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Theoretically understanding stochastic gradient descent (SGD) in overparameterized models has led to the development of several optimization algorithms that are widely used in practice today. Recent work by~\citet{zou2021benign} provides…

Machine Learning · Computer Science 2025-06-19 Alexandru Meterez , Depen Morwani , Costin-Andrei Oncescu , Jingfeng Wu , Cengiz Pehlevan , Sham Kakade

This paper considers the scenario that multiple data owners wish to apply a machine learning method over the combined dataset of all owners to obtain the best possible learning output but do not want to share the local datasets owing to…

Machine Learning · Computer Science 2019-07-09 Le Trieu Phong , Tran Thi Phuong

We propose a new per-layer adaptive step-size procedure for stochastic first-order optimization methods for minimizing empirical loss functions in deep learning, eliminating the need for the user to tune the learning rate (LR). The proposed…

Machine Learning · Computer Science 2023-07-07 Achraf Bahamou , Donald Goldfarb

The learning rate is perhaps the single most important parameter in the training of neural networks and, more broadly, in stochastic (nonconvex) optimization. Accordingly, there are numerous effective, but poorly understood, techniques for…

Machine Learning · Computer Science 2020-04-16 Bin Shi , Weijie J. Su , Michael I. Jordan

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We…

Machine Learning · Statistics 2018-05-23 Ashia C. Wilson , Rebecca Roelofs , Mitchell Stern , Nathan Srebro , Benjamin Recht

We study the asynchronous stochastic gradient descent algorithm for distributed training over $n$ workers which have varying computation and communication frequency over time. In this algorithm, workers compute stochastic gradients in…

Machine Learning · Computer Science 2022-06-17 Anastasia Koloskova , Sebastian U. Stich , Martin Jaggi

Modern machine learning is trained by stochastic gradient descent (SGD), whose performance critically depends on how the learning rate (LR) is adjusted and decreased over time. Yet existing LR regimes may be intricate, or need to tune one…

Machine Learning · Computer Science 2025-08-20 Zhuang Yang

Neural networks are usually trained by some form of stochastic gradient descent (SGD)). A number of strategies are in common use intended to improve SGD optimization, such as learning rate schedules, momentum, and batching. These are…

Neural and Evolutionary Computing · Computer Science 2015-08-13 Thomas M. Breuel

This paper proposes an algorithm for Federated Learning (FL) with a two-layer structure that achieves both variance reduction and a faster convergence rate to an optimal solution in the setting where each agent has an arbitrary probability…

Machine Learning · Computer Science 2023-04-04 M. R. Rostami , S. S. Kia

Stochastic gradient descent (SGD) and adaptive gradient methods, such as Adam and RMSProp, have been widely used in training deep neural networks. We empirically show that while the difference between the standard generalization performance…

Machine Learning · Computer Science 2023-11-30 Avery Ma , Yangchen Pan , Amir-massoud Farahmand

Embedding learning has found widespread applications in recommendation systems and natural language modeling, among other domains. To learn quality embeddings efficiently, adaptive learning rate algorithms have demonstrated superior…

Machine Learning · Computer Science 2021-11-24 Yan Li , Dhruv Choudhary , Xiaohan Wei , Baichuan Yuan , Bhargav Bhushanam , Tuo Zhao , Guanghui Lan

This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is…

Machine Learning · Statistics 2024-02-20 Matteo Sordello , Niccolò Dalmasso , Hangfeng He , Weijie Su

Stochastic gradient descent (SGD) is a powerful optimization technique that is particularly useful in online learning scenarios. Its convergence analysis is relatively well understood under the assumption that the data samples are…

Machine Learning · Computer Science 2024-10-03 Ethan Che , Jing Dong , Xin T. Tong

Stochastic Gradient Descent (SGD) methods are prominent for training machine learning and deep learning models. The performance of these techniques depends on their hyperparameter tuning over time and varies for different models and…

Machine Learning · Statistics 2019-08-22 Tomer Lancewicki , Selcuk Kopru

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

Machine Learning · Statistics 2023-06-23 Gerard Ben Arous , Reza Gheissari , Aukosh Jagannath

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Machine Learning · Computer Science 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…

Machine Learning · Statistics 2026-01-01 Xin Chen , Jason M. Klusowski

This paper presents a holistic approach to gradient leakage resilient distributed Stochastic Gradient Descent (SGD). First, we analyze two types of strategies for privacy-enhanced federated learning: (i) gradient pruning with random…

Machine Learning · Computer Science 2023-05-12 Wenqi Wei , Ling Liu , Jingya Zhou , Ka-Ho Chow , Yanzhao Wu

Differentially private stochastic gradient descent (DP-SGD) is broadly considered to be the gold standard for training and fine-tuning neural networks under differential privacy (DP). With the increasing availability of high-quality…

Applying Differentially Private Stochastic Gradient Descent (DPSGD) to training modern, large-scale neural networks such as transformer-based models is a challenging task, as the magnitude of noise added to the gradients at each iteration…

Machine Learning · Computer Science 2022-07-07 Ryuichi Ito , Seng Pei Liew , Tsubasa Takahashi , Yuya Sasaki , Makoto Onizuka