We present a novel technique for jointly predicting semantic arguments for lexical predicates. The task is to find the best matching between semantic roles and sentential spans, subject to structural constraints that come from expert linguistic knowledge (e.g., in the FrameNet lexicon). We formulate this task as an integer linear program (ILP); instead of using an off-the-shelf tool to solve the ILP, we employ a dual decomposition algorithm, which we adapt for exact decoding via a branch-and-bound technique. Compared to a baseline that makes local predictions, we achieve better argument identification scores and avoid all structural violations. Runtime is nine times faster than a proprietary ILP solver.

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