As it is the case for "usual", i.e., single-level, optimization problems, bilevel optimization problems can and most likely should be considered under uncertainty as well. In single-level optimization, uncertainty is due to noisy or incomplete data that defines the problem at hand. For bilevel optimization, the sources of uncertainty are richer. Besides data uncertainty, the two-player nature of these problems leads to cases in which (the observation of) the decision of the other player might be unknown to some extend - a setting that we call decision uncertainty and that cannot appear in single-level optimization.
In this talk, we give a brief overview over the young field of bilevel optimization under uncertainty and present a specific example for the modeling of decision uncertainty. Finally, we highlight the newly established connections between robust and bilevel optimization that might lead to a stronger connection of the two fields.
This talk is based on joint work with Yasmine Beck, Marc Goerigk, Jannis Kurtz, Ivana Ljubic, and Johannes Thürauf.