Given a question and a set of answer candidates, answer triggering determines whether the candidate set contains any correct answers. If yes, it then outputs a correct one. In contrast to existing pipeline methods which first consider individual candidate answers separately and then make a prediction based on a threshold, we propose an end-to-end deep neural network framework, which is trained by a novel group-level objective function that directly optimizes the answer triggering performance. Our objective function penalizes three potential types of error and allows training the framework in an end-to-end manner. Experimental results on the WikiQA benchmark show that our framework outperforms the state of the arts by a 6.6% absolute gain under F1 measure.