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In the context of stochastic gradient descent(SGD) and adaptive moment estimation (Adam),researchers have recently proposed optimization techniques that transition from Adam to SGD with the goal of improving both convergence and…
Training deep neural networks requires intricate initialization and careful selection of learning rates. The emergence of stochastic gradient optimization methods that use adaptive learning rates based on squared past gradients, e.g.,…
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…
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…
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…
Existing convergence analyses of Q-learning mostly focus on the vanilla stochastic gradient descent (SGD) type of updates. Despite the Adaptive Moment Estimation (Adam) has been commonly used for practical Q-learning algorithms, there 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…
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,…
Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…
Adaptive gradient-descent optimizers are the standard choice for training neural network models. Despite their faster convergence than gradient-descent and remarkable performance in practice, the adaptive optimizers are not as well…
Several variants of stochastic gradient descent (SGD) have been proposed to improve the learning effectiveness and efficiency when training deep neural networks, among which some recent influential attempts would like to adaptively control…
Establishing a fast rate of convergence for optimization methods is crucial to their applicability in practice. With the increasing popularity of deep learning over the past decade, stochastic gradient descent and its adaptive variants…
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,…
Efficient computation of min-max problems is a central question in optimization, learning, games, and controls. Arguably the most natural algorithm is gradient-descent-ascent (GDA). However, since the 1970s, conventional wisdom has argued…
Many popular adaptive gradient methods such as Adam and RMSProp rely on an exponential moving average (EMA) to normalize their stepsizes. While the EMA makes these methods highly responsive to new gradient information, recent research has…
Gradient descent is slow to converge for ill-conditioned problems and non-convex problems. An important technique for acceleration is step-size adaptation. The first part of this paper contains a detailed review of step-size adaptation…
Since the 21st century, artificial intelligence has been leading a new round of industrial revolution. Under the training framework, the optimization algorithm aims to stably converge high-dimensional optimization to local and even global…
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…
Adaptive learning rate methods have been successfully applied in many fields, especially in training deep neural networks. Recent results have shown that adaptive methods with exponential increasing weights on squared past gradients (i.e.,…
We study convergence rates of AdaGrad-Norm as an exemplar of adaptive stochastic gradient methods (SGD), where the step sizes change based on observed stochastic gradients, for minimizing non-convex, smooth objectives. Despite their…