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Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of…

Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…

Stochastic Gradient Descent (SGD) is a popular optimization method which has been applied to many important machine learning tasks such as Support Vector Machines and Deep Neural Networks. In order to parallelize SGD, minibatch training is…

Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…

Despite the strong theoretical guarantees that variance-reduced finite-sum optimization algorithms enjoy, their applicability remains limited to cases where the memory overhead they introduce (SAG/SAGA), or the periodic full gradient…

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

When training a machine learning model with observational data, it is often encountered that some values are systemically missing. Learning from the incomplete data in which the missingness depends on some covariates may lead to biased…

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…

Machine learning, especially deep neural networks, has been rapidly developed in fields including computer vision, speech recognition and reinforcement learning. Although Mini-batch SGD is one of the most popular stochastic optimization…

Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD…

Stochastic gradient descent (SGD) is a powerful optimization technique that is particularly useful in online learning scenarios. Its convergence analysis is relatively well understood under the assumption that the data samples are…

In many applications involving large dataset or online updating, stochastic gradient descent (SGD) provides a scalable way to compute parameter estimates and has gained increasing popularity due to its numerical convenience and memory…

Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a…

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…

Stochastic Gradient Descent or SGD is the most popular optimization algorithm for large-scale problems. SGD estimates the gradient by uniform sampling with sample size one. There have been several other works that suggest faster epoch-wise…

Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite…