On the computational complexity and generalization properties of multi-stage and stage-wise coupled scenario programs

We discuss the computational complexity and feasibility properties of scenario sampling techniques for uncertain optimization programs. We propose an alternative way of dealing with a special class of stage-wise coupled programs and compare it with existing methods in the literature in terms of feasibility and computational complexity. We identify trade-offs between different methods depending on the problem structure and the desired probability of constraint satisfaction. To illustrate our results, an example from the area of approximate dynamic programming is considered.