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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…

We study the learning dynamics of a multi-pass, mini-batch Stochastic Gradient Descent (SGD) procedure for empirical risk minimization in high-dimensional multi-index models with isotropic random data. In an asymptotic regime where the…

Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…

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…

Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy intermediate-scale quantum (NISQ) processors. Such systems leverage classical optimization to tune the parameters of a…

Distributed stochastic gradient descent (SGD) algorithms are widely deployed in training large-scale deep learning models, while the communication overhead among workers becomes the new system bottleneck. Recently proposed gradient…

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…

We develop a high-dimensional scaling limit for Stochastic Gradient Descent with Polyak Momentum (SGD-M) and adaptive step-sizes. This provides a framework to rigourously compare online SGD with some of its popular variants. We show that…

Stochastic Gradient Descent (SGD) has become one of the most popular optimization methods for training machine learning models on massive datasets. However, SGD suffers from two main drawbacks: (i) The noisy gradient updates have high…

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

We investigate the problem of learning a Single Index Model (SIM)- a popular model for studying the ability of neural networks to learn features - from anisotropic Gaussian inputs by training a neuron using vanilla Stochastic Gradient…

Explaining the generalization characteristics of deep learning is an emerging topic in advanced machine learning. There are several unanswered questions about how learning under stochastic optimization really works and why certain…

Stochastic gradient descent (SGD) is one of the most widely used optimization methods for solving various machine learning problems. SGD solves an optimization problem by iteratively sampling a few data points from the input data, computing…

Low-precision training has become crucial for reducing the computational and memory costs of large-scale deep learning. However, quantizing gradients introduces magnitude shrinkage, which can change how stochastic gradient descent (SGD)…

Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and…

Generalization is one of the most important problems in deep learning (DL). In the overparameterized regime in neural networks, there exist many low-loss solutions that fit the training data equally well. The key question is which solution…

We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\boldsymbol{x}\in \mathbb{R}^d$ is Gaussian and the target $y \in \mathbb{R}$ follows a…

Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms.…

We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on…

Understanding the implicit bias of Stochastic Gradient Descent (SGD) is one of the key challenges in deep learning, especially for overparametrized models, where the local minimizers of the loss function $L$ can form a manifold.…