On extensions of Polyak's averaging approach to stochastic approximation

Stochastic approximation algorithms are considered and Polyak's averaging approach (cf. [1]) is revisited. Under much weaker conditions, convergence and rate of convergence results are developed. In lieu of uncorrelated noise, φ-mixing type of random disturbances are treated. By means of weak convergence methods, it is shown that the multistage algorithms via averaging have asymptotically optimal convergence speed and are efficient procedures