While agreement-based joint training has proven to deliver state-of-the-art alignment accuracy, the produced word alignments are usually restricted to one-to-one mappings because of the hard constraint on agreement. We propose a general framework to allow for arbitrary loss functions that measure the disagreement between asymmetric alignments. The loss functions can not only be defined between asymmetric alignments but also between alignments and other latent structures such as phrase segmentations. We use a Viterbi EM algorithm to train the joint model since the inference is intractable. Experiments on Chinese-English translation show that joint training with generalized agreement achieves significant improvements over two state-of-the-art alignment methods.
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