Linear Approximation to ADMM for MAP inference

Maximum a posteriori (MAP) inference is one of the fundamental inference tasks in graphical models. MAP inference is in general NP-hard, making approximate methods of interest for many problems. One successful class of approximate inference algorithms is based on linear programming (LP) relaxations. The augmented Lagrangian method can be used to overcome a lack of strict convexity in LP relaxations, and the Alternating Direction Method of Multipliers (ADMM) provides an elegant algorithm for finding the saddle point of the augmented Lagrangian. Here we present an ADMM-based algorithm to solve the primal form of the MAPLP whose closed form updates are based on a linear approximation technique. Our technique gives efficient, closed form updates that converge to the global optimum of the LP relaxation. We compare our algorithm to two existing ADMM-based MAP-LP methods, showing that our technique is faster on general, non-binary or non-pairwise models.