Related papers: Adam Can Converge Without Any Modification On Upda…

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…

Stochastic optimization algorithms using exponential moving averages of the past gradients, such as ADAM, RMSProp and AdaGrad, have been having great successes in many applications, especially in training deep neural networks. ADAM in…

The Adam optimizer is a cornerstone of modern deep learning, yet the empirical necessity of each of its individual components is often taken for granted. This paper presents a focused investigation into the role of bias-correction, a…

Optimization algorithms such as AdaGrad and Adam have significantly advanced the training of deep models by dynamically adjusting the learning rate during the optimization process. However, adhoc tuning of learning rates poses a challenge,…

Adam [Kingma & Ba, 2015] is the de facto optimizer in deep learning, yet its theoretical understanding remains limited. Prior analyses show that Adam favors solutions aligned with $\ell_\infty$-geometry, but these results are restricted to…

Adam has been widely adopted for training deep neural networks due to less hyperparameter tuning and remarkable performance. To improve generalization, Adam is typically used in tandem with a squared $\ell_2$ regularizer (referred to as…

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…

Adam-type methods, the extension of adaptive gradient methods, have shown great performance in the training of both supervised and unsupervised machine learning models. In particular, Adam-type optimizers have been widely used empirically…

Adam is widely recognized as one of the most effective optimizers for training deep neural networks (DNNs). Despite its remarkable empirical success, its theoretical convergence analysis remains unsatisfactory. Existing works predominantly…

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…

Many adaptive optimization methods have been proposed and used in deep learning, in which Adam is regarded as the default algorithm and widely used in many deep learning frameworks. Recently, many variants of Adam, such as Adabound, RAdam…

Adam is a widely used optimization method for training deep learning models. It computes individual adaptive learning rates for different parameters. In this paper, we propose a generalization of Adam, called Adambs, that allows us to also…

We provide a theoretical analysis of Adam under non-stationary stochastic objectives, separating two regimes: Euclidean tracking under adaptive strong monotonicity of the Adam-preconditioned mean-gradient operator, and high-probability…

Modern recommendation systems frequently employ online learning to dynamically update their models with freshly collected data. The most commonly used optimizer for updating neural networks in these contexts is the Adam optimizer, which…

Despite its widespread adoption, Adam's advantage over Stochastic Gradient Descent (SGD) lacks a comprehensive theoretical explanation. This paper investigates Adam's sensitivity to rotations of the parameter space. We observe that Adam's…

The success of the Adam optimizer on a wide array of architectures has made it the default in settings where stochastic gradient descent (SGD) performs poorly. However, our theoretical understanding of this discrepancy is lagging,…

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…

Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an…

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 propose a batch size invariant version of Adam, for use in large-scale, distributed settings, in which the mini-batch is divided into micro-batches which are distributed among worker nodes. For the v term, standard Adam first computes…