Mining topics on social media (e.g., Twitter and Facebook) is an important task for various applications, such as hot topic discovery, advertising, and promotion activities. Topic modeling techniques are helpful to find out topics that people are talking about. However, current full-analysis models cannot perform well on a focused analysis task-find out all topics related to one particular area in short documents. One reason is that the targeted topic is usually sparse in the corpus of short texts. Another one is, during clustering, even minor errors may compound and render the model useless. This article studies these problems and proposes a targeted analysis model (TAM) with reinforcement learning (RL) to extract any specific topic in a given corpus and perform fine-grained topic generation. In this work, we design a reward function of RL to prevent the false propagation problem induced by Gibbs sampling during the clustering. We amend the targeted topic modeling techniques to the case of RL and use policy search combined with the Gibbs EM algorithm for parameter estimation. Metrics of F1 score and the proposed normalized mutual information-F1 are exploited for the evaluation of clustering and topic generation, respectively. Our experiments have demonstrated that TAM can outperform state-of-the-art models-specifically achieving 25.7% improvement on the F1 score for binary clustering on average.