Optimization of Graph Total Variation via Active-Set-based Combinatorial Reconditioning

• URL: http://arxiv.org/abs/2002.12236v1
• Date: Thu, 27 Feb 2020 16:33:09 GMT
• Title: Optimization of Graph Total Variation via Active-Set-based Combinatorial Reconditioning
• Authors: Zhenzhang Ye, Thomas M\"ollenhoff, Tao Wu, Daniel Cremers
• Abstract summary: We propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. We show that nested-forest decomposition of the inactive edges yields a guaranteed local linear convergence rate. Our results suggest that local convergence analysis can serve as a guideline for selecting variable metrics in proximal algorithms.
• Score: 48.42916680063503
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our preconditioner is driven by a sharp analysis of the local linear convergence rate depending on the "active set" at the current iterate. We show that nested-forest decomposition of the inactive edges yields a guaranteed local linear convergence rate. Further, we propose a practical greedy heuristic which realizes such nested decompositions and show in several numerical experiments that our reconditioning strategy, when applied to proximal gradient or primal-dual hybrid gradient algorithm, achieves competitive performances. Our results suggest that local convergence analysis can serve as a guideline for selecting variable metrics in proximal algorithms.

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