Self-training achieves enormous success in various semi-supervised and weakly-supervised learning tasks. The method can be interpreted as a teacher-student framework, where the teacher generates pseudo-labels, and the student makes predictions. The two models are updated alternatingly. However, such a straightforward alternating update rule leads to training instability. This is because a small change in the teacher may result in a significant change in the student. To address this issue, we propose {ours}, short for differentiable self-training, that treats teacher-student as a Stackelberg game. In this game, a leader is always in a more advantageous position than a follower. In self-training, the student contributes to the prediction performance, and the teacher controls the training process by generating pseudo-labels. Therefore, we treat the student as the leader and the teacher as the follower. The leader procures its advantage by acknowledging the followers strategy, which involves differentiable pseudo-labels and differentiable sample weights. Consequently, the leader-follower interaction can be effectively captured via Stackelberg gradient, obtained by differentiating the followers strategy. Experimental results on semi- and weakly-supervised classification and named entity recognition tasks show that our model outperforms existing approaches by large margins.
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