This paper has a valuable contribution to meta-learning and greatly improves the state-of-the-art. The proposed idea that explicitly separates the meta-learning algorithm and meta-objective learning into two distinct phases is significantly effective as shown in experiments. The idea is quite original compared to the current trend of unified the deep learning black box.Theoretical convergence analysis shows the proposed method significantly improved sample efficiency compared to some reference examples. The authors addressed a comparison to PEARL, adequately and the additional insight will strengthen the paper a lot. Given that the rebuttal was strong and the analysis well made, I found that the paper be accepted.