Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods

2017/10/20 by Robert M. Gower, Gower, Robert M., Nicolas Le Roux +3 · 1 citation
Computer Science · Mathematics · #68W20 #90C15 #90C25 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #cs.LG #math.OC #msc:68W20 #msc:90C15 #msc:90C25 #stat.ML

paper · pdf · doi:10.48550/arxiv.1710.07462

17 pages, 2 figures, 1 table

arxiv created 2018/03/31 · arxiv updated 2018/04/03

Abstract

Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control variates and leading to faster theoretical convergence close to the optimum. We then propose accurate and computationally efficient approximations to the Hessian, both using a diagonal and a low-rank matrix. Finally, we demonstrate the effectiveness of our method on a wide range of problems.

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