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

Classical stochastic gradient methods for optimization rely on noisy gradient approximations that become progressively less accurate as iterates approach a solution. The large noise and small signal in the resulting gradients makes it…

For nonconvex objective functions, including those found in training deep neural networks, stochastic gradient descent (SGD) with momentum is said to converge faster and have better generalizability than SGD without momentum. In particular,…

Momentum methods were originally introduced for their superiority to stochastic gradient descent (SGD) in deterministic settings with convex objective functions. However, despite their widespread application to deep neural networks -- a…

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)…

This paper theoretically reanalyzes the convergence of the mini-batch stochastic gradient descent (SGD) for a structured minimization problem involving a finite-sum function with its gradient being stochastically approximated, and an…

Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which…

Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…

Stochastic gradient descent (SGD) is an estimation tool for large data employed in machine learning and statistics. Due to the Markovian nature of the SGD process, inference is a challenging problem. An underlying asymptotic normality of…

Momentum plays a crucial role in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated…

It is well known that, for most datasets, the use of large-size minibatches for Stochastic Gradient Descent (SGD) typically leads to slow convergence and poor generalization. On the other hand, large minibatches are of great practical…

In value-based deep reinforcement learning with replay memories, the batch size parameter specifies how many transitions to sample for each gradient update. Although critical to the learning process, this value is typically not adjusted…

Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…

SGD with momentum (SGDM) has been widely applied in many machine learning tasks, and it is often applied with dynamic stepsizes and momentum weights tuned in a stagewise manner. Despite of its empirical advantage over SGD, the role of…

Stochastic Gradient Descent (SGD) and its variants are almost universally used to train neural networks and to fit a variety of other parametric models. An important hyperparameter in this context is the batch size, which determines how…

LLM training is resource-intensive. Quantized training improves computational and memory efficiency but introduces quantization noise, which can hinder convergence and degrade model accuracy. Stochastic Rounding (SR) has emerged as a…

With an increasing demand for training powers for deep learning algorithms and the rapid growth of computation resources in data centers, it is desirable to dynamically schedule different distributed deep learning tasks to maximize resource…

Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…

Training deep neural networks with Stochastic Gradient Descent, or its variants, requires careful choice of both learning rate and batch size. While smaller batch sizes generally converge in fewer training epochs, larger batch sizes offer…

The convergence behavior of mini-batch stochastic gradient descent (SGD) is highly sensitive to the batch size and learning rate settings. Recent theoretical studies have identified the existence of a critical batch size that minimizes…

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…