Abstract: Document-level machine translation focuses on the translation of entire documents from a source to a target language. It is widely regarded as a challenging task since the translation of the individual sentences in the document needs to retain aspects of the discourse at document level. However, document-level translation models are usually not trained to explicitly ensure discourse quality. Therefore, in this paper we propose a training approach that explicitly optimizes two established discourse metrics, lexical cohesion and coherence, by using a reinforcement learning objective. Experiments over four different language pairs and three translation domains have shown that our training approach has been able to achieve more cohesive and coherent document translations than other competitive approaches, yet without compromising the faithfulness to the reference translation. In the case of the Zh-En language pair, our method has achieved an improvement of 2.46 percentage points (pp) in LC and 1.17 pp in COH over the runner-up, while at the same time improving 0.63 pp in BLEU score and 0.47 pp in F-BERT.