  Beam search is a desirable choice of test-time decoding algorithm for neural
sequence models because it potentially avoids search errors made by simpler
greedy methods. However, typical cross entropy training procedures for these
models do not directly consider the behaviour of the final decoding method. As
a result, for cross-entropy trained models, beam decoding can sometimes yield
reduced test performance when compared with greedy decoding. In order to train
models that can more effectively make use of beam search, we propose a new
training procedure that focuses on the final loss metric (e.g. Hamming loss)
evaluated on the output of beam search. While well-defined, this "direct loss"
objective is itself discontinuous and thus difficult to optimize. Hence, in our
approach, we form a sub-differentiable surrogate objective by introducing a
novel continuous approximation of the beam search decoding procedure. In
experiments, we show that optimizing this new training objective yields
substantially better results on two sequence tasks (Named Entity Recognition
and CCG Supertagging) when compared with both cross entropy trained greedy
decoding and cross entropy trained beam decoding baselines.
