相关论文: Optimal Adaptive and Accelerated Stochastic Gradie…

There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error…

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In practically relevant training problems, usually not the plain…

In this paper, we revisit stochastic gradient descent (SGD) with AdaGrad-type preconditioning. Our contributions are twofold. First, we develop a unified convergence analysis of SGD with adaptive preconditioning under anisotropic or matrix…

Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…

In this paper, we study the performance of a large family of SGD variants in the smooth nonconvex regime. To this end, we propose a generic and flexible assumption capable of accurate modeling of the second moment of the stochastic…

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…

Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…

There is an increased interest in building data analytics frameworks with advanced algebraic capabilities both in industry and academia. Many of these frameworks, e.g., TensorFlow and BIDMach, implement their compute-intensive primitives in…

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…

As one of the most fundamental stochastic optimization algorithms, stochastic gradient descent (SGD) has been intensively developed and extensively applied in machine learning in the past decade. There have been some modified SGD-type…

Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization schemes are frequently employed in applications involving…

Adaptive gradient approaches that automatically adjust the learning rate on a per-feature basis have been very popular for training deep networks. This rich class of algorithms includes Adagrad, RMSprop, Adam, and recent extensions. All…

Stochastic momentum methods have been widely adopted in training deep neural networks. However, their theoretical analysis of convergence of the training objective and the generalization error for prediction is still under-explored. This…

Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…

A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…

Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA)…

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…

Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian…