  We present Grid Beam Search (GBS), an algorithm which extends beam search to
allow the inclusion of pre-specified lexical constraints. The algorithm can be
used with any model that generates a sequence $ \mathbf{\hat{y}} =
\{y_{0}\ldots y_{T}\} $, by maximizing $ p(\mathbf{y} | \mathbf{x}) =
\prod\limits_{t}p(y_{t} | \mathbf{x}; \{y_{0} \ldots y_{t-1}\}) $. Lexical
constraints take the form of phrases or words that must be present in the
output sequence. This is a very general way to incorporate additional knowledge
into a model's output without requiring any modification of the model
parameters or training data. We demonstrate the feasibility and flexibility of
Lexically Constrained Decoding by conducting experiments on Neural
Interactive-Predictive Translation, as well as Domain Adaptation for Neural
Machine Translation. Experiments show that GBS can provide large improvements
in translation quality in interactive scenarios, and that, even without any
user input, GBS can be used to achieve significant gains in performance in
domain adaptation scenarios.
