AbstractCoreference evaluation metrics are hard to optimize directly as they are non-differentiable functions, not easily decomposable into elementary decisions. Consequently, most approaches optimize objectives only indirectly related to the end goal, resulting in suboptimal performance. Instead, we propose a differentiable relaxation that lends itself to gradient-based optimisation, thus bypassing the need for reinforcement learning or heuristic modification of cross-entropy. We show that by modifying the training objective of a competitive neural coreference system, we obtain a substantial gain in performance. This suggests that our approach can be regarded as a viable alternative to using reinforcement learning or more computationally expensive imitation learning.