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Simultaneous Perturbation Stochastic Approximation with Norm‐Limited Update Vector
Author(s) -
Tanaka Yosuke,
Azuma Shunichi,
Sugie Toshiharu
Publication year - 2015
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1153
Subject(s) - simultaneous perturbation stochastic approximation , norm (philosophy) , perturbation (astronomy) , stochastic approximation , mathematical optimization , bernoulli's principle , mathematics , computer science , stochastic process , asynchronous communication , physics , computer network , statistics , quantum mechanics , political science , law , thermodynamics
This paper addresses the convergence of simultaneous perturbation stochastic approximation (SPSA) with a norm‐limited update vector. We first illustrate an unstable solution of the standard SPSA algorithm which motivates the consideration of a modified version, where the norm of the update vector is limited to a certain value. Next, a result on the almost‐sure convergence is presented by reducing the modified algorithm into the standard SPSA algorithm and restricting the probability distribution for the perturbation to a Bernoulli distribution. Finally, we apply the modified algorithm to a system identification problem to demonstrate its performance.