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In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…

Optimization and Control · Mathematics 2018-08-09 Ion Necoara , Martin Takac

Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal…

Optimization and Control · Mathematics 2016-05-24 Yitan Li , Linli Xu , Xiaowei Zhong , Qing Ling

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Machine Learning · Computer Science 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

Variants of the coordinate descent approach for minimizing a nonlinear function are distinguished in part by the order in which coordinates are considered for relaxation. Three common orderings are cyclic (CCD), in which we cycle through…

Optimization and Control · Mathematics 2018-06-05 Ching-Pei Lee , Stephen J. Wright

We describe an asynchronous parallel stochastic proximal coordinate descent algorithm for minimizing a composite objective function, which consists of a smooth convex function plus a separable convex function. In contrast to previous…

Optimization and Control · Mathematics 2015-12-14 Ji Liu , Stephen J. Wright

Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For…

Optimization and Control · Mathematics 2018-04-04 Daoli Zhu , Lei Zhao

While classical forms of stochastic gradient descent algorithm treat the different coordinates in the same way, a framework allowing for adaptive (non uniform) coordinate sampling is developed to leverage structure in data. In a non-convex…

Machine Learning · Statistics 2022-10-18 Rémi Leluc , François Portier

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of…

Machine Learning · Statistics 2020-09-07 Andrei Kulunchakov , Julien Mairal

We propose a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent applied to the problem of minimizing a strongly convex composite function represented as the sum of an…

Machine Learning · Computer Science 2014-10-20 Jakub Konečný , Jie Liu , Peter Richtárik , Martin Takáč

Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…

Optimization and Control · Mathematics 2026-01-15 Amir M. Vahedi , Horea T. Ilies

We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…

Computation · Statistics 2022-04-19 Hanyu Li , Chengmei Niu

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

Optimization and Control · Mathematics 2019-12-19 Jonathan Lacotte , Mert Pilanci , Marco Pavone

Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts…

Machine Learning · Statistics 2017-02-23 Xi-Lin Li

Randomized coordinate descent (RCD) methods are state-of-the-art algorithms for training linear predictors via minimizing regularized empirical risk. When the number of examples ($n$) is much larger than the number of features ($d$), a…

Optimization and Control · Mathematics 2016-05-31 Dominik Csiba , Peter Richtárik

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

Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…

Optimization and Control · Mathematics 2022-10-06 Melinda Hagedorn , Florian Jarre

We present and analyse a backtracking strategy for a general Fast Iterative Shrinkage/Thresholding Algorithm which has been recently proposed in (Chambolle, Pock, 2016) for strongly convex objective functions. Differently from classical…

Optimization and Control · Mathematics 2019-01-04 Luca Calatroni , Antonin Chambolle

Recent theoretical developments in coset coding theory have provided continuous-valued functions which give the equivocation and maximum likelihood (ML) decoding probability of coset secrecy codes. In this work, we develop a method for…

Information Theory · Computer Science 2024-05-28 David Hunn , Willie K. Harrison

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform…

Machine Learning · Statistics 2015-01-05 Peilin Zhao , Tong Zhang

We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have…

Computation · Statistics 2007-12-18 Jerome Friedman , Trevor Hastie , Holger Höfling , Robert Tibshirani