  The discrepancy between maximum likelihood estimation (MLE) and task measures
such as BLEU score has been studied before for autoregressive neural machine
translation (NMT) and resulted in alternative training algorithms (Ranzato et
al., 2016; Norouzi et al., 2016; Shen et al., 2016; Wu et al., 2018). However,
MLE training remains the de facto approach for autoregressive NMT because of
its computational efficiency and stability. Despite this mismatch between the
training objective and task measure, we notice that the samples drawn from an
MLE-based trained NMT support the desired distribution -- there are samples
with much higher BLEU score comparing to the beam decoding output. To benefit
from this observation, we train an energy-based model to mimic the behavior of
the task measure (i.e., the energy-based model assigns lower energy to samples
with higher BLEU score), which is resulted in a re-ranking algorithm based on
the samples drawn from NMT: energy-based re-ranking (EBR). We use both marginal
energy models (over target sentence) and joint energy models (over both source
and target sentences). Our EBR with the joint energy model consistently
improves the performance of the Transformer-based NMT: +4 BLEU points on
IWSLT'14 German-English, +3.0 BELU points on Sinhala-English, +1.2 BLEU on
WMT'16 English-German tasks.
