Confidence level solutions for stochastic programming

We propose an alternative approach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable. We propose a solution concept in which the probability that the random algorithm produces a solution with an expected objective value departing from the optimal one by more than ϵϵ is small enough. We derive complexity bounds on the number of iterations of this process. We show that by repeating the basic process on independent samples, one can significantly reduce the number of iterations.