Non-Convex Bilevel Games with Critical Point Selection Maps

Understand

Bilevel optimization problems involve two nested objectives, where an upper-level objective depends on a solution to a lower-level problem.

• When the latter is non-convex, multiple critical points may be present, leading to an ambiguous definition of the problem.
• In this paper, we introduce a key ingredient for resolving this ambiguity through the concept of a selection map which allows one to choose a particular solution to the lower-level problem.
• Using such maps, we define a class of hierarchical games between two agents that resolve the ambiguity in bilevel problems.