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It is well known that both gradient descent and stochastic coordinate descent achieve a global convergence rate of $O(1/k)$ in the objective value, when applied to a scheme for minimizing a Lipschitz-continuously differentiable,…

Optimization and Control · Mathematics 2019-05-15 Ching-pei Lee , Stephen J. Wright

We investigate the convergence rate of the recently proposed subgradient-push method for distributed optimization over time-varying directed graphs. The subgradient-push method can be implemented in a distributed way without requiring…

Optimization and Control · Mathematics 2015-02-17 Angelia Nedic , Alex Olshevsky

In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…

Optimization and Control · Mathematics 2023-03-23 Max Grieshammer , Lukas Pflug , Michael Stingl , Andrian Uihlein

We propose a first-order method for stochastic strongly convex optimization that attains $O(1/n)$ rate of convergence, analysis show that the proposed method is simple, easily to implement, and in worst case, asymptotically four times…

Optimization and Control · Mathematics 2011-10-14 Peng Cheng

The proximal inertial gradient descent is efficient for the composite minimization and applicable for broad of machine learning problems. In this paper, we revisit the computational complexity of this algorithm and present other novel…

Optimization and Control · Mathematics 2019-07-19 Tao Sun , Linbo Qiao , Dongsheng Li

We establish the O($\frac{1}{k}$) convergence rate for distributed stochastic gradient methods that operate over strongly convex costs and random networks. The considered class of methods is standard each node performs a weighted average of…

Optimization and Control · Mathematics 2018-03-22 Dusan Jakovetic , Dragana Bajovic , Anit Kumar Sahu , Soummya Kar

We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…

Optimization and Control · Mathematics 2019-12-17 Andrzej Ruszczynski

Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep…

Optimization and Control · Mathematics 2020-02-12 Yu-Guan Hsieh , Franck Iutzeler , Jérôme Malick , Panayotis Mertikopoulos

Sign stochastic gradient descent (signSGD) is a communication-efficient method that transmits only the sign of stochastic gradients for parameter updating. Existing literature has demonstrated that signSGD can achieve a convergence rate of…

Machine Learning · Computer Science 2024-12-16 Wei Jiang , Sifan Yang , Wenhao Yang , Lijun Zhang

In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a…

Optimization and Control · Mathematics 2018-09-19 Damek Davis , Benjamin Grimmer

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in…

Optimization and Control · Mathematics 2016-05-12 Mark Schmidt , Nicolas Le Roux , Francis Bach

We prove that the proximal stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$. As a consequence, we resolve an open question on the convergence…

Optimization and Control · Mathematics 2018-02-21 Damek Davis , Dmitriy Drusvyatskiy

Recently, distributed dual averaging has received increasing attention due to its superiority in handling constraints and dynamic networks in multiagent optimization. However, all distributed dual averaging methods reported so far…

Optimization and Control · Mathematics 2020-03-20 Changxin Liu , Huiping Li , Yang Shi

Projective splitting is a family of methods for solving inclusions involving sums of maximal monotone operators. First introduced by Eckstein and Svaiter in 2008, these methods have enjoyed significant innovation in recent years, becoming…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Jonathan Eckstein

We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…

Optimization and Control · Mathematics 2021-07-09 Vyacheslav Kungurtsev , Vladimir Shikhman

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

The aim of this paper is to deepen the convergence analysis of the scaled gradient projection (SGP) method, proposed by Bonettini et al. in a recent paper for constrained smooth optimization. The main feature of SGP is the presence of a…

Numerical Analysis · Mathematics 2015-09-10 Silvia Bonettini , Marco Prato

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

Optimization and Control · Mathematics 2025-02-25 Chenhao Yu , Yusu Hong , Junhong Lin

We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…

Optimization and Control · Mathematics 2018-12-04 Tomoya Murata , Taiji Suzuki

This work establishes new convergence guarantees for gradient descent in smooth convex optimization via a computer-assisted analysis technique. Our theory allows nonconstant stepsize policies with frequent long steps potentially violating…

Optimization and Control · Mathematics 2024-02-06 Benjamin Grimmer