Abstract Document summarisation can be formulated as a sequential decision-making problem, which can be solved by Reinforcement Learning (RL) algorithms. The predominant RL paradigm for summarisation learns a cross-input policy, which requires considerable time, data and parameter tuning due to the huge search spaces and the delayed rewards. Learning input-specifific RL policies is a more effificient alternative but so far depends on handcrafted rewards, which are diffificult to design and yield poor performance. We propose RELIS, a novel RL paradigm that learns a reward function with Learning-to-Rank (L2R) algorithms at training time and uses this reward function to train an input-specifific RL policy at test time. We prove that RELIS guarantees to generate near-optimal summaries with appropriate L2R and RL algorithms. Empirically, we evaluate our approach on extractive multi-document summarisation. We show that RELIS reduces the training time by two orders of magnitude compared to the state-of-the-art models while performing on par with them