Related papers: Large deviations rates for stochastic gradient des…
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…
Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the…
Stochastic Gradient Descent (SGD) and its variants are the most used algorithms in machine learning applications. In particular, SGD with adaptive learning rates and momentum is the industry standard to train deep networks. Despite the…
The stochastic gradient noise (SGN) is a significant factor in the success of stochastic gradient descent (SGD). Following the central limit theorem, SGN was initially modeled as Gaussian, and lately, it has been suggested that stochastic…
The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the \emph{classical} central limit theorem (CLT) kicks in. This assumption is often made…
In this paper, we are concerned with differentially private {stochastic gradient descent (SGD)} algorithms in the setting of stochastic convex optimization (SCO). Most of the existing work requires the loss to be Lipschitz continuous and…
In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an…
We investigate how the final parameters found by stochastic gradient descent are influenced by over-parameterization. We generate families of models by increasing the number of channels in a base network, and then perform a large…
Understanding stochastic gradient descent (SGD) and its variants is essential for machine learning. However, most of the preceding analyses are conducted under amenable conditions such as unbiased gradient estimator and bounded objective…
Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…
The stochastic gradient descent (SGD) method and its variants are algorithms of choice for many Deep Learning tasks. These methods operate in a small-batch regime wherein a fraction of the training data, say $32$-$512$ data points, is…
Stochastic gradient descent (SGD) has been studied extensively over the past decades due to its simplicity and broad applicability in machine learning. In this work, we analyze the local behavior of gradient descent and stochastic gradient…
Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…
We study trade-offs between convergence rate and robustness to gradient errors in the context of first-order methods. Our focus is on generalized momentum methods (GMMs)--a broad class that includes Nesterov's accelerated gradient,…
Stochastic Gradient Descent (SGD) has become a cornerstone of neural network optimization due to its computational efficiency and generalization capabilities. However, the gradient noise introduced by SGD is often assumed to be uncorrelated…
We study how the batch size affects the total gradient variance in differentially private stochastic gradient descent (DP-SGD), seeking a theoretical explanation for the usefulness of large batch sizes. As DP-SGD is the basis of modern DP…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. The current mathematical theory in the lens of regularization theory predicts that…
The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale…
Previous works on stochastic gradient descent (SGD) often focus on its success. In this work, we construct worst-case optimization problems illustrating that, when not in the regimes that the previous works often assume, SGD can exhibit…
Accelerated stochastic gradient descent (ASGD) is a workhorse in deep learning and often achieves better generalization performance than SGD. However, existing optimization theory can only explain the faster convergence of ASGD, but cannot…