Abstractive summarization approaches based on Reinforcement Learning (RL) have recently been proposed to overcome classical likelihood maximization. RL enables to consider complex, possibly non differentiable, metrics that globally assess the quality and relevance of the generated outputs. ROUGE, the most used summarization metric, is known to suffer from bias towards lexical similarity as well as from sub-optimal accounting for fluency and readability of the generated abstracts. We thus explore and propose alternative evaluation measures: the reported human-evaluation analysis shows that the proposed metrics, based on Question Answering, favorably compare to ROUGE – with the additional property of not requiring reference summaries. Training a RL-based model on these metrics leads to improvements (both in terms of human or automated metrics) over current approaches that use ROUGE as reward.