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Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…

Optimization and Control · Mathematics 2019-02-06 Yi Xu , Zhuoning Yuan , Sen Yang , Rong Jin , Tianbao Yang

We consider the nonsmooth convex composition optimization problem where the objective is a composition of two finite-sum functions and analyze stochastic compositional variance reduced gradient (SCVRG) methods for them. SCVRG and its…

Optimization and Control · Mathematics 2019-08-01 Tianyi Lin , Chenyou Fan , Mengdi Wang

This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…

Optimization and Control · Mathematics 2021-10-15 Shengjun Zhang , Colleen P. Bailey

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…

Machine Learning · Computer Science 2015-07-28 Elad Hazan , Kfir Y. Levy , Shai Shalev-Shwartz

We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…

Optimization and Control · Mathematics 2025-12-24 Zepeng Wang , Juan Peypouquet

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

In this paper, we propose a new SVRG-style acceleated stochastic algorithm for solving a family of non-convex optimization problems whose objective consists of a sum of $n$ smooth functions and a non-smooth convex function. Our major goal…

Optimization and Control · Mathematics 2019-03-12 Zaiyi Chen , Yi Xu , Haoyuan Hu , Tianbao Yang

We study the problem of minimizing the average of a very large number of smooth functions, which is of key importance in training supervised learning models. One of the most celebrated methods in this context is the SAGA algorithm. Despite…

Machine Learning · Computer Science 2019-01-28 Xu Qian , Zheng Qu , Peter Richtárik

This paper studies an acceleration technique for incremental aggregated gradient ({\sf IAG}) method through the use of \emph{curvature} information for solving strongly convex finite sum optimization problems. These optimization problems of…

Optimization and Control · Mathematics 2020-03-02 Hoi-To Wai , Wei Shi , Cesar A. Uribe , Angelia Nedich , Anna Scaglione

In this work, we present and analyze C-SAGA, a (deterministic) cyclic variant of SAGA. C-SAGA is an incremental gradient method that minimizes a sum of differentiable convex functions by cyclically accessing their gradients. Even though the…

Optimization and Control · Mathematics 2020-01-10 Youngsuk Park , Ernest K. Ryu

We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses…

Optimization and Control · Mathematics 2018-10-30 Hoi-To Wai , Nikolaos M. Freris , Angelia Nedic , Anna Scaglione

The stochastic proximal gradient method is a powerful generalization of the widely used stochastic gradient descent (SGD) method and has found numerous applications in Machine Learning. However, it is notoriously known that this method…

Optimization and Control · Mathematics 2024-12-10 Yuan Gao , Anton Rodomanov , Sebastian U. Stich

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Optimization and Control · Mathematics 2025-07-22 Raghu Bollapragada , Shagun Gupta

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the…

Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the…

Machine Learning · Computer Science 2022-05-23 Ziyi Chen , Shaocong Ma , Yi Zhou

We study accelerated optimization methods in the Gaussian phase retrieval problem. In this setting, we prove that gradient methods with Polyak or Nesterov momentum have similar implicit regularization to gradient descent. This implicit…

Optimization and Control · Mathematics 2023-11-23 Tyler Maunu , Martin Molina-Fructuoso

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function $F(w)=\frac{1}{n}…

Optimization and Control · Mathematics 2019-04-24 Lam M. Nguyen , Marten van Dijk , Dzung T. Phan , Phuong Ha Nguyen , Tsui-Wei Weng , Jayant R. Kalagnanam

In this paper, we investigate accelerated first-order methods for smooth convex optimization problems under inexact information on the gradient of the objective. The noise in the gradient is considered to be additive with two possibilities:…

Optimization and Control · Mathematics 2023-01-10 Vasin Artem , Alexander Gasnikov , Pavel Dvurechensky , Vladimir Spokoiny

We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems. SAPALM is the first…

Optimization and Control · Mathematics 2016-06-09 Damek Davis , Brent Edmunds , Madeleine Udell

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

Optimization and Control · Mathematics 2018-05-01 James V. Burke , Frank E. Curtis , Adrian S. Lewis , Michael L. Overton , Lucas E. A. Simões