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The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any…
Within the current sphere of deep learning research, despite the extensive application of optimization algorithms such as Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), there remains a pronounced inadequacy in…
In this paper, we propose SGEM, Stochastic Gradient with Energy and Momentum, to solve a large class of general non-convex stochastic optimization problems, based on the AEGD method that originated in the work [AEGD: Adaptive Gradient…
Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…
Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic…
In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimization of non-convex loss functions. Since the pioneering work of…
We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual…
Adaptive moment methods have been remarkably successful in deep learning optimization, particularly in the presence of noisy and/or sparse gradients. We further the advantages of adaptive moment techniques by proposing a family of double…
In this paper, we propose a generalized framework for developing learning-rate-free momentum stochastic gradient descent (SGD) methods in the minimization of nonsmooth nonconvex functions, especially in training nonsmooth neural networks.…
This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is…
In this paper we study the problem of convergence and generalization error bound of stochastic momentum for deep learning from the perspective of regularization. To do so, we first interpret momentum as solving an $\ell_2$-regularized…
Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…
Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…
A commonly used heuristic in non-convex optimization is Normalized Gradient Descent (NGD) - a variant of gradient descent in which only the direction of the gradient is taken into account and its magnitude ignored. We analyze this heuristic…
Modern machine learning is trained by stochastic gradient descent (SGD), whose performance critically depends on how the learning rate (LR) is adjusted and decreased over time. Yet existing LR regimes may be intricate, or need to tune one…
Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received…
The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate…
We provide an improved analysis of normalized SGD showing that adding momentum provably removes the need for large batch sizes on non-convex objectives. Then, we consider the case of objectives with bounded second derivative and show that…
Stochastic gradient descent (SGD) is a premium optimization method for training neural networks, especially for learning objectively defined labels such as image objects and events. When a neural network is instead faced with subjectively…