Abstract: We present Neural Machine Translation (NMT) training using document-level metrics with batch-level documents. Previous sequence-objective approaches to NMT training focus exclusively on sentence-level metrics like sentence BLEU which do not correspond to the desired evaluation metric, typically document BLEU. Meanwhile research into document-level NMT training focuses on data or model architecture rather than training procedure. We find that each of these lines of research has a clear space in it for the other, and propose merging them with a scheme that allows a document-level evaluation metric to be used in the NMT training objective. We first sample pseudo-documents from sentence samples. We then approximate the expected document BLEU gradient with Monte Carlo sampling for use as a cost function in Minimum Risk Training (MRT). This two-level sampling procedure gives NMT performance gains over sequence MRT and maximum-likelihood training. We demonstrate that training is more robust for document-level metrics than with sequence metrics. We further demonstrate improvements on NMT with TER and Grammatical Error Correction (GEC) using GLEU, both metrics used at the document level for evaluations.