Seminar Details
2025-09-16 (14:00) : Safety in the Face of Uncertainty: When is a Scenario Decision-Making Algorithm Safe?
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Guillaume Berger (UCLouvain)
Abstract :
Making risk-aware decisions in the face of uncertainty is a central problem in many applications of engineering such as autonomous transportation, energy planning, medical devices, etc. Indeed, in these applications, failures or errors come at a high cost, so that it is important to bound the probability of such events. Nevertheless, this problem is often very challenging in practice because the probability distribution of the uncertainty is often unknown to the decision maker, which must thus make decisions in a black-box way. Scenario decision-making is a powerful data-driven approach to risk-aware decision-making, consisting in drawing samples (called scenarios) of the uncertainty and making a decision based on these samples. A key question is when such scenario-based decisions have a low risk. In this talk, I will review the main techniques from the literature for providing such bounds on the risk, and will show that they are incomparable, in that none is more general (i.e., non-vacuous on a larger class of problems) or less conservative than the other. I will then present a more general bound, inspired by the connection between scenario decision-making algorithms, set operators and VC theory. Finally, I will demonstrate the usefulness of the new bound on problems from scenario optimization.