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Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…

机器学习 · 计算机科学 2026-05-26 Natanael Alpay , Emeric Battaglia

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

最优化与控制 · 数学 2024-02-08 Xufeng Cai , Cheuk Yin Lin , Jelena Diakonikolas

In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimisation methods in machine learning, imaging and…

机器学习 · 计算机科学 2023-02-13 Z. Kereta , B. Jin

We prove explicit bounds on the exponential rate of convergence for the momentum stochastic gradient descent scheme (MSGD) for arbitrary, fixed hyperparameters (learning rate, friction parameter) and its continuous-in-time counterpart in…

最优化与控制 · 数学 2024-11-07 Benjamin Gess , Sebastian Kassing

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…

机器学习 · 计算机科学 2023-05-30 Liu Ziyin , Botao Li , James B. Simon , Masahito Ueda

In this paper, we examine the time it takes for stochastic gradient descent (SGD) to reach the global minimum of a general, non-convex loss function. We approach this question through the lens of randomly perturbed dynamical systems and…

最优化与控制 · 数学 2025-06-10 Waïss Azizian , Franck Iutzeler , Jérôme Malick , Panayotis Mertikopoulos

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

机器学习 · 统计学 2017-09-12 Stephan Mandt , Matthew D. Hoffman , David M. Blei

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…

神经与进化计算 · 计算机科学 2015-08-13 Thomas M. Breuel

We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…

最优化与控制 · 数学 2020-03-12 Antonio Orvieto , Aurelien Lucchi

Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely unexplored. In this paper we study SGD with increasing…

概率论 · 数学 2026-05-11 Bartosz Glowacki , Rafal Kulik , Philippe Soulier

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…

无序系统与神经网络 · 物理学 2022-09-07 Francesca Mignacco , Pierfrancesco Urbani

Stochastic Gradient Descent (SGD) is an out-of-equilibrium algorithm used extensively to train artificial neural networks. However very little is known on to what extent SGD is crucial for to the success of this technology and, in…

机器学习 · 计算机科学 2023-12-19 Persia Jana Kamali , Pierfrancesco Urbani

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…

机器学习 · 计算机科学 2024-01-24 Gregory Dexter , Borja Ocejo , Sathiya Keerthi , Aman Gupta , Ayan Acharya , Rajiv Khanna

We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for…

机器学习 · 计算机科学 2018-02-19 Ilja Kuzborskij , Christoph H. Lampert

Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…

分布式、并行与集群计算 · 计算机科学 2018-06-25 Dan Alistarh , Christopher De Sa , Nikola Konstantinov

We study the problem of non-convex optimization using Stochastic Gradient Langevin Dynamics (SGLD). SGLD is a natural and popular variation of stochastic gradient descent where at each step, appropriately scaled Gaussian noise is added. To…

机器学习 · 计算机科学 2024-07-08 August Y. Chen , Ayush Sekhari , Karthik Sridharan

This work investigates the performance of the final iterate produced by stochastic gradient descent (SGD) under temporally dependent data. We consider two complementary sources of dependence: $(i)$ martingale-type dependence in both the…

统计理论 · 数学 2026-01-06 Yinan Shen , Yichen Zhang , Wen-Xin Zhou

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…

最优化与控制 · 数学 2021-06-11 Vien V. Mai , Mikael Johansson

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…

机器学习 · 计算机科学 2025-03-06 Tehila Dahan , Kfir Y. Levy

We consider stochastic optimization problems where the objective depends on some parameter, as commonly found in hyperparameter optimization for instance. We investigate the behavior of the derivatives of the iterates of Stochastic Gradient…

最优化与控制 · 数学 2024-11-21 Franck Iutzeler , Edouard Pauwels , Samuel Vaiter