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arXiv · 1212.6550

Alternating Directions Dual Decomposition

Andre F. T. Martins·Mario A. T. Figueiredo·Pedro M. Q. Aguiar·Noah A. Smith·Eric P. Xing
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Abstract

We propose AD3, a new algorithm for approximate maximum a posteriori (MAP) inference on factor graphs based on the alternating directions method of multipliers. Like dual decomposition algorithms, AD3 uses worker nodes to iteratively solve local subproblems and a controller node to combine these local solutions into a global update. The key characteristic of AD3 is that each local subproblem has a quadratic regularizer, leading to a faster consensus than subgradient-based dual decomposition, both theoretically and in practice. We provide closed-form solutions for these AD3 subproblems for binary pairwise factors and factors imposing first-order logic constraints. For arbitrary factors (large or combinatorial), we introduce an active set method which requires only an oracle for computing a local MAP configuration, making AD3 applicable to a wide range of problems. Experiments on synthetic and realworld problems show that AD3 compares favorably with the state-of-the-art.

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Andre F. T. Martins, Mario A. T. Figueiredo, Pedro M. Q. Aguiar, Noah A. Smith, Eric P. Xing. 2012-12-28. Alternating Directions Dual Decomposition. https://arxiv.org/abs/1212.6550

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