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The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…

Machine Learning · Statistics 2023-11-02 Xi Chen , Jason D. Lee , Xin T. Tong , Yichen Zhang

Deep neural networks have been shown to achieve state-of-the-art performance in several machine learning tasks. Stochastic Gradient Descent (SGD) is the preferred optimization algorithm for training these networks and asynchronous SGD…

Machine Learning · Computer Science 2016-04-06 Wei Zhang , Suyog Gupta , Xiangru Lian , Ji Liu

As deep learning models continue to scale, the growing computational demands have amplified the need for effective coreset selection techniques. Coreset selection aims to accelerate training by identifying small, representative subsets of…

Machine Learning · Computer Science 2025-11-24 Wei-Kai Chang , Rajiv Khanna

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty…

Machine Learning · Computer Science 2024-11-26 Daniel Haimovich , Dima Karamshuk , Fridolin Linder , Niek Tax , Milan Vojnovic

Modern deep networks are trained with stochastic gradient descent (SGD) whose key hyperparameters are the number of data considered at each step or batch size $B$, and the step size or learning rate $\eta$. For small $B$ and large $\eta$,…

Machine Learning · Computer Science 2024-02-29 Antonio Sclocchi , Matthieu Wyart

Modern deep neural networks often require distributed training with many workers due to their large size. As the number of workers increases, communication overheads become the main bottleneck in data-parallel minibatch stochastic gradient…

Machine Learning · Statistics 2024-11-07 Tim Tsz-Kit Lau , Weijian Li , Chenwei Xu , Han Liu , Mladen Kolar

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

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

Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…

Machine Learning · Computer Science 2013-03-28 Tom Schaul , Yann LeCun

Stochastic Gradient Descent (SGD) is arguably the most popular of the machine learning methods applied to training deep neural networks (DNN) today. It has recently been demonstrated that SGD can be statistically biased so that certain…

Machine Learning · Computer Science 2015-09-21 Andrew J. R. Simpson

An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…

Machine Learning · Computer Science 2023-07-10 Zhenxun Zhuang

Stochastic gradient descent (SGD), which updates the model parameters by adding a local gradient times a learning rate at each step, is widely used in model training of machine learning algorithms such as neural networks. It is observed…

Machine Learning · Computer Science 2017-06-01 Chang Xu , Tao Qin , Gang Wang , Tie-Yan Liu

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

Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…

Machine Learning · Computer Science 2026-03-13 Sascha Marton

We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…

Neural and Evolutionary Computing · Computer Science 2019-03-26 William La Cava , Tilak Raj Singh , James Taggart , Srinivas Suri , Jason H. Moore

We study a continuous-time approximation of the stochastic gradient descent process for minimizing the population expected loss in learning problems. The main results establish general sufficient conditions for the convergence, extending…

Machine Learning · Computer Science 2025-11-03 Gabor Lugosi , Eulalia Nualart

One of the most important parts of Artificial Neural Networks is minimizing the loss functions which tells us how good or bad our model is. To minimize these losses we need to tune the weights and biases. Also to calculate the minimum value…

Machine Learning · Computer Science 2021-01-08 Kaustubh Yadav

We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its…

Machine Learning · Computer Science 2020-10-28 Clare Lyle , Lisa Schut , Binxin Ru , Yarin Gal , Mark van der Wilk

Very large deep learning models trained using gradient descent are remarkably resistant to memorization given their huge capacity, but are at the same time capable of fitting large datasets of pure noise. Here methods are introduced by…

Machine Learning · Computer Science 2022-12-22 Benjamin L. Badger

Previous works on stochastic gradient descent (SGD) often focus on its success. In this work, we construct worst-case optimization problems illustrating that, when not in the regimes that the previous works often assume, SGD can exhibit…

Machine Learning · Computer Science 2023-05-30 Liu Ziyin , Botao Li , James B. Simon , Masahito Ueda