Related papers: SAAGs: Biased Stochastic Variance Reduction Method…
Stochastic Gradient Boosting (SGB) is a widely used approach to regularization of boosting models based on decision trees. It was shown that, in many cases, random sampling at each iteration can lead to better generalization performance of…
We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…
We present a principled approach for designing stochastic Newton methods for solving finite sum optimization problems. Our approach has two steps. First, we re-write the stationarity conditions as a system of nonlinear equations that…
Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions…
In this paper, we propose a StochAstic Recursive grAdient algoritHm (SARAH), as well as its practical variant SARAH+, as a novel approach to the finite-sum minimization problems. Different from the vanilla SGD and other modern stochastic…
Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…
Stochastic Gradient Descent (SGD) with adaptive steps is widely used to train deep neural networks and generative models. Most theoretical results assume that it is possible to obtain unbiased gradient estimators, which is not the case in…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
We begin by briefly surveying some results on the convergence of the Stochastic Gradient Descent (SGD) Method, proved in a companion paper by the present authors. These results are based on viewing SGD as a version of Stochastic…
Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set…
We study the problem of minimizing the average of a very large number of smooth functions, which is of key importance in training supervised learning models. One of the most celebrated methods in this context is the SAGA algorithm. Despite…
We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings:…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…
We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal…
We present and analyze several strategies for improving the performance of stochastic variance-reduced gradient (SVRG) methods. We first show that the convergence rate of these methods can be preserved under a decreasing sequence of errors…
We present a novel approach for black-box VI that bypasses the difficulties of stochastic gradient ascent, including the task of selecting step-sizes. Our approach involves using a sequence of sample average approximation (SAA) problems.…
In this paper we study a family of variance reduction methods with randomized batch size---at each step, the algorithm first randomly chooses the batch size and then selects a batch of samples to conduct a variance-reduced stochastic…
In this paper, we propose a novel sufficient decrease technique for variance reduced stochastic gradient descent methods such as SAG, SVRG and SAGA. In order to make sufficient decrease for stochastic optimization, we design a new…
Stochastic optimization algorithms are widely used for machine learning with large-scale data. However, their convergence often suffers from non-vanishing variance. Variance Reduction (VR) methods, such as SVRG and SARAH, address this issue…