Random directions methods in stochastic approximation

This work treats various random directions Kiefer-Wolfowitz type algorithms in stochastic approximation. The key point is the scaling of the random direction vectors. Under mild conditions, methods that choose the random direction vectors to be symmetric (with respect to the axes) with 0 mean and squared Euclidean length r (where r is the dimension of the underlying optimization problem) behave more or less the same, no matter how the actual direction vectors are selected. There can be advantages to using random directions if the dimension is high and bias is reasonable. But caution is needed if the number of iterations is not high