Abstract :
This work is concerned with passive stochastic approximation PSA.algorithms
having vanishing or decreasing step size and window width. Unlike the traditional
stochastic approximation methods, the passive stochastic approximation algorithms
utilize passive strategies. Under the framework of PSA, not only the measurement
noise is unobservable, but also the ‘‘state’’ xn4is a randomly generated sequence.
In our formulation, both the observation noise and the randomly generated xn4
are correlated random processes. Under rather general conditions, w.p.1. convergence
of the algorithms is established. Then upper bounds on estimation errors are
obtained. It is shown that the bounds depend on the smoothness of the function
under consideration in an essential way, which reveals another distinct feature of
the passive algorithms.
