English
Related papers

Related papers: Modified Step Size for Enhanced Stochastic Gradien…

200 papers

We propose a stochastic variant of the classical Polyak step-size (Polyak, 1987) commonly used in the subgradient method. Although computing the Polyak step-size requires knowledge of the optimal function values, this information is readily…

Optimization and Control · Mathematics 2021-03-23 Nicolas Loizou , Sharan Vaswani , Issam Laradji , Simon Lacoste-Julien

Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning…

Machine Learning · Computer Science 2023-10-04 Farshed Abdukhakimov , Chulu Xiang , Dmitry Kamzolov , Martin Takáč

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

Machine Learning · Statistics 2022-10-07 Saad Mohamad , Hamad Alamri , Abdelhamid Bouchachia

Communication has been seen as a significant bottleneck in industrial applications over large-scale networks. To alleviate the communication burden, sign-based optimization algorithms have gained popularity recently in both industrial and…

Optimization and Control · Mathematics 2021-09-07 Xiuxian Li , Kuo-Yi Lin , Li Li , Yiguang Hong , Jie Chen

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

We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix…

Optimization and Control · Mathematics 2020-03-31 Bin Hu , Peter Seiler , Laurent Lessard

This work considers stepsize schedules for gradient descent on smooth convex objectives. We extend the existing literature and propose a unified technique for constructing stepsizes with analytic bounds for an arbitrary number of…

Optimization and Control · Mathematics 2026-02-17 Zehao Zhang , Rujun Jiang

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

This paper studies the last iterate of subgradient method with Polyak step size when applied to the minimization of a nonsmooth convex function with bounded subgradients. We show that the subgradient method with Polyak step size achieves a…

Optimization and Control · Mathematics 2024-07-23 Moslem Zamani , François Glineur

Many problems require to optimize empirical risk functions over large data sets. Gradient descent methods that calculate the full gradient in every descent step do not scale to such datasets. Various flavours of Stochastic Gradient Descent…

Machine Learning · Computer Science 2020-11-26 Francesco Cosentino , Harald Oberhauser , Alessandro Abate

Recently, Stochastic Gradient Descent (SGD) and its variants have become the dominant methods in the large-scale optimization of machine learning (ML) problems. A variety of strategies have been proposed for tuning the step sizes, ranging…

Machine Learning · Computer Science 2022-08-02 Xiaoyu Li

This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…

Optimization and Control · Mathematics 2013-07-09 Angelia Nedich , Soomin Lee

Stochastic gradient descent (SGD) is one of the most widely used optimization methods for parallel and distributed processing of large datasets. One of the key limitations of distributed SGD is the need to regularly communicate the…

Optimization and Control · Mathematics 2018-10-25 Xiaojian Xu , Ulugbek S. Kamilov

Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…

Machine Learning · Statistics 2023-02-03 Nhat Ho , Tongzheng Ren , Sujay Sanghavi , Purnamrita Sarkar , Rachel Ward

We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings:…

Machine Learning · Computer Science 2023-06-13 Amit Attia , Tomer Koren

This work establishes new convergence guarantees for gradient descent in smooth convex optimization via a computer-assisted analysis technique. Our theory allows nonconstant stepsize policies with frequent long steps potentially violating…

Optimization and Control · Mathematics 2024-02-06 Benjamin Grimmer

This work considers gradient descent for L-smooth convex optimization with stepsizes larger than the classic regime where descent can be ensured. The stepsize schedules considered are similar to but differ slightly from the recent silver…

Optimization and Control · Mathematics 2024-04-15 Benjamin Grimmer , Kevin Shu , Alex L. Wang

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…

Signal Processing · Electrical Eng. & Systems 2020-07-10 Zhan Gao , Alec Koppel , Alejandro Ribeiro

We consider the well-studied setting of minimizing a convex Lipschitz function using either gradient descent (GD) or its stochastic variant (SGD), and examine the last iterate convergence. By now, it is known that standard stepsize choices…

Optimization and Control · Mathematics 2026-04-16 Guy Kornowski , Ohad Shamir

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…

Machine Learning · Computer Science 2013-01-01 Ohad Shamir , Tong Zhang