Adaptability via sampling

There has recently been considerable attention devoted to sample-based approaches to chance constraints in stochastic programming, and also multi-stage optimization formulations. In this short paper, we consider the merits of a joint approach. A specific motivation for us, is the possibility of developing techniques suitable for integer-constrained future stages. We propose a technique based on structured adaptability, and some recent sampling techniques, that results in sample complexity that is polynomial in the number of stages. Thus we circumvent a difficulty that has traditionally plagued sample-based approaches for multi-stage formulations. This allows us to provide a hierarchy of adaptability schemes, not only for continuous problems, but also for discrete problems.