How can we effectively regularize BERT? Although BERT proves its effectiveness in various downstream natural language processing tasks, it often overfits when there are only a small number of training instances. A promising direction to regularize BERT is based on pruning its attention heads based on a proxy score for head importance. However, heuristic-based methods are usually suboptimal since they predetermine the order by which attention heads are pruned. In order to overcome such a limitation, we propose AUBER, an effective regularization method that leverages reinforcement learning to automatically prune attention heads from BERT. Instead of depending on heuristics or rule-based policies, AUBER learns a pruning policy that determines which attention heads should or should not be pruned for regularization. Experimental results show that AUBER outperforms existing pruning methods by achieving up to 10% better accuracy. In addition, our ablation study empirically demonstrates the effectiveness of our design choices for AUBER.