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We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points.…

Machine Learning · Computer Science 2015-03-10 Rong Ge , Furong Huang , Chi Jin , Yang Yuan

Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…

Machine Learning · Computer Science 2019-08-01 Zheng Li , Shi Shu

We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…

Machine Learning · Statistics 2018-03-06 Wenqing Hu , Chris Junchi Li , Lei Li , Jian-Guo Liu

In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate…

Optimization and Control · Mathematics 2022-12-01 Ziang Chen , Yingzhou Li , Jianfeng Lu

This paper studies a decentralized stochastic gradient tracking (DSGT) algorithm for non-convex empirical risk minimization problems over a peer-to-peer network of nodes, which is in sharp contrast to the existing DSGT only for convex…

Machine Learning · Computer Science 2020-08-31 Jiaqi Zhang , Keyou You

We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients…

Optimization and Control · Mathematics 2019-08-20 Jemin George , Tao Yang , He Bai , Prudhvi Gurram

Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…

Machine Learning · Statistics 2018-10-30 Ashok Cutkosky , Robert Busa-Fekete

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that…

Optimization and Control · Mathematics 2020-03-11 Shi Pu , Angelia Nedić

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

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…

Optimization and Control · Mathematics 2025-06-10 Waïss Azizian , Franck Iutzeler , Jérôme Malick , Panayotis Mertikopoulos

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

Machine Learning · Computer Science 2016-01-14 Yadong Mu , Wei Liu , Wei Fan

The paper considers distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents' local expectation-valued convex cost functions. Due to the stochasticity in gradient…

Optimization and Control · Mathematics 2022-04-07 Jinlong Lei , Peng Yi , Jie Chen , Yiguang Hong

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…

Machine Learning · Statistics 2018-08-30 Chris Junchi Li , Zhaoran Wang , Han Liu

We study distributed stochastic gradient (D-SG) method and its accelerated variant (D-ASG) for solving decentralized strongly convex stochastic optimization problems where the objective function is distributed over several computational…

Optimization and Control · Mathematics 2021-10-05 Alireza Fallah , Mert Gurbuzbalaban , Asuman Ozdaglar , Umut Simsekli , Lingjiong Zhu

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

Machine Learning · Computer Science 2015-03-19 Alexander Rakhlin , Ohad Shamir , Karthik Sridharan

In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…

Machine Learning · Computer Science 2020-03-30 Naeimeh Omidvar , Mohammad Ali Maddah-Ali , Hamed Mahdavi

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

Optimization and Control · Mathematics 2025-11-21 Fabio Nobile , Matteo Raviola , Nathan Schaeffer

Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA)…

Machine Learning · Statistics 2015-03-20 Shai Shalev-Shwartz , Tong Zhang

A commonly used heuristic in non-convex optimization is Normalized Gradient Descent (NGD) - a variant of gradient descent in which only the direction of the gradient is taken into account and its magnitude ignored. We analyze this heuristic…

Machine Learning · Computer Science 2016-11-22 Kfir Y. Levy

In this paper, we study secure distributed optimization against arbitrary gradient attack in multi-agent networks. In distributed optimization, there is no central server to coordinate local updates, and each agent can only communicate with…

Optimization and Control · Mathematics 2022-10-31 Shuhua Yu , Soummya Kar