相关论文: ADOPT: Modified Adam Can Converge with Any $\beta_…

This paper studies a class of adaptive gradient based momentum algorithms that update the search directions and learning rates simultaneously using past gradients. This class, which we refer to as the "Adam-type", includes the popular…

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…

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…

Adam is shown not being able to converge to the optimal solution in certain cases. Researchers recently propose several algorithms to avoid the issue of non-convergence of Adam, but their efficiency turns out to be unsatisfactory in…

Adaptive gradient optimization methods, such as Adam, are prevalent in training deep neural networks across diverse machine learning tasks due to their ability to achieve faster convergence. However, these methods often suffer from…

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…

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…

Learning rate adaptation is a popular topic in machine learning. Gradient Descent trains neural nerwork with a fixed learning rate. Learning rate adaptation is proposed to accelerate the training process through adjusting the step size in…

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…

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, 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 gradient methods have become popular in optimizing deep neural networks; recent examples include AdaGrad and Adam. Although Adam usually converges faster, variations of Adam, for instance, the AdaBelief algorithm, have been…

Adaptive Moment Estimation (ADAM) is a very popular training algorithm for deep neural networks and belongs to the family of adaptive gradient descent optimizers. However to the best of the authors knowledge no complete convergence analysis…

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…

Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also…

Adam is the default algorithm for training neural networks, including large language models (LLMs). However, \citet{reddi2019convergence} provided an example that Adam diverges, raising concerns for its deployment in AI model training. We…

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…

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…

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…