Title :
On equivalence of some noise conditions for stochastic approximation algorithms
Author :
Wang, I-Jeng ; Chong, Edwin K P ; Kulkarni, Sanjeev R.
Author_Institution :
Sch. of Electr. & Comput. Eng., Purdue Univ., West Lafayette, IN, USA
Abstract :
We study four conditions on noise sequences for convergence of stochastic approximation algorithms on a general Hilbert space: Kushner and Clark´s condition (1978), Chen´s condition (1994), Kulkarni and Horn´s condition (1995), and a decomposition 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 sufficient for convergence of stochastic approximation algorithms under appropriate assumptions
Keywords :
Hilbert spaces; approximation theory; noise; convergence; decomposition condition; general Hilbert space; necessary and sufficient conditions; noise condition equivalence; stochastic approximation algorithms; Adaptive control; Approximation algorithms; Books; Convergence; Hilbert space; Stochastic processes; Stochastic resonance; Sufficient conditions;
Conference_Titel :
Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
0-7803-2685-7
DOI :
10.1109/CDC.1995.479198
