NDLI: Stochastic version of second-order (Newton-Raphson) optimization using only function measurements

Content Provider	IEEE Xplore Digital Library
Author	Spall, J.C.
Copyright Year	1995
Description	Author affiliation: Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD, USA (Spall, J.C.)
Abstract	Consider the problem of loss function minimization when only (possibly noisy) measurements of the loss function are available. In particular, no measurements of the gradient of the loss function are assumed available (as required in the steepest descent or Newton-Raphson algorithms). Stochastic approximation (SA) algorithms of the multivariate Kiefer-Wolfowitz (finite-difference) form have long been considered for such problems, but with only limited success. The simultaneous perturbation SA (SPSA) algorithm has successfully addressed one of the major shortcomings of those finite-difference SA algorithms by significantly reducing the number of measurements required in many multivariate problems of practical interest. This SPSA algorithm displays the classic behaviour of 1st-order search algorithms by typically exhibiting a steep initial decline in the loss function followed by a slow decline to the optimum. This paper presents a 2nd-order SPSA algorithm that is based on estimating both the loss function gradient and inverse Hessian matrix at each iteration. The aim of this approach is to emulate the acceleration properties associated with deterministic algorithms of Newton-Raphson form, particularly in the terminal phase where the 1st-order SPSA algorithm slows down in its convergence. This 2nd-order SPSA algorithm requires only three loss function measurements at each iteration, independent of the problem dimension. This paper includes a formal convergence result for this 2nd-order approach.
Starting Page	347
Ending Page	352
File Size	597575
Page Count	6
File Format	PDF
ISBN	0780330188
DOI	10.1109/WSC.1995.478756
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1995-12-03
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stochastic processes Loss measurement Approximation algorithms Convergence Particle measurements Finite difference methods Discrete event systems Noise measurement Physics Laboratories
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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