Related papers: Fast Variance Reduction Method with Stochastic Bat…
In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of…
We present a stochastic variance-reduced heavy ball power iteration algorithm for solving PCA and provide a convergence analysis for it. The algorithm is an extension of heavy ball power iteration, incorporating a step size so that progress…
The convergence behavior of mini-batch stochastic gradient descent (SGD) is highly sensitive to the batch size and learning rate settings. Recent theoretical studies have identified the existence of a critical batch size that minimizes…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…
Stochastic variance-reduced gradient (SVRG) is a classical optimization method. Although it is theoretically proved to have better convergence performance than stochastic gradient descent (SGD), the generalization performance of SVRG…
We developed a corporative stochastic approximation (CSA) type algorithm for semi-infinite programming (SIP), where the cut generation problem is solved inexactly. First, we provide general error bounds for inexact CSA. Then, we propose two…
We exploit the observation that stochastic variational inference (SVI) is a form of annealing and present a modified SVI approach -- applicable to both large and small datasets -- that allows the amount of annealing done by SVI to be tuned.…
Current deep learning adaptive optimizer methods adjust the step magnitude of parameter updates by altering the effective learning rate used by each parameter. Motivated by the known inverse relation between batch size and learning rate on…
We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on non-convex optimization. Recent studies have shown that the asynchronous stochastic…
We consider the minimization of a sum of an expectation-valued coordinate-wise $L_i$-smooth nonconvex function and a nonsmooth block-separable convex regularizer. We propose an asynchronous variance-reduced algorithm, where in each…
Retrieval-Augmented Generation (RAG) is a promising approach to mitigate hallucinations in Large Language Models (LLMs) for legal applications, but its reliability is critically dependent on the accuracy of the retrieval step. This is…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
A new amortized variance-reduced gradient (AVRG) algorithm was developed in \cite{ying2017convergence}, which has constant storage requirement in comparison to SAGA and balanced gradient computations in comparison to SVRG. One key advantage…
This paper proposes AB-SAGA, a first-order distributed stochastic optimization method to minimize a finite-sum of smooth and strongly convex functions distributed over an arbitrary directed graph. AB-SAGA removes the uncertainty caused by…
Variance reduction is a crucial tool for improving the slow convergence of stochastic gradient descent. Only a few variance-reduced methods, however, have yet been shown to directly benefit from Nesterov's acceleration techniques to match…
We analyze the convergence rate of the random reshuffling (RR) method, which is a randomized first-order incremental algorithm for minimizing a finite sum of convex component functions. RR proceeds in cycles, picking a uniformly random…
Variance reduced stochastic gradient (SGD) methods converge significantly faster than the vanilla SGD counterpart. However, these methods are not very practical on large scale problems, as they either i) require frequent passes over the…
Bagging is a commonly used ensemble technique in statistics and machine learning to improve the performance of prediction procedures. In this paper, we study the prediction risk of variants of bagged predictors under the proportional…
In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. This point of view covers the stochastic gradient…