Rate of Convergence for Constrained Stochastic Approximation Algorithms

There is a large literature on the rate of convergence problem for general unconstrained stochastic approximations. Typically, one centers the iterate n about the limit point then and normalizes by dividing by the square root of the step size n. Then some type of convergence in distribution or weak convergence of Un, the centered and normalized iterate is proved. For example, one proves that the interpolated process formed by the Un converges weakly to a stationary Gaussian di usion, and the variance of the stationary measure is taken to be a measure of the rate of convergence. See the references in 2, 16, 20, 23, 24] for algorithms where the step size either goes to zero or is small and constant. Large deviations provides an alternative approach to the rate of convergence problem 9, 12, 11, 18, 23]. When the iterates of the algorithm are constrained to lie in some bounded set, the limit point is frequently on the boundary. With the exception of the large deviations type 9, 11], the r...

• Type: Journal
• Year: 2002
• Where: SIAMCO
• Authors: Robert Buche, Harold J. Kushner
• Keywords: Convergence, Convergence Problem, Limit Point, SIAMCO 2002