We consider the problem of topic-focused abstractive summarization, where the goal is to generate an abstractive summary focused on a particular topic, a phrase of one or multiple words. We hypothesize that the task of generating topic-focused summaries can be improved by showing the model what it must not focus on. We introduce a deep reinforcement learning approach to topic-focused abstractive summarization, trained on rewards with a novel negative example baseline. We define the input in this problem as the source text preceded by the topic. We adapt the CNN-Daily Mail and New York Times summarization datasets for this task. We then show through experiments on existing rewards that the use of a negative example baseline can outperform the use of a self-critical baseline, in Rouge, BERTScore, and human evaluation metrics.