Related papers: A convergence study of SGD-type methods for stocha…
Stein Variational Gradient Descent (SVGD) is an important alternative to the Langevin-type algorithms for sampling from probability distributions of the form $\pi(x) \propto \exp(-V(x))$. In the existing theory of Langevin-type algorithms…
In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several…
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…
The article discusses distributed gradient-descent algorithms for computing local and global minima in nonconvex optimization. For local optimization, we focus on distributed stochastic gradient descent (D-SGD)--a simple network-based…
Variance reduction is a crucial tool for improving the slow convergence of stochastic gradient descent. Only a few variance-reduced methods, however, have yet been shown to directly benefit from Nesterov's acceleration techniques to match…
We study the stochastic optimization problem from a continuous-time perspective, with a focus on the Stochastic Gradient Descent with Momentum (SGDM) method. We show that the trajectory of SGDM, despite its \emph{stochastic} nature,…
In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…
As one of the most fundamental stochastic optimization algorithms, stochastic gradient descent (SGD) has been intensively developed and extensively applied in machine learning in the past decade. There have been some modified SGD-type…
This paper is concerned with convergence of stochastic gradient algorithms with momentum terms in the nonconvex setting. A class of stochastic momentum methods, including stochastic gradient descent, heavy ball, and Nesterov's accelerated…
We study first-order methods for convex optimization problems with functions $f$ satisfying the recently proposed $\ell$-smoothness condition $||\nabla^{2}f(x)|| \le \ell\left(||\nabla f(x)||\right),$ which generalizes the $L$-smoothness…
The extrapolation strategy raised by Nesterov, which can accelerate the convergence rate of gradient descent methods by orders of magnitude when dealing with smooth convex objective, has led to tremendous success in training machine…
The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any…
Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is…
First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning…
In this paper, we propose a simple variant of the original stochastic variance reduction gradient (SVRG), where hereafter we refer to as the variance reduced stochastic gradient descent (VR-SGD). Different from the choices of the snapshot…
Stochastic Gradient Descent (SGD) is a widely deployed optimization procedure throughout data-driven and simulation-driven disciplines, which has drawn a substantial interest in understanding its global behavior across a broad class of…
We consider a variant of the stochastic gradient descent (SGD) with a random learning rate and reveal its convergence properties. SGD is a widely used stochastic optimization algorithm in machine learning, especially deep learning. Numerous…
We analyze a class of stochastic gradient algorithms with momentum on a high-dimensional random least squares problem. Our framework, inspired by random matrix theory, provides an exact (deterministic) characterization for the sequence of…
Stochastic gradient descent with momentum (SGDM) is one of the most widely used optimization algorithms in machine learning. While optimization properties of SGDM have been extensively studied in the literature, it remains insufficiently…
We propose a class of \textit{Euler-Lagrange} equations indexed by a pair of parameters ($\alpha,r$) that generalizes Nesterov's accelerated gradient methods for convex ($\alpha=1$) and strongly convex ($\alpha=0$) functions from a…