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We study high-probability convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. In the proposed scenario, the model is updated in an online fashion, as new information is observed, without storing any…

Machine Learning · Computer Science 2024-05-02 Aleksandar Armacki , Pranay Sharma , Gauri Joshi , Dragana Bajovic , Dusan Jakovetic , Soummya Kar

Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the…

Machine Learning · Computer Science 2022-05-23 Ziyi Chen , Shaocong Ma , Yi Zhou

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

Optimization and Control · Mathematics 2025-04-08 Prashant Khanduri , Ioannis Tsaknakis , Yihua Zhang , Sijia Liu , Mingyi Hong

In this paper, we study stochastic constrained minimax optimization problems with nonconvex-nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its…

Optimization and Control · Mathematics 2026-02-25 Muhammad Khan , Yangyang Xu

Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…

Machine Learning · Computer Science 2024-01-11 Liang Zhang , Junchi Yang , Amin Karbasi , Niao He

This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity…

Optimization and Control · Mathematics 2021-03-31 Siqi Zhang , Junchi Yang , Cristóbal Guzmán , Negar Kiyavash , Niao He

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

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

Optimization and Control · Mathematics 2018-01-19 Bo Jiang , Tianyi Lin , Shiqian Ma , Shuzhong Zhang

Stochastic gradient descent is one of the most common iterative algorithms used in machine learning and its convergence analysis is a rich area of research. Understanding its convergence properties can help inform what modifications of it…

Optimization and Control · Mathematics 2025-11-25 Liam Madden , Emiliano Dall'Anese , Stephen Becker

Multi-objective optimization (MOO) is receiving more attention in various fields such as multi-task learning. Recent works provide some effective algorithms with theoretical analysis but they are limited by the standard $L$-smooth or…

Machine Learning · Computer Science 2025-03-11 Qi Zhang , Peiyao Xiao , Shaofeng Zou , Kaiyi Ji

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

This paper studies smooth nonconvex-concave minimax optimization and two acceleration mechanisms for single-loop first-order methods: dual perturbation and smoothing. Although both techniques improve convergence guarantees, their relative…

Optimization and Control · Mathematics 2026-04-30 Jiajin Li , Mahesh Nagarajan , Siyu Pan , Nanxi Zhang

Epoch gradient descent method (a.k.a. Epoch-GD) proposed by Hazan and Kale (2011) was deemed a breakthrough for stochastic strongly convex minimization, which achieves the optimal convergence rate of $O(1/T)$ with $T$ iterative updates for…

Optimization and Control · Mathematics 2020-06-18 Yan Yan , Yi Xu , Qihang Lin , Wei Liu , Tianbao Yang

Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…

Machine Learning · Computer Science 2020-06-15 Raef Bassily , Vitaly Feldman , Cristóbal Guzmán , Kunal Talwar

This paper focuses on stochastic methods for solving smooth non-convex strongly-concave min-max problems, which have received increasing attention due to their potential applications in deep learning (e.g., deep AUC maximization,…

Machine Learning · Computer Science 2023-04-19 Zhishuai Guo , Yan Yan , Zhuoning Yuan , Tianbao Yang

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

Optimization and Control · Mathematics 2020-05-05 Quoc Tran-Dinh , Nhan H. Pham , Dzung T. Phan , Lam M. Nguyen

The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed…

Machine Learning · Computer Science 2020-10-26 Farzan Farnia , Asuman Ozdaglar

This paper studies the complexity of finding an $\epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order…

Optimization and Control · Mathematics 2026-03-10 Lesi Chen , Junru Li , El Mahdi Chayti , Jingzhao Zhang

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular…

Optimization and Control · Mathematics 2025-02-07 Chenghan Xie , Chenxi Li , Chuwen Zhang , Qi Deng , Dongdong Ge , Yinyu Ye

In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an $\epsilon$-stochastic stationary point, where the expected violations of both constraints and…

Optimization and Control · Mathematics 2025-09-03 Zhaosong Lu , Sanyou Mei , Yifeng Xiao