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On conditions for convergence rates of stochastic approximation algorithms

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3 Author(s)
E. K. P. Chong ; Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA ; I. -J. Wang ; S. R. Kulkarni

We develop deterministic necessary and sufficient conditions on individual noise sequences of a stochastic approximation algorithm for the error of the iterates to converge at a given rate. Specifically, suppose {pn} is a given positive sequence converging monotonically to 0. Consider a stochastic approximation algorithm xn+1=xn-an(Anxn-b n)+anen, where {xn} is the iterate sequence, {an} is the step size sequence, {en } is the noise sequence, and x* is the desired zero of the function f(x)=Ax-b. We show that xn-x*=o(ρn) if and only if the sequence {en} satisfies one of five equivalent conditions. These conditions are based on well known formulas for noise sequences found in the literature

Published in:

Decision and Control, 1997., Proceedings of the 36th IEEE Conference on  (Volume:3 )

Date of Conference:

10-12 Dec 1997