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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

This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…

Optimization and Control · Mathematics 2023-10-03 Nikita Kornilov , Eduard Gorbunov , Mohammad Alkousa , Fedor Stonyakin , Pavel Dvurechensky , Alexander Gasnikov

Stochastic gradient algorithm is a key ingredient of many machine learning methods, particularly appropriate for large-scale learning.However, a major caveat of large data is their incompleteness.We propose an averaged stochastic gradient…

Statistics Theory · Mathematics 2020-06-09 Julie Josse , Aude Sportisse , Claire Boyer , Aymeric Dieuleveut

We study trade-offs between convergence rate and robustness to gradient errors in the context of first-order methods. Our focus is on generalized momentum methods (GMMs)--a broad class that includes Nesterov's accelerated gradient,…

Optimization and Control · Mathematics 2026-01-14 Mert Gürbüzbalaban , Yasa Syed , Necdet Serhat Aybat

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…

Machine Learning · Computer Science 2011-12-02 Mark Schmidt , Nicolas Le Roux , Francis Bach

We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…

Machine Learning · Statistics 2015-04-08 Nicolas Flammarion , Francis Bach

Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is…

Machine Learning · Computer Science 2021-07-30 Zeyuan Allen-Zhu

We present a totally asynchronous algorithm for convex optimization that is based on a novel generalization of Nesterov's accelerated gradient method. This algorithm is developed for fast convergence under "total asynchrony," i.e., allowing…

Optimization and Control · Mathematics 2024-06-17 Ellie Pond , April Sebok , Zachary Bell , Matthew Hale

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 present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…

Optimization and Control · Mathematics 2024-07-08 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio

The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have…

Machine Learning · Computer Science 2022-11-22 Yuri Kinoshita , Taiji Suzuki

We analyze the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system with Hessian-driven damping. We recover a convergence rate, up to a factor of 2 speedup upon Nesterov's…

Optimization and Control · Mathematics 2025-02-25 Zepeng Wang , Juan Peypouquet

We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proximal operator is available. We establish the exact worst-case…

Optimization and Control · Mathematics 2020-03-03 Adrien B. Taylor , Julien M. Hendrickx , François Glineur

This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but…

Optimization and Control · Mathematics 2013-09-06 Saeed Ghadimi , Guanghui Lan , Hongchao Zhang

In the context of finite sums minimization, variance reduction techniques are widely used to improve the performance of state-of-the-art stochastic gradient methods. Their practical impact is clear, as well as their theoretical properties.…

Optimization and Control · Mathematics 2024-08-07 Cheik Traoré , Vassilis Apidopoulos , Saverio Salzo , Silvia Villa

First-order methods with momentum such as Nesterov's fast gradient method are very useful for convex optimization problems, but can exhibit undesirable oscillations yielding slow convergence rates for some applications. An adaptive…

Optimization and Control · Mathematics 2019-06-14 Donghwan Kim , Jeffrey A. Fessler

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…

Optimization and Control · Mathematics 2015-10-27 Saeed Ghadimi , Guanghui Lan

We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…

Optimization and Control · Mathematics 2016-03-09 Tomoya Murata , Taiji Suzuki

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding…

Optimization and Control · Mathematics 2021-03-30 Konstantin Pieper , Daniel Walter

Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learning because of their efficiency. Existing theoretical studies…

Machine Learning · Computer Science 2026-05-28 Yunwen Lei , Zimeng Wang , Xiaoming Yuan