While watching television, people increasingly consume additional content related to what they are watching. We consider the task of finding video content related to a live television broadcast for which we leverage the textual stream of subtitles associated with the broadcast. We model this task as a Markov decision process and propose a method that uses reinforcement learning to directly optimize the retrieval effectiveness of queries generated from the stream of subtitles. Our dynamic query modeling approach significantly outperforms state-of-the-art baselines for stationary query modeling and for text-based retrieval in a television setting. In particular we find that carefully weighting terms and decaying these weights based on recency significantly improves effectiveness. Moreover, our method is highly efficient and can be used in a live television setting, i.e., in near real time.