Bilevel Optimization with Nonsmooth Lower Level Problems

We consider a bilevel optimization approach for parameter learning in nonsmooth variational models. Existing approaches solve this problem by applying implicit differentiation to a sufficiently smooth approximation of the nondifferentiable lower level problem. We propose an alternative method based on differentiating the iterations of a nonlinear primal–dual algorithm. Our method computes exact (sub)gradients and can be applied also in the nonsmooth setting. We show preliminary results for the case of multi-label image segmentation.

• Type: Journal
• Year: 2015
• Where: SCALESPACE
• Authors: Peter Ochs, René Ranftl, Thomas Brox, Thomas Pock
• Keywords: Computer Vision, SCALESPACE 2015