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With a weighting scheme proportional to t, a traditional stochastic gradient descent (SGD) algorithm achieves a high probability convergence rate of O({\kappa}/T) for strongly convex functions, instead of O({\kappa} ln(T)/T). We also prove…

Machine Learning · Computer Science 2013-05-13 Shenghuo Zhu

We analyze stochastic gradient algorithms for optimizing nonconvex problems. In particular, our goal is to find local minima (second-order stationary points) instead of just finding first-order stationary points which may be some bad…

Machine Learning · Computer Science 2019-06-24 Zhize Li

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

When solving finite-sum minimization problems, two common alternatives to stochastic gradient descent (SGD) with theoretical benefits are random reshuffling (SGD-RR) and shuffle-once (SGD-SO), in which functions are sampled in cycles…

Optimization and Control · Mathematics 2022-06-02 Carles Domingo-Enrich

In this paper, we consider distributed optimization problems where $n$ agents, each possessing a local cost function, collaboratively minimize the average of the local cost functions over a connected network. To solve the problem, we…

Optimization and Control · Mathematics 2023-03-24 Kun Huang , Xiao Li , Andre Milzarek , Shi Pu , Junwen Qiu

signSGD is popular in nonconvex optimization due to its communication efficiency. Yet, existing analyses typically assume data are sampled with replacement in each iteration, contradicting a common practical implementation where data are…

Machine Learning · Computer Science 2026-01-09 Zhen Qin , Zhishuai Liu , Pan Xu

We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…

Optimization and Control · Mathematics 2016-08-26 Zeyuan Allen-Zhu , Elad Hazan

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

Optimization and Control · Mathematics 2016-08-11 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

We study the asynchronous stochastic gradient descent algorithm for distributed training over $n$ workers which have varying computation and communication frequency over time. In this algorithm, workers compute stochastic gradients in…

Machine Learning · Computer Science 2022-06-17 Anastasia Koloskova , Sebastian U. Stich , Martin Jaggi

We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…

Optimization and Control · Mathematics 2016-04-06 Sashank J. Reddi , Ahmed Hefny , Suvrit Sra , Barnabas Poczos , Alex Smola

One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only…

Machine Learning · Computer Science 2023-06-29 Yuetong Xu , Baharan Mirzasoleiman

In this note we give a simple proof for the convergence of stochastic gradient (SGD) methods on $\mu$-convex functions under a (milder than standard) $L$-smoothness assumption. We show that for carefully chosen stepsizes SGD converges after…

Machine Learning · Computer Science 2019-12-24 Sebastian U. Stich

We study the problem of solving strongly convex and smooth unconstrained optimization problems using stochastic first-order algorithms. We devise a novel algorithm, referred to as Recursive One-Over-T SGD (ROOT-SGD), based on an easily…

Optimization and Control · Mathematics 2024-09-19 Chris Junchi Li , Wenlong Mou , Martin J. Wainwright , Michael I. Jordan

Random Reshuffling (RR), also known as Stochastic Gradient Descent (SGD) without replacement, is a popular and theoretically grounded method for finite-sum minimization. We propose two new algorithms: Proximal and Federated Random…

Machine Learning · Computer Science 2021-02-15 Konstantin Mishchenko , Ahmed Khaled , Peter Richtárik

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a…

Machine Learning · Computer Science 2015-02-11 Christopher De Sa , Kunle Olukotun , Christopher Ré

Stochastic gradient descent (SGD) is a prevalent optimization technique for large-scale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck…

Machine Learning · Computer Science 2021-05-24 Dmitrii Avdiukhin , Grigory Yaroslavtsev

We study stochastic gradient descent (SGD) and the stochastic heavy ball method (SHB, otherwise known as the momentum method) for the general stochastic approximation problem. For SGD, in the convex and smooth setting, we provide the first…

Machine Learning · Computer Science 2021-02-08 Othmane Sebbouh , Robert M. Gower , Aaron Defazio

We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…

Numerical Analysis · Mathematics 2017-03-02 Deanna Needell , Rachel Ward

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

We design a stochastic algorithm to train any smooth neural network to $\varepsilon$-approximate local minima, using $O(\varepsilon^{-3.25})$ backpropagations. The best result was essentially $O(\varepsilon^{-4})$ by SGD. More broadly, it…

Optimization and Control · Mathematics 2018-06-12 Zeyuan Allen-Zhu