Related papers: A convergence analysis of the perturbed compositio…
We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…
Differentially private stochastic gradient descent (DP-SGD) has become the standard algorithm for training machine learning models with rigorous privacy guarantees. Despite its widespread use, the theoretical understanding of its long-run…
Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In this article, we study these types of methods through the…
Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference. Here, the target function is given as an integral over a family of (continuously) indexed target…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
Stein variational gradient descent (SVGD) is a kernel-based and non-parametric particle method for sampling from a target distribution, such as in Bayesian inference and other machine learning tasks. Different from other particle methods,…
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…
We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two…
This paper theoretically reanalyzes the convergence of the mini-batch stochastic gradient descent (SGD) for a structured minimization problem involving a finite-sum function with its gradient being stochastically approximated, and an…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
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…
Stochastic gradient descent (SGD) is the main algorithm behind a large body of work in machine learning. In many cases, constraints are enforced via projections, leading to projected stochastic gradient algorithms. In recent years, a large…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a…
We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $\tau$ rounds ago. First, we show that without stochastic…
This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear…
In this paper, we consider the convex and non-convex composition problem with the structure $\frac{1}{n}\sum\nolimits_{i = 1}^n {{F_i}( {G( x )} )}$, where $G( x )=\frac{1}{n}\sum\nolimits_{j = 1}^n {{G_j}( x )} $ is the inner function, and…
Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…