  For sequence-to-sequence tasks it is challenging to combine individual system
outputs. Further, there is also often a mismatch between the decoding criterion
and the one used for assessment. Minimum Bayes' Risk (MBR) decoding can be used
to combine system outputs in a manner that encourages better alignment with the
final assessment criterion. This paper examines MBR decoding for Grammatical
Error Correction (GEC) systems, where performance is usually evaluated in terms
of edits and an associated F-score. Hence, we propose a novel MBR loss function
directly linked to this form of criterion. Furthermore, an approach to expand
the possible set of candidate sentences is described. This builds on a current
max-voting combination scheme, as well as individual edit-level selection.
Experiments on three popular GEC datasets and with state-of-the-art GEC systems
demonstrate the efficacy of the proposed MBR approach. Additionally, the paper
highlights how varying reward metrics within the MBR decoding framework can
provide control over precision, recall, and the F-score in combined GEC
systems.
