Exponential convergence of two-stage stochastic programming with independent samples

This paper considers a procedure of two-stage stochastic programming in which the performance function to be optimized is replaced by its empirical mean, which is obtained by conducting independent sampling. The exponential convergence for the probability of deviation of the empirical optimum from the true optimum is established using large deviation techniques. Explicit bounds on the convergence rates are obtained for the case of quadratic performance functions. Finally, numerical results are presented for the famous news vendor problem and for a resource problem, which lends experimental evidence supporting the exponential convergence.