  Many natural language processing tasks can be modeled into structured
prediction and solved as a search problem. In this paper, we distill an
ensemble of multiple models trained with different initialization into a single
model. In addition to learning to match the ensemble's probability output on
the reference states, we also use the ensemble to explore the search space and
learn from the encountered states in the exploration. Experimental results on
two typical search-based structured prediction tasks -- transition-based
dependency parsing and neural machine translation show that distillation can
effectively improve the single model's performance and the final model achieves
improvements of 1.32 in LAS and 2.65 in BLEU score on these two tasks
respectively over strong baselines and it outperforms the greedy structured
prediction models in previous literatures.
