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We study the trade-offs between convergence rate and robustness to gradient errors in designing a first-order algorithm. We focus on gradient descent (GD) and accelerated gradient (AG) methods for minimizing strongly convex functions when…

Optimization and Control · Mathematics 2019-11-07 Necdet Serhat Aybat , Alireza Fallah , Mert Gurbuzbalaban , Asuman Ozdaglar

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

In this study, we revisit the convergence of AdaGrad with momentum (covering AdaGrad as a special case) on non-convex smooth optimization problems. We consider a general noise model where the noise magnitude is controlled by the function…

Optimization and Control · Mathematics 2024-09-16 Yusu Hong , Junhong Lin

The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…

Machine Learning · Computer Science 2026-01-27 Naoki Sato , Hideaki Iiduka

We propose a novel randomized incremental gradient algorithm, namely, VAriance-Reduced Accelerated Gradient (Varag), for finite-sum optimization. Equipped with a unified step-size policy that adjusts itself to the value of the condition…

Optimization and Control · Mathematics 2019-11-01 Guanghui Lan , Zhize Li , Yi Zhou

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

Stochastic optimization naturally appear in many application areas, including machine learning. Our goal is to go further in the analysis of the Stochastic Average Gradient Accelerated (SAGA) algorithm. To achieve this, we introduce a new…

Optimization and Control · Mathematics 2024-10-08 Luis Fredes , Bernard Bercu , Eméric Gbaguidi

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

Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some…

Optimization and Control · Mathematics 2023-10-10 Binghui Xie , Chenhan Jin , Kaiwen Zhou , James Cheng , Wei Meng

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

Machine Learning · Computer Science 2022-04-19 Gideon Dresdner , Maria-Luiza Vladarean , Gunnar Rätsch , Francesco Locatello , Volkan Cevher , Alp Yurtsever

In this work we explore the fundamental structure-adaptiveness of state of the art randomized first order algorithms on regularized empirical risk minimization tasks, where the solution has intrinsic low-dimensional structure (such as…

Optimization and Control · Mathematics 2017-12-13 Junqi Tang , Francis Bach , Mohammad Golbabaee , Mike Davies

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

Machine Learning · Statistics 2015-06-11 Atsushi Nitanda

Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…

Numerical Analysis · Mathematics 2022-01-19 Bangti Jin , Zehui Zhou , Jun Zou

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…

Optimization and Control · Mathematics 2018-11-13 Aryan Mokhtari , Hamed Hassani , Amin Karbasi

We study stochastic algorithms for solving nonconvex optimization problems with a convex yet possibly nonsmooth regularizer, which find wide applications in many practical machine learning applications. However, compared to asynchronous…

Machine Learning · Computer Science 2018-09-18 Rui Zhu , Di Niu , Zongpeng Li

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

Optimization and Control · Mathematics 2019-05-15 Michael R. Metel , Akiko Takeda

We present the remote stochastic gradient (RSG) method, which computes the gradients at configurable remote observation points, in order to improve the convergence rate and suppress gradient noise at the same time for different curvatures.…

Machine Learning · Computer Science 2020-09-08 Yushu Chen , Hao Jing , Wenlai Zhao , Zhiqiang Liu , Ouyi Li , Liang Qiao , Wei Xue , Guangwen Yang

Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these…

Optimization and Control · Mathematics 2025-05-28 Tuo Liu , El Mehdi Saad , Wojciech Kotłowski , Francesco Orabona

We develop universal gradient methods for Stochastic Convex Optimization (SCO). Our algorithms automatically adapt not only to the oracle's noise but also to the H\"older smoothness of the objective function without a priori knowledge of…

Optimization and Control · Mathematics 2024-07-12 Anton Rodomanov , Ali Kavis , Yongtao Wu , Kimon Antonakopoulos , Volkan Cevher

We aim to make stochastic gradient descent (SGD) adaptive to (i) the noise $\sigma^2$ in the stochastic gradients and (ii) problem-dependent constants. When minimizing smooth, strongly-convex functions with condition number $\kappa$, we…

Optimization and Control · Mathematics 2026-03-24 Sharan Vaswani , Benjamin Dubois-Taine , Reza Babanezhad