Convergence rates of finite difference stochastic approximation algorithms part I: general sampling

Liyi Dai

doi:10.1117/12.2228250

19 May 2016 Convergence rates of finite difference stochastic approximation algorithms part I: general sampling

Liyi Dai

Proceedings Volume 9871, Sensing and Analysis Technologies for Biomedical and Cognitive Applications 2016; 98710L (2016) https://doi.org/10.1117/12.2228250
Event: SPIE Commercial + Scientific Sensing and Imaging, 2016, Baltimore, MD, United States

Abstract

Stochastic optimization is a fundamental problem that finds applications in many areas including biological and cognitive sciences. The classical stochastic approximation algorithm for iterative stochastic optimization requires gradient information of the sample object function that is typically difficult to obtain in practice. Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. The analysis is carried out under a general framework covering a wide range of updating scenarios. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the finite differences.

Citation Download Citation

Liyi Dai "Convergence rates of finite difference stochastic approximation algorithms part I: general sampling", Proc. SPIE 9871, Sensing and Analysis Technologies for Biomedical and Cognitive Applications 2016, 98710L (19 May 2016); https://doi.org/10.1117/12.2228250

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