We consider a bilevel optimization approach for parame- ter 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 nonlin- ear 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.
['Peter Ochs', 'Rene Ranftl', 'Thomas Brox', 'Thomas Pock']
Bilevel Optimization with Nonsmooth Lower Level Problems