  Most existing Grammatical Error Correction (GEC) methods based on
sequence-to-sequence mainly focus on how to generate more pseudo data to obtain
better performance. Few work addresses few-shot GEC domain adaptation. In this
paper, we treat different GEC domains as different GEC tasks and propose to
extend meta-learning to few-shot GEC domain adaptation without using any pseudo
data. We exploit a set of data-rich source domains to learn the initialization
of model parameters that facilitates fast adaptation on new resource-poor
target domains. We adapt GEC model to the first language (L1) of the second
language learner. To evaluate the proposed method, we use nine L1s as source
domains and five L1s as target domains. Experiment results on the L1 GEC domain
adaptation dataset demonstrate that the proposed approach outperforms the
multi-task transfer learning baseline by 0.50 $F_{0.5}$ score on average and
enables us to effectively adapt to a new L1 domain with only 200 parallel
sentences.
