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In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several…

Optimization and Control · Mathematics 2022-10-20 Xiao Li , Andre Milzarek

Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…

Machine Learning · Computer Science 2019-12-24 Jie Chen , Ronny Luss

While popular optimization methods such as SGD, AdamW, and Lion depend on steepest descent updates in either $\ell_2$ or $\ell_\infty$ norms, there remains a critical gap in handling the non-Euclidean structure observed in modern deep…

Machine Learning · Computer Science 2025-06-11 Xinyu Luo , Cedar Site Bai , Bolian Li , Petros Drineas , Ruqi Zhang , Brian Bullins

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Optimization and Control · Mathematics 2023-08-15 Da Li , Jingjing Wu , Qingrun Zhang

We analyze asynchronous-type algorithms for distributed SGD in the heterogeneous setting, where each worker has its own computation and communication speeds, as well as data distribution. In these algorithms, workers compute possibly stale…

Machine Learning · Computer Science 2023-11-01 Rustem Islamov , Mher Safaryan , Dan Alistarh

Various gradient compression schemes have been proposed to mitigate the communication cost in distributed training of large scale machine learning models. Sign-based methods, such as signSGD, have recently been gaining popularity because of…

Optimization and Control · Mathematics 2021-06-25 Mher Safaryan , Peter Richtárik

Traditional analyses in non-convex optimization typically rely on the smoothness assumption, namely requiring the gradients to be Lipschitz. However, recent evidence shows that this smoothness condition does not capture the properties of…

Machine Learning · Computer Science 2022-08-25 Michael Crawshaw , Mingrui Liu , Francesco Orabona , Wei Zhang , Zhenxun Zhuang

Training deep neural network is a high dimensional and a highly non-convex optimization problem. Stochastic gradient descent (SGD) algorithm and it's variations are the current state-of-the-art solvers for this task. However, due to…

Machine Learning · Computer Science 2017-01-17 Xi He , Dheevatsa Mudigere , Mikhail Smelyanskiy , Martin Takáč

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

Machine Learning · Statistics 2018-12-27 Lam M. Nguyen , Nam H. Nguyen , Dzung T. Phan , Jayant R. Kalagnanam , Katya Scheinberg

Understanding the limitations of gradient methods, and stochastic gradient descent (SGD) in particular, is a central challenge in learning theory. To that end, a commonly used tool is the Statistical Queries (SQ) framework, which studies…

Machine Learning · Computer Science 2026-02-06 Daniel Barzilai , Ohad Shamir

This paper is concerned with distributed stochastic multi-agent constrained optimization problem over time-varying network with a class of communication noise. This paper considers the problem in composite optimization setting which is more…

Optimization and Control · Mathematics 2022-12-20 Zhan Yu , Daniel W. C. Ho , Deming Yuan , Jie Liu

Distributed methods are essential for handling machine learning pipelines comprising large-scale models and datasets. However, their benefits often come at the cost of increased communication overhead between the central server and agents,…

Machine Learning · Computer Science 2025-03-03 Enea Monzio Compagnoni , Rustem Islamov , Frank Norbert Proske , Aurelien Lucchi

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

We analyze the effect of synchronization on distributed stochastic gradient algorithms. By exploiting an analogy with dynamical models of biological quorum sensing - where synchronization between agents is induced through communication with…

Optimization and Control · Mathematics 2020-12-18 Nicholas M. Boffi , Jean-Jacques E. Slotine

In machine learning and neural network optimization, algorithms like incremental gradient, and shuffle SGD are popular due to minimizing the number of cache misses and good practical convergence behavior. However, their optimization…

Machine Learning · Computer Science 2024-02-13 Anastasia Koloskova , Nikita Doikov , Sebastian U. Stich , Martin Jaggi

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a…

Numerical Analysis · Computer Science 2015-09-01 N. Denizcan Vanli , Muhammed O. Sayin , Suleyman S. Kozat

Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…

Machine Learning · Computer Science 2019-12-16 Yunwen Lei , Ting Hu , Guiying Li , Ke Tang

The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…

Machine Learning · Computer Science 2026-01-27 Naoki Sato , Hideaki Iiduka

Stochastic Gradient Descent (SGD) is a cornerstone of large-scale optimization, yet its theoretical behavior under heavy-tailed noise -- common in modern machine learning and reinforcement learning -- remains poorly understood. In this…

Optimization and Control · Mathematics 2025-08-08 Ilyas Fatkhullin , Florian Hübler , Guanghui Lan

Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and…

Machine Learning · Computer Science 2015-10-06 Christopher De Sa , Ce Zhang , Kunle Olukotun , Christopher Ré