Sentence compression reduces the length of text by removing non-essential content while preserving important facts and grammaticality. Unsupervised objective driven methods for sentence compression can be used to create customized models without the need for ground-truth training data, while allowing flexibility in the objective function(s) that are used for learning and inference. Recent unsupervised sentence compression approaches use custom objectives to guide discrete search; however, guided search is expensive at inference time. In this work, we explore the use of reinforcement learning to train effective sentence compression models that are also fast when generating predictions. In particular, we cast the task as binary sequence labelling and fine-tune a pre-trained transformer using a simple policy gradient approach. Our approach outperforms other unsupervised models while also being more efficient at inference time.