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Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks has attracted continuing studies for the theoretical principles behind its success. A recent work reports an anomaly (inverse) relation between the…
This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…
Stochastic gradient descent (SGD) with constant momentum and its variants such as Adam are the optimization algorithms of choice for training deep neural networks (DNNs). Since DNN training is incredibly computationally expensive, there is…
Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…
An increasing number of machine learning problems, such as robust or adversarial variants of existing algorithms, require minimizing a loss function that is itself defined as a maximum. Carrying a loop of stochastic gradient ascent (SGA)…
SGD is the widely adopted method to train CNN. Conceptually it approximates the population with a randomly sampled batch; then it evenly trains batches by conducting a gradient update on every batch in an epoch. In this paper, we…
The classical convergence analysis of SGD is carried out under the assumption that the norm of the stochastic gradient is uniformly bounded. While this might hold for some loss functions, it is violated for cases where the objective…
Deep learning algorithms - typically consisting of a class of deep neural networks trained by a stochastic gradient descent (SGD) optimization method - are nowadays the key ingredients in many artificial intelligence (AI) systems and have…
Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA)…
This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…
Local stochastic gradient descent (Local-SGD), also referred to as federated averaging, is an approach to distributed optimization where each device performs more than one SGD update per communication. This work presents an empirical study…
Stochastic gradient descent (SGD) algorithm is the method of choice in many machine learning tasks thanks to its scalability and efficiency in dealing with large-scale problems. In this paper, we focus on the shuffling version of SGD which…
Stochastic optimization via Stochastic Gradient Descent (SGD) is a fundamental problem in statistics and optimization. This paper revisits Stochastic Gradient Descent (SGD) for strongly convex objectives, establishing tight, uniform-in-time…
Modern machine learning focuses on highly expressive models that are able to fit or interpolate the data completely, resulting in zero training loss. For such models, we show that the stochastic gradients of common loss functions satisfy a…
Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…
Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…
We develop a framework for analyzing the training and learning rate dynamics on a variety of high- dimensional optimization problems trained using one-pass stochastic gradient descent (SGD) with data generated from multiple anisotropic…
Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD). The Normalized Gradient…