Frauke Liers: (Data-Driven) Distributional Robustness: How to 'learn' relevant uncertainties together with robust decisions?

Abstract: In many applications, determining optimized solutions that are hedged
against uncertainties is mandatory. Classical stochastic optimization
approaches, however, may be prone to the disadvantage that the
underlying probability distributions are unknown or uncertain
themselves. On the other hand, standard robust optimization may lead
to conservative results as it generates solutions that are feasible
regardless of how uncertainties manifest themselves within predefined
uncertainty sets. Distributional robustness (DRO) lies at the
interface of robust and stochastic optimization as it robustly
protects against uncertain distributions. DRO currently receives
increased attention and is considered as an alternative that can lead
to less conservative but still uncertainty-protected solutions. In
this talk, we will review some approaches in the area of
distributional robustness. We will explain some recent developments
that use scenario observations to learn more about the uncertain
distributions over time, together with best possible protected
solutions. The goal is to incorporate new information when it arrives
and to improve our solution without resolving the entire robust
counterpart. We also present results for DRO applications in energy
and in the design of nanoparticles.

The first part of the talk is joint with K. Aigner, A. Barmann, K. Braun, F. Liers, S. Pokutta, O. Schneider, K. Sharma, and S. Tschuppik.