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One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms,…

Optimization and Control · Mathematics 2016-05-24 Conghui Tan , Shiqian Ma , Yu-Hong Dai , Yuqiu Qian

Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…

Machine Learning · Computer Science 2025-04-22 Eric Lu

Most existing analyses of (stochastic) gradient descent rely on the condition that for $L$-smooth costs, the step size is less than $2/L$. However, many works have observed that in machine learning applications step sizes often do not…

Optimization and Control · Mathematics 2022-06-10 Kwangjun Ahn , Jingzhao Zhang , Suvrit Sra

In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch…

Machine Learning · Statistics 2016-05-04 Masayuki Ohzeki

Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for…

Machine Learning · Statistics 2021-06-11 Xiaoyu Li , Zhenxun Zhuang , Francesco Orabona

Following the same routine as [SSJ20], we continue to present the theoretical analysis for stochastic gradient descent with momentum (SGD with momentum) in this paper. Differently, for SGD with momentum, we demonstrate it is the two…

Machine Learning · Computer Science 2022-09-13 Bin Shi

In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on…

Optimization and Control · Mathematics 2023-07-03 Woocheol Choi , Myeong-Su Lee

Stochastic gradient descent (SGD) has been studied extensively over the past decades due to its simplicity and broad applicability in machine learning. In this work, we analyze the local behavior of gradient descent and stochastic gradient…

Optimization and Control · Mathematics 2026-05-15 Sebastian Kassing , Thomas Kruse

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…

Optimization and Control · Mathematics 2021-01-01 Lihua Lei , Michael I. Jordan

In this paper, two low-complexity adaptive step size algorithms are investigated for blind adaptive beamforming. Both of them are used in a stochastic gradient (SG) algorithm, which employs the constrained constant modulus (CCM) criterion…

Information Theory · Computer Science 2013-03-13 Lei Wang , Yunlong Cai , Rodrigo C. de Lamare

In this paper, we study the minimax optimization problem in the smooth and strongly convex-strongly concave setting when we have access to noisy estimates of gradients. In particular, we first analyze the stochastic Gradient Descent Ascent…

Optimization and Control · Mathematics 2020-02-14 Alireza Fallah , Asuman Ozdaglar , Sarath Pattathil

This paper presents a sufficient condition for stochastic gradients not to slow down the convergence of Nesterov's accelerated gradient method. The new condition has the strong-growth condition by Schmidt \& Roux as a special case, and it…

Optimization and Control · Mathematics 2022-07-26 Víctor Valls , Shiqiang Wang , Yuang Jiang , Leandros Tassiulas

The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex optimization problems,…

Optimization and Control · Mathematics 2025-12-22 Dimitris Oikonomou , Nicolas Loizou

Most stochastic gradient tracking (GT) methods adopt pre-scheduled stepsize rules, while a few recent works studied adaptive stepsizes that attempt to respond to the problem's local landscape. These methods are typically built upon the…

Optimization and Control · Mathematics 2026-05-19 Leilei Mei , Junyu Zhang

Modern proximal and stochastic gradient descent (SGD) methods are believed to efficiently minimize large composite objective functions, but such methods have two algorithmic challenges: (1) a lack of fast or justified stop conditions, and…

Optimization and Control · Mathematics 2017-01-05 Vivak Patel

The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice…

Optimization and Control · Mathematics 2021-02-19 Xiaoyu Wang , Sindri Magnússon , Mikael Johansson

In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique.…

Optimization and Control · Mathematics 2019-02-18 Feihu Huang , Songcan Chen

This paper studies fixed step-size stochastic approximation (SA) schemes, including stochastic gradient schemes, in a Riemannian framework. It is motivated by several applications, where geodesics can be computed explicitly, and their use…

Machine Learning · Statistics 2021-02-22 Alain Durmus , Pablo Jiménez , Éric Moulines , Salem Said

We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method, describes how the performance degrades as the step size…

Optimization and Control · Mathematics 2026-05-27 Fabian Schaipp , Robert M. Gower , Adrien Taylor

We consider the optimization of a smooth and strongly convex objective using constant step-size stochastic gradient descent (SGD) and study its properties through the prism of Markov chains. We show that, for unbiased gradient estimates…

Machine Learning · Statistics 2025-11-25 Ibrahim Merad , Stéphane Gaïffas