Title :
A deterministic analysis of stochastic approximation with randomized directions
Author :
Wang, I-Jeng ; Chong, Edwin K P
Author_Institution :
Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD, USA
fDate :
12/1/1998 12:00:00 AM
Abstract :
We study the convergence of two stochastic approximation algorithms with randomized directions: the simultaneous perturbation stochastic approximation algorithm and the random direction Kiefer-Wolfowitz algorithm. We establish deterministic necessary and sufficient conditions on the random directions and noise sequences for both algorithms, and these conditions demonstrate the effect of the “random” directions on the “sample-path” behavior of the algorithms studied. We discuss ideas for further research in the analysis and design of these algorithms
Keywords :
approximation theory; bifurcation; convergence of numerical methods; probability; stochastic processes; Kiefer-Wolfowitz algorithm; convergence; deterministic analysis; noise sequences; probability; random directions; simultaneous perturbation; stochastic approximation; Asymptotic stability; Backstepping; Bifurcation; Control design; Control systems; Feedback; Hysteresis; Lyapunov method; Stochastic processes; Surges;
Journal_Title :
Automatic Control, IEEE Transactions on
