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Convergence rate of moments in stochastic approximation with simultaneous perturbation gradient approximation and resetting

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

The sequence of recursive estimators for function minimization generated by Spall's (1998) simultaneous perturbation stochastic approximation (SPSA) method, combined with a suitable restarting mechanism is considered. It is proved that this sequence converges under certain conditions with rate O(n-β/2) for some β>0, the best value being β=2/3, where the rate is measured by the Lq-norm of the estimation error for any 1⩽q<∞. The authors also present higher order SPSA methods. It is shown that the error exponent β/2 can be arbitrarily close to 1/2 if the Hessian matrix of the cost function at the minimizing point has all its eigenvalues to the right of 1/2, the cost function is sufficiently smooth, and a sufficiently high-order approximation of the derivative is used

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Automatic Control, IEEE Transactions on  (Volume:44 ,  Issue: 5 )