相关论文: Increasing Batch Size Improves Convergence of Stoc…

Stochastic gradient descent~(SGD) and its variants have been the dominating optimization methods in machine learning. Compared to SGD with small-batch training, SGD with large-batch training can better utilize the computational power of…

The performance of mini-batch stochastic gradient descent (SGD) strongly depends on setting the batch size and learning rate to minimize the empirical loss in training the deep neural network. In this paper, we present theoretical analyses…

Stochastic gradient descent with momentum (SGDM) has been widely used in many machine learning and statistical applications. Despite the observed empirical benefits of SGDM over traditional SGD, the theoretical understanding of the role of…

We analyze the convergence behavior of stochastic gradient descent with momentum (SGDM) under dynamic learning-rate and batch-size schedules by introducing a novel and simpler Lyapunov function. We extend the existing theoretical framework…

Momentum has become a crucial component in deep learning optimizers, necessitating a comprehensive understanding of when and why it accelerates stochastic gradient descent (SGD). To address the question of ''when'', we establish a…

Mini-batch stochastic gradient descent (SGD) and variants thereof approximate the objective function's gradient with a small number of training examples, aka the batch size. Small batch sizes require little computation for each model update…

The mini-batch stochastic gradient descent (SGD) algorithm is widely used in training machine learning models, in particular deep learning models. We study SGD dynamics under linear regression and two-layer linear networks, with an easy…

Modern deep neural network training is typically based on mini-batch stochastic gradient optimization. While the use of large mini-batches increases the available computational parallelism, small batch training has been shown to provide…

Momentum is known to accelerate the convergence of gradient descent in strongly convex settings without stochastic gradient noise. In stochastic optimization, such as training neural networks, folklore suggests that momentum may help deep…

We investigate the dynamical and convergent properties of stochastic gradient descent (SGD) applied to Deep Neural Networks (DNNs). Characterizing the relation between learning rate, batch size and the properties of the final minima, such…

Mini-batch stochastic gradient methods (SGD) are state of the art for distributed training of deep neural networks. Drastic increases in the mini-batch sizes have lead to key efficiency and scalability gains in recent years. However,…

The goal of this paper is to accelerate the training of machine learning models, a critical challenge since the training of large-scale deep neural models can be computationally expensive. Stochastic gradient descent (SGD) and its variants…

Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…

Increasing the mini-batch size for stochastic gradient descent offers significant opportunities to reduce wall-clock training time, but there are a variety of theoretical and systems challenges that impede the widespread success of this…

Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received…

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well…

Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple…

The stochastic gradient descent (SGD) method and its variants are algorithms of choice for many Deep Learning tasks. These methods operate in a small-batch regime wherein a fraction of the training data, say $32$-$512$ data points, is…

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…

In order to extract the best possible performance from asynchronous stochastic gradient descent one must increase the mini-batch size and scale the learning rate accordingly. In order to achieve further speedup we introduce a technique that…