Non-convex scenario optimization with application to system identification

Abstract

Convex scenario optimization is a well-recognized approach to data-based optimization where the solution comes accompanied by precise generalization guarantees. It has been used in system identification as a driving methodology to construct interval prediction models. With this paper, scenario optimization breaks into the realm of non-convex optimization. In non-convex optimization, the number of scenarios that determine the solution - the so-called support scenarios - cannot be bounded beforehand, and one has to wait until the solution is computed to evaluate the size of the support scenario set. A theory is developed in this paper such that the generalization property of the solution is a-posteriori evaluated based on the registered number of support scenarios. This new perspective empowers the method and opens up new important possibilities for it to be applied to system identification involving non-convex optimization.