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Asynchronous stochastic gradient descent (ASGD) is a standard way to exploit heterogeneous compute resources in distributed learning: instead of forcing fast workers to wait for slow ones, the server updates the model whenever a gradient…
Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…
Stochastic Gradient Descent (SGD) is widely used in machine learning problems to efficiently perform empirical risk minimization, yet, in practice, SGD is known to stall before reaching the actual minimizer of the empirical risk. SGD…
Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some…
With the fast development of deep learning, it has become common to learn big neural networks using massive training data. Asynchronous Stochastic Gradient Descent (ASGD) is widely adopted to fulfill this task for its efficiency, which is,…
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…
Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimensional settings are rarely understood. In this paper, we provide…
The existing analysis of asynchronous stochastic gradient descent (SGD) degrades dramatically when any delay is large, giving the impression that performance depends primarily on the delay. On the contrary, we prove much better guarantees…
The increasing scale of data propels the popularity of leveraging parallelism to speed up the optimization. Minibatch stochastic gradient descent (minibatch SGD) and local SGD are two popular methods for parallel optimization. The existing…
We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for…
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…
Continual learning, focused on sequentially learning multiple tasks, has gained significant attention recently. Despite the tremendous progress made in the past, the theoretical understanding, especially factors contributing to catastrophic…
Exponential moving average (EMA) has recently gained significant popularity in training modern deep learning models, especially diffusion-based generative models. However, there have been few theoretical results explaining the effectiveness…
In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…
We study the problem of transfer learning and fine-tuning in linear models for both regression and binary classification. In particular, we consider the use of stochastic gradient descent (SGD) on a linear model initialized with pretrained…
Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regression and online stochastic gradient descent (SGD) are…
Stochastic gradient descent (SGD) is a pillar of modern machine learning, serving as the go-to optimization algorithm for a diverse array of problems. While the empirical success of SGD is often attributed to its computational efficiency…
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…
Variance reduction (VR) techniques for convergence rate acceleration of stochastic gradient descent (SGD) algorithm have been developed with great efforts recently. VR's two variants, stochastic variance-reduced-gradient (SVRG-SGD) and…
We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…