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Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

Machine Learning · Computer Science 2024-02-13 Anuraganand Sharma

This paper considers decentralized stochastic optimization over a network of $n$ nodes, where each node possesses a smooth non-convex local cost function and the goal of the networked nodes is to find an $\epsilon$-accurate first-order…

Optimization and Control · Mathematics 2021-06-15 Ran Xin , Usman A. Khan , Soummya Kar

We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. We show that a combination of gradient clipping, momentum, and normalized gradient descent yields convergence…

Machine Learning · Computer Science 2021-11-10 Ashok Cutkosky , Harsh Mehta

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

Statistics Theory · Mathematics 2023-05-11 Yinan Shen , Jingyang Li , Jian-Feng Cai , Dong Xia

First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning…

Machine Learning · Computer Science 2020-11-23 Matilde Gargiani , Andrea Zanelli , Quoc Tran-Dinh , Moritz Diehl , Frank Hutter

Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…

Machine Learning · Statistics 2019-06-24 Thanh Huy Nguyen , Umut Şimşekli , Mert Gürbüzbalaban , Gaël Richard

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

Optimization and Control · Mathematics 2024-02-08 Xufeng Cai , Cheuk Yin Lin , Jelena Diakonikolas

Stochastic gradient descent (SGD) is a pillar of modern machine learning, serving as the go-to optimization algorithm for a diverse array of problems. While the empirical success of SGD is often attributed to its computational efficiency…

Machine Learning · Statistics 2022-06-16 Courtney Paquette , Elliot Paquette , Ben Adlam , Jeffrey Pennington

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…

Machine Learning · Computer Science 2024-01-24 Gregory Dexter , Borja Ocejo , Sathiya Keerthi , Aman Gupta , Ayan Acharya , Rajiv Khanna

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the…

Optimization and Control · Mathematics 2023-07-17 Yassine Laguel , Necdet Serhat Aybat , Mert Gürbüzbalaban

Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-25 Dan Alistarh , Christopher De Sa , Nikola Konstantinov

Stochastic gradient descent (SGD) is a workhorse algorithm for solving large-scale optimization problems in data science and machine learning. Understanding the convergence of SGD is hence of fundamental importance. In this work we examine…

Numerical Analysis · Mathematics 2024-12-11 Lehan Chen , Yuji Nakatsukasa

In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability…

Optimization and Control · Mathematics 2020-10-26 Eduard Gorbunov , Marina Danilova , Alexander Gasnikov

Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence…

Machine Learning · Computer Science 2021-03-03 Anastasia Koloskova , Nicolas Loizou , Sadra Boreiri , Martin Jaggi , Sebastian U. Stich

Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…

Optimization and Control · Mathematics 2024-12-19 Andrey Sadchikov , Savelii Chezhegov , Aleksandr Beznosikov , Alexander Gasnikov

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…

Optimization and Control · Mathematics 2024-09-02 Eduard Gorbunov , Marina Danilova , Innokentiy Shibaev , Pavel Dvurechensky , Alexander Gasnikov

The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the \emph{classical} central limit theorem (CLT) kicks in. This assumption is often made…

Machine Learning · Statistics 2019-12-03 Umut Şimşekli , Mert Gürbüzbalaban , Thanh Huy Nguyen , Gaël Richard , Levent Sagun

We provide sharp path-dependent generalization and excess risk guarantees for the full-batch Gradient Descent (GD) algorithm on smooth losses (possibly non-Lipschitz, possibly nonconvex). At the heart of our analysis is an upper bound on…

Machine Learning · Statistics 2023-02-13 Konstantinos E. Nikolakakis , Farzin Haddadpour , Amin Karbasi , Dionysios S. Kalogerias

In this work, we describe a generic approach to show convergence with high probability for both stochastic convex and non-convex optimization with sub-Gaussian noise. In previous works for convex optimization, either the convergence is only…

Optimization and Control · Mathematics 2023-03-01 Zijian Liu , Ta Duy Nguyen , Thien Hang Nguyen , Alina Ene , Huy Lê Nguyen

In this paper, we are concerned with differentially private {stochastic gradient descent (SGD)} algorithms in the setting of stochastic convex optimization (SCO). Most of the existing work requires the loss to be Lipschitz continuous and…

Machine Learning · Statistics 2022-03-23 Puyu Wang , Yunwen Lei , Yiming Ying , Hai Zhang