This work focuses on online dereverberation for hearing devices using the weighted prediction error (WPE) algorithm. WPE filtering requires an estimate of the target speech power spectral density (PSD). Recently deep neural networks (DNNs) have been used for this task. However, these approaches optimize the PSD estimate which only indirectly affects the WPE output, thus potentially resulting in limited dereverberation. In this paper, we propose an end-to-end approach specialized for online processing, that directly optimizes the dereverberated output signal. In addition, we propose to adapt it to the needs of different types of hearing-device users by modifying the optimization target as well as the WPE algorithm characteristics used in training. We show that the proposed end-to-end approach outperforms the traditional and conventional DNN-supported WPEs on a noise-free version of the WHAMR! dataset.