English
Related papers

Related papers: Decentralized Nonconvex Optimization under Heavy-T…

200 papers

This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…

Optimization and Control · Mathematics 2025-05-12 Chao Sun , Huiming Zhang , Bo Chen , Li Yu

We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized,…

Optimization and Control · Mathematics 2022-04-07 Dusan Jakovetic , Dragana Bajovic , Anit Kumar Sahu , Soummya Kar , Nemanja Milosevic , Dusan Stamenkovic

In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…

Optimization and Control · Mathematics 2025-05-15 Jun Hu , Chao Sun , Bo Chen , Jianzheng Wang , Zheming Wang

The injection of heavy-tailed noise into the iterates of stochastic gradient descent (SGD) has garnered growing interest in recent years due to its theoretical and empirical benefits for optimization and generalization. However, its…

Machine Learning · Statistics 2025-05-13 Umut Şimşekli , Mert Gürbüzbalaban , Sinan Yıldırım , Lingjiong Zhu

Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process. To manage this realistic and challenging setting, new mechanisms, such as gradient clipping and gradient…

Optimization and Control · Mathematics 2026-05-19 Zijian Liu

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

This paper considers decentralized stochastic optimization over a network of $n$ nodes, where each node possesses a smooth non-convex local cost function and the goal of the networked nodes is to find an $\epsilon$-accurate first-order…

Optimization and Control · Mathematics 2021-06-15 Ran Xin , Usman A. Khan , Soummya Kar

Understanding the generalization properties of optimization algorithms under heavy-tailed noise has gained growing attention. However, the existing theoretical results mainly focus on stochastic gradient descent (SGD) and the analysis of…

Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…

Machine Learning · Statistics 2019-06-24 Thanh Huy Nguyen , Umut Şimşekli , Mert Gürbüzbalaban , Gaël Richard

We develop a worst-case complexity theory for stochastically preconditioned stochastic gradient descent (SPSGD) and its accelerated variants under heavy-tailed noise, a setting that encompasses widely used adaptive methods such as Adam,…

Machine Learning · Computer Science 2026-02-17 Yuchen Fang , James Demmel , Javad Lavaei

We consider a first order stochastic optimization framework where, at each iteration, $K$ independent identically distributed (i.i.d.) data point samples are drawn, based on which stochastic gradients can be queried. We allow gradient noise…

Optimization and Control · Mathematics 2026-05-11 Manojlo Vukovic , Dusan Jakovetic

In this paper, we design two compressed decentralized algorithms for solving nonconvex stochastic optimization under two different scenarios. Both algorithms adopt a momentum technique to achieve fast convergence and a message-compression…

Machine Learning · Computer Science 2025-08-08 Wei Liu , Anweshit Panda , Ujwal Pandey , Christopher Brissette , Yikang Shen , George M. Slota , Naigang Wang , Jie Chen , Yangyang Xu

It has repeatedly been observed that loss minimization by stochastic gradient descent (SGD) leads to heavy-tailed distributions of neural network parameters. Here, we analyze a continuous diffusion approximation of SGD, called homogenized…

Machine Learning · Statistics 2024-02-05 Zhe Jiao , Martin Keller-Ressel

We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save…

Optimization and Control · Mathematics 2023-03-01 Yonggui Yan , Jie Chen , Pin-Yu Chen , Xiaodong Cui , Songtao Lu , Yangyang Xu

Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…

Machine Learning · Computer Science 2025-10-27 Xingyu Wang , Chang-Han Rhee

We study high-probability convergence in online learning, in the presence of heavy-tailed noise. To combat the heavy tails, a general framework of nonlinear SGD methods is considered, subsuming several popular nonlinearities like sign,…

Machine Learning · Computer Science 2025-03-24 Aleksandar Armacki , Shuhua Yu , Pranay Sharma , Gauri Joshi , Dragana Bajovic , Dusan Jakovetic , Soummya Kar

Heavy-tailed stochastic gradient noise, commonly observed in transformer models, can destabilize the optimization process. Recent works mainly focus on developing and understanding approaches to address heavy-tailed noise in the centralized…

Machine Learning · Computer Science 2026-02-23 Junfei Sun , Dixi Yao , Xuchen Gong , Tahseen Rabbani , Manzil Zaheer , Tian Li

We study convergence in high-probability of SGD-type methods in non-convex optimization and the presence of heavy-tailed noise. To combat the heavy-tailed noise, a general black-box nonlinear framework is considered, subsuming…

Machine Learning · Statistics 2026-02-11 Aleksandar Armacki , Dragana Bajovic , Dusan Jakovetic , Soummya Kar

In distributed and federated learning algorithms, communication overhead is often reduced by performing multiple local updates between communication rounds. However, due to data heterogeneity across nodes and the local gradient noise within…

Machine Learning · Computer Science 2025-12-02 Yan Huang , Jinming Xu , Jiming Chen , Karl Henrik Johansson

In this paper, we provide novel optimal (or near optimal) convergence rates for a clipped version of the stochastic subgradient method. We consider nonsmooth convex problems over possibly unbounded domains, under heavy-tailed noise that…

Optimization and Control · Mathematics 2025-04-21 Daniela Angela Parletta , Andrea Paudice , Saverio Salzo