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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

There is an increasing realization that algorithmic inductive biases are central in preventing overfitting; empirically, we often see a benign overfitting phenomenon in overparameterized settings for natural learning algorithms, such as…

Machine Learning · Computer Science 2021-10-14 Difan Zou , Jingfeng Wu , Vladimir Braverman , Quanquan Gu , Sham M. Kakade

Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…

Optimization and Control · Mathematics 2023-11-15 Pascal Den Boef , Jos Maubach , Wil Schilders , Nathan van de Wouw

The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms. For example, stable solutions of gradient descent (GD) correspond to flat minima, which have been…

Machine Learning · Computer Science 2026-02-17 Rotem Mulayoff , Sebastian U. Stich

Stochastic gradient algorithms are often unstable when applied to functions that do not have Lipschitz-continuous and/or bounded gradients. Gradient clipping is a simple and effective technique to stabilize the training process for problems…

Optimization and Control · Mathematics 2021-06-11 Vien V. Mai , Mikael Johansson

The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and…

Machine Learning · Statistics 2022-10-18 Masaaki Imaizumi , Johannes Schmidt-Hieber

We showcase important features of the dynamics of the Stochastic Gradient Descent (SGD) in the training of neural networks. We present empirical observations that commonly used large step sizes (i) lead the iterates to jump from one side of…

Machine Learning · Computer Science 2023-06-08 Maksym Andriushchenko , Aditya Varre , Loucas Pillaud-Vivien , Nicolas Flammarion

Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…

Optimization and Control · Mathematics 2024-12-19 Andrey Sadchikov , Savelii Chezhegov , Aleksandr Beznosikov , Alexander Gasnikov

Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted…

Disordered Systems and Neural Networks · Physics 2022-09-07 Francesca Mignacco , Pierfrancesco Urbani

While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new…

Machine Learning · Computer Science 2019-07-26 Xinyan Li , Qilong Gu , Yingxue Zhou , Tiancong Chen , Arindam Banerjee

Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…

Machine Learning · Statistics 2022-06-20 Carmina Fjellström , Kaj Nyström

Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to…

Machine Learning · Computer Science 2022-07-12 Difan Zou , Jingfeng Wu , Vladimir Braverman , Quanquan Gu , Dean P. Foster , Sham M. Kakade

Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

Machine Learning · Computer Science 2024-02-13 Anuraganand Sharma

This paper presents a new generalization error analysis for Decentralized Stochastic Gradient Descent (D-SGD) based on algorithmic stability. The obtained results overhaul a series of recent works that suggested an increased instability due…

Machine Learning · Computer Science 2024-06-14 Batiste Le Bars , Aurélien Bellet , Marc Tommasi , Kevin Scaman , Giovanni Neglia

Stochastic Gradient Descent (SGD) has become the method of choice for solving a broad range of machine learning problems. However, some of its learning properties are still not fully understood. We consider least squares learning in…

Machine Learning · Statistics 2020-06-22 Nicole Mücke , Enrico Reiss

It is often observed that stochastic gradient descent (SGD) and its variants implicitly select a solution with good generalization performance; such implicit bias is often characterized in terms of the sharpness of the minima. Kleinberg et…

Machine Learning · Statistics 2024-05-28 Atsushi Nitanda , Ryuhei Kikuchi , Shugo Maeda , Denny Wu

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing. Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually…

Machine Learning · Computer Science 2023-01-10 Matteo Cacciola , Antonio Frangioni , Masoud Asgharian , Alireza Ghaffari , Vahid Partovi Nia

Distributed stochastic gradient descent (SGD) has attracted considerable recent attention due to its potential for scaling computational resources, reducing training time, and helping protect user privacy in machine learning. However, the…

Machine Learning · Computer Science 2025-02-27 Siyuan Yu , Wei Chen , H. Vincent Poor

We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…

Machine Learning · Computer Science 2023-01-13 Tomer Koren , Roi Livni , Yishay Mansour , Uri Sherman