Central limit theorem and sample complexity of stationary stochastic programs

Abstract

In this paper we discuss sample complexity of solving stationary stochastic programs by the Sample Average Approximation (SAA) method. We investigate this in the framework of Optimal Control (in discrete time) setting. In particular we derive a Central Limit Theorem type asymptotics for the optimal values of the SAA problems. The main conclusion is that the sample size, required to attain a given relative error of the SAA solution, is not sensitive to the discount factor, even if the discount factor is very close to one. We consider the risk neutral and risk averse settings. The presented numerical experiments confirm the theoretical analysis.