Related papers: Convergence of Adam for Non-convex Objectives: Rel…
Adam is a popular variant of stochastic gradient descent for finding a local minimizer of a function. In the constant stepsize regime, assuming that the objective function is differentiable and non-convex, we establish the convergence in…
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…
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…
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…
Adam-type algorithms have become a preferred choice for optimisation in the deep learning setting, however, despite success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type…
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…
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 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,…
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…
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…
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…
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…
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 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…
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 has become one of the most popular optimizers for training modern deep neural networks, such as transformers. However, its applicability is largely restricted to single-level optimization problems. In this paper, we aim to extend…
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…
We provide a simple proof of convergence covering both the Adam and Adagrad adaptive optimization algorithms when applied to smooth (possibly non-convex) objective functions with bounded gradients. We show that in expectation, the squared…
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)…