Though we are doing lattice reranking rather than k-best reranking, the learning problem for our fine model is similar to that for k-best reranking in that the decoder is exact (i.e., there is no pruning that could lead to different patterns of search error as the parameters change).
phrase lattice generation and pruning (described in Section 6.3.2) only depend on the coarse phrase-based feature weights and the maximum dependency length constraints (described in Section 6.3.3); they do not depend on the fine model parameters.