Multi-face tracking in unconstrained videos is a challenging problem as faces of one person often can appear drastically different in multiple shots due to significant variations in scale, pose, expression, illumination, and make-up. Existing multi-target tracking methods often use low-level features which are not sufficiently discriminative for identifying faces with such large appearance variations. In this paper, we tackle this problem by learning discriminative, video-specific face representations using convolutional neural networks (CNNs). Unlike existing CNN-based approaches which are only trained on large-scale face image datasets offline, we automatically generate a large number of training samples using the contextual constraints for a given video, and further adapt the pre-trained face CNN to the characters in the specific videos using discovered training samples. The embedding feature space is fine-tuned so that the Euclidean distance in the space corresponds to the semantic face similarity. To this end, we devise a symmetric triplet loss function which optimizes the network more effectively than the conventional triplet loss. With the learned discriminative features, we apply an EM clustering algorithm to link tracklets across multiple shots to generate the final trajectories. We extensively evaluate the proposed algorithm on two sets of TV sitcoms and YouTube music videos, analyze the contribution of each component, and demonstrate significant performance improvement over existing techniques.