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Communication has been seen as a significant bottleneck in industrial applications over large-scale networks. To alleviate the communication burden, sign-based optimization algorithms have gained popularity recently in both industrial and…
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…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
Since the 21st century, artificial intelligence has been leading a new round of industrial revolution. Under the training framework, the optimization algorithm aims to stably converge high-dimensional optimization to local and even global…
Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid…
Stochastic gradient descent (SGD) and its many variants are the widespread optimization algorithms for training deep neural networks. However, SGD suffers from inevitable drawbacks, including vanishing gradients, lack of theoretical…
Adam is known to perform significantly better than Stochastic Gradient Descent (SGD) in language models, a phenomenon for which a number of explanations have been proposed. In this work, we revisit this "optimizer gap" through a series of…
The adaptive moment estimation (Adam) optimizer proposed by Kingma & Ba (2014) is presumably the most popular stochastic gradient descent (SGD) optimization method for the training of deep neural networks (DNNs) in artificial intelligence…
Adam-type optimizers, as a class of adaptive moment estimation methods with the exponential moving average scheme, have been successfully used in many applications of deep learning. Such methods are appealing due to the capability on…
This article introduces a novel family of optimization algorithms - Anisotropic Gaussian Smoothing Gradient Descent (AGS-GD), AGS-Stochastic Gradient Descent (AGS-SGD), and AGS-Adam - that employ anisotropic Gaussian smoothing to enhance…
We give a sharp convergence rate for the asynchronous stochastic gradient descent (ASGD) algorithms when the loss function is a perturbed quadratic function based on the stochastic modified equations introduced in [An et al. Stochastic…
Adam is a popular and widely used adaptive gradient method in deep learning, which has also received tremendous focus in theoretical research. However, most existing theoretical work primarily analyzes its full-batch version, which differs…
Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence…
Stochastic gradient algorithms are often unstable when applied to functions that do not have Lipschitz-continuous and/or bounded gradients. Gradient clipping is a simple and effective technique to stabilize the training process for problems…
Stochastic gradient descent (SGD) is a workhorse algorithm for solving large-scale optimization problems in data science and machine learning. Understanding the convergence of SGD is hence of fundamental importance. In this work we examine…
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 introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…
Adaptive optimizers, such as Adam, have achieved remarkable success in deep learning. A key component of these optimizers is the so-called preconditioning matrix, providing enhanced gradient information and regulating the step size of each…
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…
Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…