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In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors…

Machine Learning · Computer Science 2018-10-31 Fanhua Shang , Kaiwen Zhou , Hongying Liu , James Cheng , Ivor W. Tsang , Lijun Zhang , Dacheng Tao , Licheng Jiao

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…

Machine Learning · Computer Science 2020-10-20 Dongruo Zhou , Pan Xu , Quanquan Gu

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…

Machine Learning · Computer Science 2016-08-06 Reza Babanezhad , Mohamed Osama Ahmed , Alim Virani , Mark Schmidt , Jakub Konečný , Scott Sallinen

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…

Machine Learning · Statistics 2018-02-01 Ke Ma , Jinshan Zeng , Jiechao Xiong , Qianqian Xu , Xiaochun Cao , Wei Liu , Yuan Yao

This paper proposes two innovative vector transport operators, leveraging the Cayley transform, for the generalized Stiefel manifold embedded with a non-standard metric. Specifically, it introduces the differentiated retraction and an…

Optimization and Control · Mathematics 2024-05-28 Xuejie Wang , Kangkang Deng , Zheng Peng , Chengcheng Yan

Despite the strong theoretical guarantees that variance-reduced finite-sum optimization algorithms enjoy, their applicability remains limited to cases where the memory overhead they introduce (SAG/SAGA), or the periodic full gradient…

Optimization and Control · Mathematics 2021-03-24 Ayoub El Hanchi , David A. Stephens

Recent advances in policy gradient methods and deep learning have demonstrated their applicability for complex reinforcement learning problems. However, the variance of the performance gradient estimates obtained from the simulation is…

Machine Learning · Computer Science 2018-03-30 Tianbing Xu , Qiang Liu , Jian Peng

In this study, we investigate stochastic optimization on Riemannian manifolds, focusing on the crucial variance reduction mechanism used in both Euclidean and Riemannian settings. Riemannian variance-reduced methods usually involve a…

Machine Learning · Computer Science 2024-03-12 Yury Demidovich , Grigory Malinovsky , Peter Richtárik

In this paper we combine concepts from Riemannian Optimization and the theory of Sobolev gradients to derive a new conjugate gradient method for direct minimization of the Gross-Pitaevskii energy functional with rotation. The conservation…

Optimization and Control · Mathematics 2018-01-17 Ionut Danaila , Bartosz Protas

In this paper, we proposed a new technique, {\em variance controlled stochastic gradient} (VCSG), to improve the performance of the stochastic variance reduced gradient (SVRG) algorithm. To avoid over-reducing the variance of gradient by…

Machine Learning · Computer Science 2021-02-22 Jia Bi , Steve R. Gunn

In this paper, we consider to improve the stochastic variance reduce gradient (SVRG) method via incorporating the curvature information of the objective function. We propose to reduce the variance of stochastic gradients using the…

Optimization and Control · Mathematics 2022-08-24 Hardik Tankaria , Nobuo Yamashita

One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms,…

Optimization and Control · Mathematics 2016-05-24 Conghui Tan , Shiqian Ma , Yu-Hong Dai , Yuqiu Qian

In this paper, we propose a novel reinforcement- learning algorithm consisting in a stochastic variance-reduced version of policy gradient for solving Markov Decision Processes (MDPs). Stochastic variance-reduced gradient (SVRG) methods…

Machine Learning · Computer Science 2018-06-15 Matteo Papini , Damiano Binaghi , Giuseppe Canonaco , Matteo Pirotta , Marcello Restelli

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…

Machine Learning · Statistics 2019-08-20 Hao Jin , Dachao Lin , Zhihua Zhang

Variance reduction (VR) methods for finite-sum minimization typically require the knowledge of problem-dependent constants that are often unknown and difficult to estimate. To address this, we use ideas from adaptive gradient methods to…

Machine Learning · Computer Science 2021-11-04 Benjamin Dubois-Taine , Sharan Vaswani , Reza Babanezhad , Mark Schmidt , Simon Lacoste-Julien

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Optimization and Control · Mathematics 2019-04-30 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio

In this paper, we study decentralized empirical risk minimization problems, where the goal is to minimize a finite-sum of smooth and strongly-convex functions available over a network of nodes. In this Part I, we propose…

Optimization and Control · Mathematics 2019-12-12 Ran Xin , Usman A. Khan , Soummya Kar

Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization…

Machine Learning · Statistics 2016-09-13 Xiyu Yu , Dacheng Tao

We propose a stochastic trust-region method for unconstrained nonconvex optimization that incorporates stochastic variance-reduced gradients (SVRG) to accelerate convergence. Unlike classical trust-region methods, the proposed algorithm…

Optimization and Control · Mathematics 2026-01-22 Yuchen Fang , Xinshou Zheng , Javad Lavaei

This article deals with the conjugate gradient method on a Riemannian manifold with interest in global convergence analysis. The existing conjugate gradient algorithms on a manifold endowed with a vector transport need the assumption that…

Optimization and Control · Mathematics 2016-06-20 Hiroyuki Sato , Toshihiro Iwai