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The mathematics of noise-free SPSA

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2 Author(s)
L. Gerencser ; Comput. & Autom. Inst., Hungarian Acad. of Sci., Budapest, Hungary ; Z. Vago

We consider discrete-time fixed gain stochastic approximation processes that are defined in terms of a random field that is identically zero at some point θ*. The boundedness of the estimator process is enforced by a resetting mechanism. Under appropriate technical conditions the estimator sequence is shown to converge to θ* with geometric rate almost surely. This result is in striking contrast to classical stochastic approximation theory where the typical convergence rate is n-1/2. For the proof a discrete-time version of the ODE-method is developed and used, and the techniques of Gerencser (1996) are extended. The paper is motivated by the study of simultaneous perturbation stochastic approximation (SPSA) methods applied to noise-free problems and to direct adaptive control

Published in:

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on  (Volume:5 )

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