MAP inference via Block-Coordinate Frank-Wolfe Algorithm

TL;DR

This paper introduces a novel block-coordinate Frank-Wolfe algorithm for MAP inference that leverages Lagrangean relaxation and outperforms existing methods on complex structured energy minimization tasks.

Contribution

It proposes a new proximal bundle method utilizing a multi-plane block-coordinate Frank-Wolfe approach tailored for structured MAP inference problems.

Findings

Outperforms state-of-the-art Lagrangean decomposition algorithms

Effective on challenging Markov Random Field problems

Improves efficiency in multi-label discrete tomography and graph matching

Abstract

We present a new proximal bundle method for Maximum-A-Posteriori (MAP) inference in structured energy minimization problems. The method optimizes a Lagrangean relaxation of the original energy minimization problem using a multi plane block-coordinate Frank-Wolfe method that takes advantage of the specific structure of the Lagrangean decomposition. We show empirically that our method outperforms state-of-the-art Lagrangean decomposition based algorithms on some challenging Markov Random Field, multi-label discrete tomography and graph matching problems.