochastic version of this method for finding a critical point of g(·) := maxy Psi(·,y) in a setting which is not convex-concave.