On using perturbation analysis to do sensitivity analysis: derivatives versus differences

One use of perturbation analysis is to compute the derivative of a performance measure P with respect to a parameter θ for use in iterative optimization schemes to locate local maxima by driving the derivative to zero. It has been pointed out that in stochastic approximation contexts, there is an advantage in using derivatives as opposed to differences. Another use of perturbation analysis is just to do a sensitivity analysis with respect to a parameter without relation to any optimization. The advantages of using differences rather than derivatives for sensitivity analysis are identified. This prompts the use of noninfinitesimal perturbation analysis (or other techniques) whereby perturbation information can be obtained from a single run