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Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…
Optimizer is an essential component for the success of deep learning, which guides the neural network to update the parameters according to the loss on the training set. SGD and Adam are two classical and effective optimizers on which…
Stochastic gradient descent (SGD) with constant momentum and its variants such as Adam are the optimization algorithms of choice for training deep neural networks (DNNs). Since DNN training is incredibly computationally expensive, there is…
1-bit gradient compression and local steps are two representative techniques that enable drastic communication reduction in distributed SGD. Their benefits, however, remain an open question on Adam-based large model pre-training (e.g. BERT…
Training large language models (LLMs) typically relies on adaptive optimizers like Adam (Kingma & Ba, 2015) which store additional state information to accelerate convergence but incur significant memory overhead. Recent efforts, such as…
Stochastic gradient descent~(SGD) and its variants have been the dominating optimization methods in machine learning. Compared to SGD with small-batch training, SGD with large-batch training can better utilize the computational power of…
We introduce a novel optimization problem formulation that departs from the conventional way of minimizing machine learning model loss as a black-box function. Unlike traditional formulations, the proposed approach explicitly incorporates…
Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…
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…
Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…
The rapid development of machine learning and deep learning has introduced increasingly complex optimization challenges that must be addressed. Indeed, training modern, advanced models has become difficult to implement without leveraging…
This paper formalizes and analyzes Gaussian smoothing applied to two prominent optimization methods: Stochastic Gradient Descent (GSmoothSGD) and Adam (GSmoothAdam) in deep learning. By attenuating small fluctuations, Gaussian smoothing…
Over the last decades, Stochastic Gradient Descent (SGD) has been intensively studied by the Machine Learning community. Despite its versatility and excellent performance, the optimization of large models via SGD still is a time-consuming…
We give a new separation result between the generalization performance of stochastic gradient descent (SGD) and of full-batch gradient descent (GD) in the fundamental stochastic convex optimization model. While for SGD it is well-known that…
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…
Adaptive gradient methods have been widely adopted in training large-scale deep neural networks, especially large foundation models. Despite the huge success in practice, their theoretical advantages over classical gradient methods with…
Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by…
Adaptive optimizers such as Adam have achieved great success in training large-scale models like large language models and diffusion models. However, they often generalize worse than non-adaptive methods, such as SGD on classical…
Adaptive optimization methods are well known to achieve superior convergence relative to vanilla gradient methods. The traditional viewpoint in optimization, particularly in convex optimization, explains this improved performance by arguing…
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…