Related papers: On the Convergence Proof of AMSGrad and a New Vers…

Since its invention in 2014, the Adam optimizer has received tremendous attention. On one hand, it has been widely used in deep learning and many variants have been proposed, while on the other hand their theoretical convergence property…

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not…

One of the most popular training algorithms for deep neural networks is the Adaptive Moment Estimation (Adam) introduced by Kingma and Ba. Despite its success in many applications there is no satisfactory convergence analysis: only local…

Adaptive gradient methods such as Adam have gained extreme popularity due to their success in training complex neural networks and less sensitivity to hyperparameter tuning compared to SGD. However, it has been recently shown that Adam can…

Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In practically relevant training problems, usually not the plain…

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…

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving…

Following the introduction of Adam, several novel adaptive optimizers for deep learning have been proposed. These optimizers typically excel in some tasks but may not outperform Adam uniformly across all tasks. In this work, we introduce…

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared…

Adaptive Moment Estimation (Adam) is a cornerstone optimization algorithm in deep learning, widely recognized for its flexibility with adaptive learning rates and efficiency in handling large-scale data. However, despite its practical…

Optimization is essential in deep learning. The foundational method upon which most optimizers are built is momentum-based stochastic gradient descent. However, it suffers from two key drawbacks. First, it has noisy and varying gradients,…

A common way to train neural networks is the Backpropagation. This algorithm includes a gradient descent method, which needs an adaptive step size. In the area of neural networks, the ADAM-Optimizer is one of the most popular adaptive step…

Beside the standard stochastic gradient descent (SGD) method, the Adam optimizer due to Kingma & Ba (2014) is currently probably the best-known optimization method for the training of deep neural networks in artificial intelligence (AI)…

In this paper, we provide a rigorous proof of convergence of the Adaptive Moment Estimate (Adam) algorithm for a wide class of optimization objectives. Despite the popularity and efficiency of the Adam algorithm in training deep neural…

Adam is one of the most popular optimization algorithms in deep learning. However, it is known that Adam does not converge in theory unless choosing a hyperparameter, i.e., $\beta_2$, in a problem-dependent manner. There have been many…

Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…

Adaptive learning rate methods have been successfully applied in many fields, especially in training deep neural networks. Recent results have shown that adaptive methods with exponential increasing weights on squared past gradients (i.e.,…

Adam is a widely used stochastic optimization method for deep learning applications. While practitioners prefer Adam because it requires less parameter tuning, its use is problematic from a theoretical point of view since it may not…

Adam and RMSProp are two of the most influential adaptive stochastic algorithms for training deep neural networks, which have been pointed out to be divergent even in the convex setting via a few simple counterexamples. Many attempts, such…

Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of…