Related papers: Differential Equations for Modeling Asynchronous A…
The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any…
We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions which consist of the sum of…
A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (i) To find a lower bound on the number of times that the…
We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…
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…
Asynchronous stochastic gradient descent (SGD) is attractive from a speed perspective because workers do not wait for synchronization. However, the Transformer model converges poorly with asynchronous SGD, resulting in substantially lower…
We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two…
Recently, Stochastic Gradient Descent (SGD) and its variants have become the dominant methods in the large-scale optimization of machine learning (ML) problems. A variety of strategies have been proposed for tuning the step sizes, ranging…
We propose AEGD, a new algorithm for first-order gradient-based optimization of non-convex objective functions, based on a dynamically updated energy variable. The method is shown to be unconditionally energy stable, irrespective of the…
Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…
In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…
Due to its simplicity and outstanding ability to generalize, stochastic gradient descent (SGD) is still the most widely used optimization method despite its slow convergence. Meanwhile, adaptive methods have attracted rising attention of…
Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with…
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…
In the realm of big data and machine learning, data-parallel, distributed stochastic algorithms have drawn significant attention in the present days.~While the synchronous versions of these algorithms are well understood in terms of their…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
Many machine learning applications and tasks rely on the stochastic gradient descent (SGD) algorithm and its variants. Effective step length selection is crucial for the success of these algorithms, which has motivated the development of…
The stochastic gradient descent (SGD) algorithm is widely used for parameter estimation, especially for huge data sets and online learning. While this recursive algorithm is popular for computation and memory efficiency, quantifying…
Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate…