Alternating Directions Dual Decomposition

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.