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Understanding the convergence performance of asynchronous stochastic gradient descent method (Async-SGD) has received increasing attention in recent years due to their foundational role in machine learning. To date, however, most of the…

We propose mS2GD: a method incorporating a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent (S2GD). We consider the problem of minimizing a strongly convex function…

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

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…

We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The…

We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive…

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…

Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theoretical analyses of stochastic gradient algorithms. In this…

Stochastic gradient descent (SGD) has been shown to generalize well in many deep learning applications. In practice, one often runs SGD with a geometrically decaying stepsize, i.e., a constant initial stepsize followed by multiple geometric…

Stochastic gradient descent (SGD) and projected stochastic gradient descent (PSGD) are scalable algorithms to compute model parameters in unconstrained and constrained optimization problems. In comparison with SGD, PSGD forces its iterative…

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…

Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…

Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for…

We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in $\reals^d$. A simple and…

In this book chapter, we briefly describe the main components that constitute the gradient descent method and its accelerated and stochastic variants. We aim at explaining these components from a mathematical point of view, including…

Minimax optimal convergence rates for classes of stochastic convex optimization problems are well characterized, where the majority of results utilize iterate averaged stochastic gradient descent (SGD) with polynomially decaying step sizes.…

We give a sharp convergence rate for the asynchronous stochastic gradient descent (ASGD) algorithms when the loss function is a perturbed quadratic function based on the stochastic modified equations introduced in [An et al. Stochastic…

This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and…

In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and…

Stochastic gradient descent (SGD) is one of the most widely used optimization methods for parallel and distributed processing of large datasets. One of the key limitations of distributed SGD is the need to regularly communicate the…