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We present the first real-world application of methods for improving neural machine translation (NMT) with human reinforcement, based on explicit and implicit user feedback collected on the eBay e-commerce platform. Previous work has been confined to simulation experiments, whereas in this paper we work with real logged feedback for offline bandit learning of NMT parameters. We conduct a thorough analysis of the available explicit user judgments—five-star ratings of translation quality—and show that they are not reliable enough to yield significant improvements in bandit learning. In contrast, we successfully utilize implicit task-based feedback collected in a cross-lingual search task to improve task-specific and machine translation quality metrics.