Related papers: Gradient-Based Non-Linear Inverse Learning
Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…
Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received…
In this paper, we introduce the tamed stochastic gradient descent method (TSGD) for optimization problems. Inspired by the tamed Euler scheme, which is a commonly used method within the context of stochastic differential equations, TSGD is…
We study the asynchronous stochastic gradient descent algorithm for distributed training over $n$ workers which have varying computation and communication frequency over time. In this algorithm, workers compute stochastic gradients in…
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…
We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix…
Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
Theoretically understanding stochastic gradient descent (SGD) in overparameterized models has led to the development of several optimization algorithms that are widely used in practice today. Recent work by~\citet{zou2021benign} provides…
Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…
Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD)…
We consider stochastic gradient descent and its averaging variant for binary classification problems in a reproducing kernel Hilbert space. In the traditional analysis using a consistency property of loss functions, it is known that the…
We study continual learning on multiple linear classification tasks by sequentially running gradient descent (GD) for a fixed budget of iterations per task. When all tasks are jointly linearly separable and are presented in a cyclic/random…
In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\bf RSGD}, can achieve a \textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems…
Many real-world data are sequentially collected over time and often exhibit skewed class distributions, resulting in imbalanced data streams. While existing approaches have explored several strategies, such as resampling and reweighting,…
We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable dataset. The classifier is described by a nonlinear ReLU model and the objective function adopts the exponential…
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…
We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty…