Related papers: Theoretical analysis of Adam using hyperparameters…
Adam is widely adopted in practical applications due to its fast convergence. However, its theoretical analysis is still far from satisfactory. Existing convergence analyses for Adam rely on the bounded smoothness assumption, referred to as…
Although ADAM is a very popular algorithm for optimizing the weights of neural networks, it has been recently shown that it can diverge even in simple convex optimization examples. Several variants of ADAM have been proposed to circumvent…
Adam is one of the most influential adaptive stochastic algorithms for training deep neural networks, which has been pointed out to be divergent even in the simple convex setting via a few simple counterexamples. Many attempts, such as…
In this paper, we study the convergence of the Adaptive Moment Estimation (Adam) algorithm under unconstrained non-convex smooth stochastic optimizations. Despite the widespread usage in machine learning areas, its theoretical properties…
In neural network training, RMSProp and Adam remain widely favoured optimisation algorithms. One of the keys to their performance lies in selecting the correct step size, which can significantly influence their effectiveness. Additionally,…
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…
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…
This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which…
The Adaptive Momentum Estimation (Adam) algorithm is highly effective in training various deep learning tasks. Despite this, there's limited theoretical understanding for Adam, especially when focusing on its vanilla form in non-convex…
Optimizing deep neural networks is largely thought to be an empirical process, requiring manual tuning of several hyper-parameters, such as learning rate, weight decay, and dropout rate. Arguably, the learning rate is the most important of…
The generalization performance of deep neural networks with regard to the optimization algorithm is one of the major concerns in machine learning. This performance can be affected by various factors. In this paper, we theoretically prove…
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…
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)…
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…
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…
Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…
Although adaptive optimization algorithms such as Adam show fast convergence in many machine learning tasks, this paper identifies a problem of Adam by analyzing its performance in a simple non-convex synthetic problem, showing that Adam's…
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…
This paper deals with nonconvex stochastic optimization problems in deep learning and provides appropriate learning rates with which adaptive learning rate optimization algorithms, such as Adam and AMSGrad, can approximate a stationary…
It is known that the standard stochastic gradient descent (SGD) optimization method, as well as accelerated and adaptive SGD optimization methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (as,…