Joint Robustness on Noise and Liapunov Functions for Parallel Stochastic Approximation Algorithms

Joint robustness with respect to measurement errors and Liapunov functions for parallel stochastic approximation algorithms is developed. A parallel computation model is analyzed. In lieu of using the classical approach, a collection of parallel processors is utilized to carry out the desired iterations, By means of decomposition methods, a large dimensional computation task is split into a series of tasks each with relatively small dimension. The efforts are directed toward finding allowable tolerance and deviations from usual assumptions on the convergence property. The measure of the joint robustness is described by a function depending on two parameters. Marginal or individual robustness with respect to either the measurement noise or the Liapunov function is also obtained. Moreover, the strong consistency as well as the necessary and sufficient condition for convergence is derived.