The Mathematics of Noise-Free SPSA
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چکیده
We consider discrete-time xed gain stochastic approximation processes that are de ned in terms of a random eld that is identically zero at some point . The boundedness of the estimator process is enforced by a resetting mechanism. Under appropriate technical conditions the estimator sequence is shown to converge to with geometric rate almost surely. This result is in striking contrast to classical stochastic approximation theory where the typical convergence rate is n . For the proof a discrete-time version of the ODE-method is developed and used, and the techniques of [8] 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, see [13].
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