Related papers: Katyusha X: Practical Momentum Method for Stochast…

Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding…

We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…

In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum hemivariational inequality (HVI) problem. In this HVI problem, the associated function is assumed to be differentiable, and both the vector…

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…

The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: $\min_x~(\mathbb{E}_iF_i \circ \mathbb{E}_j G_j)(x).$ It summarizes many important applications…

We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…

This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient…

This paper considers a class of convex constrained nonsmooth convex stochastic composite optimization problems whose objective function is given by the summation of a differentiable convex component, together with a general nonsmooth but…

Many classical algorithms are found until several years later to outlive the confines in which they were conceived, and continue to be relevant in unforeseen settings. In this paper, we show that SVRG is one such method: being originally…

The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…

In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors…

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…

In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), a new algorithm for the convex finite-sum minimization problems. Our method integrates the traditional Nesterov's acceleration momentum with different shuffling…

We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in…

Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learning because of their efficiency. Existing theoretical studies…

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…

In convex optimization, the problem of finding near-stationary points has not been adequately studied yet, unlike other optimality measures such as the function value. Even in the deterministic case, the optimal method (OGM-G, due to Kim…

Consider the problem of minimizing the expected value of a cost function parameterized by a random variable. The classical sample average approximation (SAA) method for solving this problem requires minimization of an ensemble average of…

It is known that adaptive optimization algorithms represent the key pillar behind the rise of the Machine Learning field. In the Optimization literature numerous studies have been devoted to accelerated gradient methods but only recently…