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Equivalent Necessary and Su cient Conditions on Noise Sequences for

Summary: Equivalent Necessary and Su cient Conditions on
Noise Sequences for
Stochastic Approximation Algorithms
I-Jeng Wang Edwin K. P. Chong
Sanjeev R. Kulkarniy
To appear in Adv. Appl. Prob., Sept. 1996
We consider stochastic approximation algorithms on a general Hilbert space,
and study four conditions on noise sequences for their analysis: Kushner and
Clark's condition, Chen's condition, a decomposition condition, and Kulkarni
and Horn's condition. We discuss various properties of these conditions. In our
main result we show that the four conditions are all equivalent, and are both
necessary and su cient for convergence of stochastic approximation algorithms
under appropriate assumptions.
Keywords: stochastic approximation, convergence, equivalent necessary and su -
cient conditions, noise sequences
AMS Classi cation: Primary 62L20 Secondary 62L12, 65D99
School of Electrical Engineering, Purdue University, West Lafayette, IN 47907-1285. E-mail:
fiwang, echongg@ecn.purdue.edu. This research was supported in part by a Purdue Research Foun-
dation Fellowship, and by the National Science Foundation through grants ECS-9410313 and ECS-


Source: Amir, Yair - Department of Computer Science, Johns Hopkins University


Collections: Computer Technologies and Information Sciences