As regards directly integrating beam-search, we found (a) that beam-search often produces a set of similar top-N candidates, and (b) that decoding with only the objective p(Y |X) can easily lead to irrelevant candidates.
(See section 7.3) we use the selective-sampling method to generate candidates for all our experiments; this (a) samples stochastically then (b) selects using a learned objective from data.