  In natural language processing tasks performance of the models is often
measured with some non-differentiable metric, such as BLEU score. To use
efficient gradient-based methods for optimization, it is a common workaround to
optimize some surrogate loss function. This approach is effective if
optimization of such loss also results in improving target metric. The
corresponding problem is referred to as loss-evaluation mismatch. In the
present work we propose a method for calculation of differentiable lower bound
of expected BLEU score that does not involve computationally expensive sampling
procedure such as the one required when using REINFORCE rule from reinforcement
learning (RL) framework.
