The risk of making decisions from data through the lens of the scenario approach

In previous contributions, it has been shown that the “complexity” is a key indicator to quantify the “risk” associated to data-driven scenario-based solutions. Depending on the context of application, risk is interpreted as probability of misprediction, or probability of underperforming or meeting shortfalls in various control endeavors, and the acquired ability to tightly evaluate the risk is a vital element in a world where data-driven methods are being increasingly used not only for decision support but also for automated decision making. The present contribution is meant to significantly expand the area of applicability of these results: all achievements so far have been based on an assumption, called “non-degeneracy”, that hardly applies e.g. to optimization problems that are not convex. Here, we show that these results maintain their integrity in a non-convex optimization setup, and beyond into a broad domain of decision making that contains non-convex optimization as a particular case.