Related papers: Theoretical analysis of Adam using hyperparameters…
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…
Despite the popularity of the Adam optimizer in practice, most theoretical analyses study Stochastic Gradient Descent (SGD) as a proxy for Adam, and little is known about how the solutions found by Adam differ. In this paper, we show that…
Adjusting the learning rate schedule in stochastic gradient methods is an important unresolved problem which requires tuning in practice. If certain parameters of the loss function such as smoothness or strong convexity constants are known,…
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 analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…
Adaptive gradient methods such as Adam have been shown to be very effective for training deep neural networks (DNNs) by tracking the second moment of gradients to compute the individual learning rates. Differently from existing methods, we…
We generalize the notion of average Lipschitz smoothness proposed by Ashlagi et al. (COLT 2021) by extending it to H\"older smoothness. This measure of the "effective smoothness" of a function is sensitive to the underlying distribution and…
We aim to design adaptive online learning algorithms that take advantage of any special structure that might be present in the learning task at hand, with as little manual tuning by the user as possible. A fundamental obstacle that comes up…
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…
Adam is the go-to optimizer for training modern machine learning models, but it requires additional memory to maintain the moving averages of the gradients and their squares. While various low-memory optimizers have been proposed that…
Adaptive Moment Estimation (Adam), which combines Adaptive Learning Rate and Momentum, would be the most popular stochastic optimizer for accelerating the training of deep neural networks. However, it is empirically known that Adam often…
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…
In this work, we offer a theoretical analysis of two modern optimization techniques for training large and complex models: (i) adaptive optimization algorithms, such as Adam, and (ii) the model exponential moving average (EMA).…
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 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…
AdamZ is an advanced variant of the Adam optimiser, developed to enhance convergence efficiency in neural network training. This optimiser dynamically adjusts the learning rate by incorporating mechanisms to address overshooting and…
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…
We prove local convergence of several notable gradient descent algorithms used in machine learning, for which standard stochastic gradient descent theory does not apply directly. This includes, first, online algorithms for recurrent models…
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…
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,…