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In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…

Optimization and Control · Mathematics 2026-03-06 Yan Gao , Yongchao Liu

We provide a unified analysis of two-timescale gradient descent ascent (TTGDA) for solving structured nonconvex minimax optimization problems in the form of $\min_\textbf{x} \max_{\textbf{y} \in Y} f(\textbf{x}, \textbf{y})$, where the…

Machine Learning · Computer Science 2025-01-28 Tianyi Lin , Chi Jin , Michael. I. Jordan

Nonconvex minimax problems appear frequently in emerging machine learning applications, such as generative adversarial networks and adversarial learning. Simple algorithms such as the gradient descent ascent (GDA) are the common practice…

Optimization and Control · Mathematics 2020-02-25 Junchi Yang , Negar Kiyavash , Niao He

In this work, we investigate a stochastic gradient descent method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at…

Numerical Analysis · Mathematics 2024-09-10 Ruixue Gu , Zhenwu Fu , Bo Han , Hongsun Fu

Nonconvex-concave (NC-C) finite-sum minimax problems have wide applications in signal processing and machine learning tasks. Conventional stochastic gradient algorithms, which rely on uniform sampling for gradient estimation, often suffer…

Optimization and Control · Mathematics 2025-10-14 Xia Jiang , Linglingzhi Zhu , Taoli Zheng , Anthony Man-Cho So

Stochastic gradient descent ascent (SGDA) and its variants have been the workhorse for solving minimax problems. However, in contrast to the well-studied stochastic gradient descent (SGD) with differential privacy (DP) constraints, there is…

Machine Learning · Computer Science 2022-08-01 Zhenhuan Yang , Shu Hu , Yunwen Lei , Kush R. Varshney , Siwei Lyu , Yiming Ying

In the paper, we study a class of useful minimax problems on Riemanian manifolds and propose a class of effective Riemanian gradient-based methods to solve these minimax problems. Specifically, we propose an effective Riemannian gradient…

Machine Learning · Computer Science 2023-01-04 Feihu Huang , Shangqian Gao

Gradient descent ascent (GDA), the simplest single-loop algorithm for nonconvex minimax optimization, is widely used in practical applications such as generative adversarial networks (GANs) and adversarial training. Albeit its desirable…

Machine Learning · Computer Science 2021-12-13 Junchi Yang , Antonio Orvieto , Aurelien Lucchi , Niao He

Minimax optimization problems have attracted significant attention in recent years due to their widespread application in numerous machine learning models. To solve the minimax problem, a wide variety of stochastic optimization methods have…

Machine Learning · Computer Science 2024-06-12 Hongchang Gao

Gradient Descent Ascent (GDA) methods are the mainstream algorithms for minimax optimization in generative adversarial networks (GANs). Convergence properties of GDA have drawn significant interest in the recent literature. Specifically,…

Optimization and Control · Mathematics 2022-07-05 Haochuan Li , Farzan Farnia , Subhro Das , Ali Jadbabaie

We propose a new stochastic method SAPD+ for solving nonconvex-concave minimax problems of the form $\min\max\mathcal{L}(x,y)=f(x)+\Phi(x,y)-g(y)$, where $f,g$ are closed convex and $\Phi(x,y)$ is a smooth function that is weakly convex in…

Optimization and Control · Mathematics 2024-10-15 Xuan Zhang , Necdet Serhat Aybat , Mert Gürbüzbalaban

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a…

Machine Learning · Computer Science 2015-02-11 Christopher De Sa , Kunle Olukotun , Christopher Ré

Local SGD is a promising approach to overcome the communication overhead in distributed learning by reducing the synchronization frequency among worker nodes. Despite the recent theoretical advances of local SGD in empirical risk…

Machine Learning · Computer Science 2021-03-01 Yuyang Deng , Mehrdad Mahdavi

We propose a novel single-loop decentralized algorithm called DGDA-VR for solving the stochastic nonconvex strongly-concave minimax problem over a connected network of $M$ agents. By using stochastic first-order oracles to estimate the…

Optimization and Control · Mathematics 2024-03-21 Xuan Zhang , Gabriel Mancino-Ball , Necdet Serhat Aybat , Yangyang Xu

Minimax problems of the form $\min_x \max_y \Psi(x,y)$ have attracted increased interest largely due to advances in machine learning, in particular generative adversarial networks. These are typically trained using variants of stochastic…

Optimization and Control · Mathematics 2023-04-14 Radu Ioan Boţ , Axel Böhm

The gradient descent-ascent (GDA) algorithm has been widely applied to solve minimax optimization problems. In order to achieve convergent policy parameters for minimax optimization, it is important that GDA generates convergent variable…

Optimization and Control · Mathematics 2021-02-18 Ziyi Chen , Yi Zhou , Tengyu Xu , Yingbin Liang

Stochastic nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose an accelerated first-order regularized momentum descent ascent…

Optimization and Control · Mathematics 2024-10-16 Huiling Zhang , Zi Xu

Nonsmooth nonconvex-concave minimax problems have attracted significant attention due to their wide applications in many fields. In this paper, we consider a class of nonsmooth nonconvex-concave minimax problems on Riemannian manifolds.…

Optimization and Control · Mathematics 2026-03-24 Xiyuan Xie , Qia Li

In this paper, we propose GT-GDA, a distributed optimization method to solve saddle point problems of the form: $\min_{\mathbf{x}} \max_{\mathbf{y}} \{F(\mathbf{x},\mathbf{y}) :=G(\mathbf{x}) + \langle \mathbf{y}, \overline{P} \mathbf{x}…

Optimization and Control · Mathematics 2022-07-04 Muhammad I. Qureshi , Usman A. Khan

In this paper, we propose a novel reformulation of the smooth nonconvex-strongly-concave (NC-SC) minimax problems that casts the problem as a joint minimization. We show that our reformulation preserves not only first-order stationarity,…

Optimization and Control · Mathematics 2026-01-16 Bohao Ma , Nachuan Xiao , Junyu Zhang