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The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice…
Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for…
Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…
To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune. Existing adaptive strategies based on…
The choice of batch sizes in minibatch stochastic gradient optimizers is critical in large-scale model training for both optimization and generalization performance. Although large-batch training is arguably the dominant training paradigm…
Stochastic Gradient Descent (SGD) and its variants are mainstream methods for training deep networks in practice. SGD is known to find a flat minimum that often generalizes well. However, it is mathematically unclear how deep learning can…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. The current mathematical theory in the lens of regularization theory predicts that…
Distance metric learning (DML) is an important task that has found applications in many domains. The high computational cost of DML arises from the large number of variables to be determined and the constraint that a distance metric has to…
Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…
Stochastic gradient descent (SGD) is a scalable and memory-efficient optimization algorithm for large datasets and stream data, which has drawn a great deal of attention and popularity. The applications of SGD-based estimators to…
Many popular learning-rate schedules for deep neural networks combine a decaying trend with local perturbations that attempt to escape saddle points and bad local minima. We derive convergence guarantees for bandwidth-based step-sizes, a…
Stochastic gradient descent (SGD) now acts as a fundamental part of optimization in current machine learning. Meanwhile, deep learning architectures have shown outstanding performance in a wide range of fields, such as natural language…
Stochastic dual coordinate ascent (SDCA) is an effective technique for solving regularized loss minimization problems in machine learning. This paper considers an extension of SDCA under the mini-batch setting that is often used in…
Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…
A fundamental challenge in Deep Learning is to find optimal step sizes for stochastic gradient descent automatically. In traditional optimization, line searches are a commonly used method to determine step sizes. One problem in Deep…
The question of how to parallelize the stochastic gradient descent (SGD) method has received much attention in the literature. In this paper, we focus instead on batch methods that use a sizeable fraction of the training set at each…
Differentially private stochastic gradient descent (DP-SGD) is known to have poorer training and test performance on large neural networks, compared to ordinary stochastic gradient descent (SGD). In this paper, we perform a detailed study…
The stochastic gradient descent (SGD) method is most widely used for deep neural network (DNN) training. However, the method does not always converge to a flat minimum of the loss surface that can demonstrate high generalization capability.…
Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD…
The existing analysis of asynchronous stochastic gradient descent (SGD) degrades dramatically when any delay is large, giving the impression that performance depends primarily on the delay. On the contrary, we prove much better guarantees…