We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem with an iterative algorithm that is guaranteed to converge to a minimizer of the problem. Using suitable non-linear proximal distance functions, the update mappings of such an iterative algorithm can be differentiable, notwithstanding the fact that the minimization problem is non-smooth.
Quite recently, REF proposed techniques for approximating bilevel optimization problems with non-smooth "convex" lower level problems.
Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Computer Science Mathematics