Designing RNA molecules has garnered recent interest in medicine, synthetic biology, biotechnology and bioinformatics since many functional RNA molecules were shown to be involved in regulatory processes for transcription, epigenetics and translation. Since an RNA's function depends on its structural properties, the RNA Design problem is to find an RNA sequence which satisfies given structural constraints. Here, we propose a new algorithm for the RNA Design problem, dubbed LEARNA. LEARNA uses deep reinforcement learning to train a policy network to sequentially design an entire RNA sequence given a specified target structure. By meta-learning across 65000 different RNA Design tasks for one hour on 20 CPU cores, our extension Meta-LEARNA constructs an RNA Design policy that can be applied out of the box to solve novel RNA Design tasks. Methodologically, for what we believe to be the first time, we jointly optimize over a rich space of architectures for the policy network, the hyperparameters of the training procedure and the formulation of the decision process. Comprehensive empirical results on two widely-used RNA Design benchmarks, as well as a third one that we introduce, show that our approach achieves new state-of-the-art performance on the former while also being orders of magnitudes faster in reaching the previous state-of-the-art performance. In an ablation study, we analyze the importance of our method's different components.