Recently several end-to-end speaker verification systems based on deep neural networks (DNNs) have been proposed. These systems have been proven to be competitive for text-dependent tasks as well as for text-independent tasks with short utterances. However, for text-independent tasks with longer utterances, end-to-end systems are still outperformed by standard i-vector + PLDA systems. In this work, we develop an end-to-end speaker verification system that is initialized to mimic an i-vector + PLDA baseline. The system is then further trained in an end-to-end manner but regularized so that it does not deviate too far from the initial system. In this way we mitigate overfitting which normally limits the performance of end-to-end systems. The proposed system outperforms the i-vector + PLDA baseline on both long and short duration utterances.