A stopping rule for simultaneous perturbation stochastic approximation

A stopping rule is developed for simultaneous perturbation stochastic approximation (SPSA) which is an iterative method for minimizing an unknown objective function via its noise corrupted measurements. It is shown that, when the number of iterations reaches a constant determined by the stopping rule, SPSA for the quadratic convex problem provides us with a suboptimal solution which is close to the optimal solution with a specified probabilistic guarantee. Furthermore, the number is determined by the specified guarantee and polynomial in the problem size.