Message Passing For Soft Constraint Dual Decomposition

Dual decomposition provides the opportunity to build complex, yet tractable, structured prediction models using linear constraints to link together submodels that have available MAP inference routines. However, since some constraints might not hold on every single example, such models can often be improved by relaxing the requirement that these constraints always hold, and instead replacing them with soft constraints that merely impose a penalty if violated. A dual objective for the resulting MAP inference problem differs from the hard constraint problem's associated dual decomposition objective only in that the dual variables are subject to box constraints. This paper introduces a novel primaldual block coordinate descent algorithm for minimizing this general family of box-constrained objectives. Through experiments on two natural language corpus-wide inference tasks, we demonstrate the advantages of our approach over the current alternative, based on copying variables, adding auxiliary submodels and using traditional dual decomposition. Our algorithm performs inference in the same model as was previously published for these tasks, and thus is capable of achieving the same accuracy, but provides a 2-10x speedup over the current state of the art.