Summary: Weighted Averaging and Stochastic Approximation
I-Jeng Wang Edwin K.P. Chong y
Sanjeev R. Kulkarni z
To appear in Mathematics of Control, Signals, and Systems
We explore the relationship between weighted averaging and stochastic approxima-
tion algorithms, and study their convergence via a sample-path analysis. We prove
that the convergence of a stochastic approximation algorithm is equivalent to the con-
vergence of the weighted average of the associated noise sequence. We also present
necessary and su cient noise conditions for convergence of the average of the output
of a stochastic approximation algorithm in the linear case. We show that the averaged
stochastic approximation algorithms can tolerate a larger class of noise sequences than
the stand-alone stochastic approximation algorithms.
Keywords: stochastic approximation, weighted averaging, convergence, necessary and suf-
cient noise conditions, noise sequences.
Institute for Systems Research, University of Maryland, College Park, MD 20742. E-mail:
ySchool of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285. E-
mail: firstname.lastname@example.org. This research was supported by the National Science Foundation through
grants ECS-9410313 and ECS-9501652.