Central Limit Theorem and Sample Complexity of Stationary Stochastic Programs

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 … Read more

Dual bounds for periodical stochastic programs

In this paper we discuss construction of the dual of a periodical formulation of infinite horizon linear stochastic programs with a discount factor. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound especially when the … Read more

Periodical Multistage Stochastic Programs

In some applications the considered multistage stochastic programs have a periodical behavior. We show that in such cases it is possible to drastically reduce the number of stages by introducing a periodical analog of the so-called Bellman equations for discounted infinite horizon problems, used in Markov Decision Processes and Stochastic Optimal Control. Furthermore, we describe … Read more

Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming

In this tutorial we discuss several aspects of modeling and solving multistage stochastic programming problems. In particular we discuss distributionally robust and risk averse approaches to multistage stochastic programming, and the involved concept of time consistency. This tutorial is aimed at presenting a certain point of view of multistage stochastic programming, and can be viewed … Read more