Convergence rates of finite difference stochastic approximation algorithms part II: implementation via common random numbers

Liyi Dai

doi:10.1117/12.2228251

19 May 2016 Convergence rates of finite difference stochastic approximation algorithms part II: implementation via common random numbers

Liyi Dai

Author Affiliations +

Proceedings Volume 9871, Sensing and Analysis Technologies for Biomedical and Cognitive Applications 2016; 98710J (2016) https://doi.org/10.1117/12.2228251
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, by approximating gradient using finite differences generated through common random numbers. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the finite differences. Particularly, it is shown that the rate can be increased to n^−2/5 in general and to n^−1/2, the best possible rate of stochastic approximation, in Monte Carlo optimization for a broad class of problems, in the iteration number n.

Citation Download Citation

Liyi Dai "Convergence rates of finite difference stochastic approximation algorithms part II: implementation via common random numbers", Proc. SPIE 9871, Sensing and Analysis Technologies for Biomedical and Cognitive Applications 2016, 98710J (19 May 2016); https://doi.org/10.1117/12.2228251

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available