Objective. Deep neural networks (DNNs) have shown unprecedented success in various brain-machine interface applications such as epileptic seizure prediction. However, existing approaches typically train models in a patient-specific fashion due to the highly personalized characteristics of epileptic signals. Therefore, only a limited number of labeled recordings from each subject can be used for training. As a consequence, current DNN based methods demonstrate poor generalization ability to some extent due to the insufficiency of training data. On the other hand, patient-independent models attempt to utilize more patient data to train a universal model for all patients by pooling patient data together. Despite different techniques applied, results show that patient-independent models perform worse than patient-specific models due to high individual variation across patients. A substantial gap thus exists between patient-specific and patient-independent models. Approach. In this paper, we propose a novel training scheme based on knowledge distillation which makes use of a large amount of data from multiple subjects. It first distills informative features from signals of all available subjects with a pre-trained general model. A patient-specific model can then be obtained with the help of distilled knowledge and additional personalized data. Main results. Four state-of-the-art seizure prediction methods are trained on the Children's Hospital of Boston-MIT sEEG database with our proposed scheme. The resulting accuracy, sensitivity, and false prediction rate show that our proposed training scheme consistently improves the prediction performance of state-of-the-art methods by a large margin. Significance. The proposed training scheme significantly improves the performance of patient-specific seizure predictors and bridges the gap between patient-specific and patient-independent predictors.