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Maximum a posteriori (MAP) inference in discrete-valued Markov random fieldsis a fundamental problem in machine learning that involves identifying the mostlikely configuration of random variables given a distribution. Due to thedifficulty of this combinatorial problem, linear programming (LP) relaxationsare commonly used to derive specialized message passing algorithms that areoften interpreted as coordinate descent on the dual LP. To achieve moredesirable computational properties, a number of methods regularize the LP withan entropy term, leading to a class of smooth message passing algorithms withconvergence guarantees. In this paper, we present randomized methods foraccelerating these algorithms by leveraging techniques that underlie classicalaccelerated gradient methods. The proposed algorithms incorporate the familiarsteps of standard smooth message passing algorithms, which can be viewed ascoordinate minimization steps. We show that these accelerated variants achievefaster rates for finding $\epsilon$-optimal points of the unregularizedproblem, and, when the LP is tight, we prove that the proposed algorithmsrecover the true MAP solution in fewer iterations than standard message passingalgorithms.

Accelerated Message Passing for Entropy-Regularized MAP Inference