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We consider solving a convex, possibly stochastic optimization problem over a randomly time-varying multi-agent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the…

Optimization and Control · Mathematics 2016-11-29 Mingyi Hong , Tsung-Hui Chang

We consider a multi agent optimization problem where a set of agents collectively solves a global optimization problem with the objective function given by the sum of locally known convex functions. We focus on the case when information…

Optimization and Control · Mathematics 2016-03-14 Ali Makhdoumi , Asuman Ozdaglar

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…

Optimization and Control · Mathematics 2015-07-10 Tianyi Lin , Shiqian Ma , Shuzhong Zhang

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

This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed…

Optimization and Control · Mathematics 2015-03-20 Bahman Gharesifard , Jorge Cortes

In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…

Optimization and Control · Mathematics 2020-04-16 Darina Dvinskikh , Alexander Tyurin , Alexander Gasnikov , Sergey Omelchenko

We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…

Optimization and Control · Mathematics 2013-03-12 Nicolas Le Roux , Mark Schmidt , Francis Bach

We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…

Optimization and Control · Mathematics 2016-01-05 Ali Makhdoumi , Asuman Ozdaglar

In this paper, we propose a new framework to study distributed optimization problems with stochastic gradients by employing a multi-agent system with continuous-time dynamics. Here the goal of the agents is to cooperatively minimize the sum…

Systems and Control · Electrical Eng. & Systems 2026-02-10 Jianhua Sun , Kaihong Lu , Xin Yu

In this paper we consider the question of whether it is possible to apply a gradient averaging strategy to improve on the sublinear convergence rates without any increase in storage. Our analysis reveals that a positive answer requires an…

Optimization and Control · Mathematics 2020-02-26 Xin Xu , Xiaopeng Luo

We perform the first tight convergence analysis of the gradient method with varying step sizes when applied to smooth hypoconvex (weakly convex) functions. Hypoconvex functions are smooth nonconvex functions whose curvature is bounded and…

Optimization and Control · Mathematics 2022-06-22 Teodor Rotaru , François Glineur , Panagiotis Patrinos

We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…

Optimization and Control · Mathematics 2018-02-28 Benjamin Grimmer

The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and…

Machine Learning · Statistics 2020-03-03 Takayuki Kawashima , Hironori Fujisawa

We study the so-called distributed two-time-scale gradient method for solving convex optimization problems over a network of agents when the communication bandwidth between the nodes is limited, and so information that is exchanged between…

Systems and Control · Electrical Eng. & Systems 2021-06-01 Marcos M. Vasconcelos , Thinh T. Doan , Urbashi Mitra

It is well known that the optimal convergence rate for stochastic optimization of smooth functions is $O(1/\sqrt{T})$, which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing…

Machine Learning · Computer Science 2013-07-30 Mehrdad Mahdavi , Rong Jin

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Statistics Theory · Mathematics 2022-01-12 Antoine Godichon-Baggioni

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

Optimization and Control · Mathematics 2016-05-30 James Renegar

This paper considers a distributed optimization problem over a multi-agent network, in which the objective function is a sum of individual cost functions at the agents. We focus on the case when communication between the agents is described…

Optimization and Control · Mathematics 2017-11-01 Chenguang Xi , Van Sy Mai , Ran Xin , Eyad H. Abed , Usman A. Khan

Consider the problem of minimizing functions that are Lipschitz and strongly convex, but not necessarily differentiable. We prove that after $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/T)$ with…

Machine Learning · Computer Science 2018-12-14 Nicholas J. A. Harvey , Christopher Liaw , Yaniv Plan , Sikander Randhawa

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…

Machine Learning · Computer Science 2013-06-11 Francis Bach , Eric Moulines