Coreference resolution systems are typically trained with heuristic loss functions that require careful tuning. In this paper we instead apply reinforcement learning to directly optimize a neural mention-ranking model for coreference evaluation metrics. We experiment with two approaches: the REINFORCE policy gradient algorithm and a reward-rescaled max-margin objective. We find the latter to be more effective, resulting in a significant improvement over the current state-of-the-art on the English and Chinese portions of the CoNLL 2012 Shared Task.