Simultaneous Perturbation Stochastic Approximation with Norm-Limited Update Vector

Abstract

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.