In this work, we develop new self-learning techniques with an attention-based sequence-to-sequence (seq2seq) model for automatic speech recognition (ASR). For untranscribed speech data, the hypothesis from an ASR system must be used as a label. However, the imperfect ASR result makes unsupervised learning difficult to consistently improve recognition performance especially in the case that multiple powerful teacher models are unavailable. In contrast to conventional unsupervised learning approaches, we adopt the multi-task learning (MTL) framework where the n-th best ASR hypothesis is used as the label of each task. The seq2seq network is updated through the MTL framework so as to find the common representation that can cover multiple hypotheses. By doing so, the effect of the hard-decision errors can be alleviated. We first demonstrate the effectiveness of our self-learning methods through ASR experiments in an accent adaptation task between the US and British English speech. Our experiment results show that our method can reduce the WER on the British speech data from 14.55% to 10.36% compared to the baseline model trained with the US English data only. Moreover, we investigate the effect of our proposed methods in a federated learning scenario.