Related papers: Adam: A Method for Stochastic Optimization
Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based…
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…
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…
Adam-type optimizers, as a class of adaptive moment estimation methods with the exponential moving average scheme, have been successfully used in many applications of deep learning. Such methods are appealing due to the capability on…
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…
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…
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)…
We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…
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 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…
We implement the adaptive step size scheme from the optimization methods AdaGrad and Adam in a novel variant of the Proximal Gradient Method (PGM). Our algorithm, dubbed AdaProx, avoids the need for explicit computation of the Lipschitz…
We present a stochastic setting for optimization problems with nonsmooth convex separable objective functions over linear equality constraints. To solve such problems, we propose a stochastic Alternating Direction Method of Multipliers…
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…
The success of deep learning can be attributed to various factors such as increase in computational power, large datasets, deep convolutional neural networks, optimizers etc. Particularly, the choice of optimizer affects the generalization,…
Distributed adaptive stochastic gradient methods have been widely used for large-scale nonconvex optimization, such as training deep learning models. However, their communication complexity on finding $\varepsilon$-stationary points has…
First-order optimization algorithms have been proven prominent in deep learning. In particular, algorithms such as RMSProp and Adam are extremely popular. However, recent works have pointed out the lack of ``long-term memory" in Adam-like…
Optimal selection of optimization algorithms is crucial for training deep learning models. The Adam optimizer has gained significant attention due to its efficiency and wide applicability. However, to enhance the adaptability of optimizers…
Accelerated gradient-based methods are being extensively used for solving non-convex machine learning problems, especially when the data points are abundant or the available data is distributed across several agents. Two of the prominent…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
This paper aims to clearly distinguish between Stochastic Gradient Descent with Momentum (SGDM) and Adam in terms of their convergence rates. We demonstrate that Adam achieves a faster convergence compared to SGDM under the condition of…