Supervised models suffer from the problem of domain shifting where distribution mismatch in the data across domains greatly affect model performance. To solve the problem, training data selection (TDS) has been proven to be a prospective solution for domain adaptation in leveraging appropriate data. However, conventional TDS methods normally requires a predefined threshold which is neither easy to set nor can be applied across tasks, and models are trained separately with the TDS process. To make TDS self-adapted to data and task, and to combine it with model training, in this paper, we propose a reinforcement learning (RL) framework that synchronously searches for training instances relevant to the target domain and learns better representations for them. A selection distribution generator (SDG) is designed to perform the selection and is updated according to the rewards computed from the selected data, where a predictor is included in the framework to ensure a task-specific model can be trained on the selected data and provides feedback to rewards. Experimental results from part-of-speech tagging, dependency parsing, and sentiment analysis, as well as ablation studies, illustrate that the proposed framework is not only effective in data selection and representation, but also generalized to accommodate different NLP tasks.