A study of Nesterov's scheme for Lagrangian decomposition and MAP labeling

Bogdan Savchynskyy, Jorg Kappes, Stefan Schmidt, Christoph Schnorr
2011 CVPR 2011  
We study the MAP-labeling problem for graphical models by optimizing a dual problem obtained by Lagrangian decomposition. In this paper, we focus specifically on Nesterov's optimal first-order optimization scheme for nonsmooth convex programs, that has been studied for a range of other problems in computer vision and machine learning in recent years. We show that in order to obtain an efficiently convergent iteration, this approach should be augmented with a dynamic estimation of a
more » ... Lipschitz constant, leading to a runtime complexity of O( 1 ) in terms of the desired precision . Additionally, we devise a stopping criterion based on a duality gap as a sound basis for competitive comparison and show how to compute it efficiently. We evaluate our results using the publicly available Middlebury database and a set of computer generated graphical models that highlight specific aspects, along with other state-of-the-art methods for MAP-inference. c 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
doi:10.1109/cvpr.2011.5995652 dblp:conf/cvpr/SavchynskyyKSS11 fatcat:z3fgazxkbzevpbvqbxooheqqie