In this paper, we propose an end-to-end graph learning framework, namely Iterative Deep Graph Learning (IDGL), for jointly learning graph structure and graph embedding simultaneously. We first cast graph structure learning problem as similarity metric learning problem and leverage an adapted graph regularization for controlling smoothness, connectivity and sparsity of the generated graph. We further propose a novel iterative method for searching for hidden graph structure that augments the initial graph structure. Our iterative method dynamically stops when the learned graph structure approaches close enough to the optimal graph. Our extensive experiments demonstrate that the proposed IDGL model can consistently outperform or match state-of-the-art baselines in terms of both downstream task performance and computational time. The proposed approach can cope with both transductive training and inductive training.
The paper proposes an extension of learning graph structure and GNN concurrently, by considering that real-world graphs are often noisy and incomplete. The idea of optimizing the intrinsic graph structure iteratively for down-stream prediction tasks is interesting. Experimental results demonstrate the effectiveness of proposed method. 
Strengths:
1）the paper proposes a learnable similarity metric function and a graph regularization for learning an optimal graph structure for prediction.
2）Besides raw node features, the paper attempts to optimize graph structures via learned node embeddings in an iterative manner. 
3）The paper is easy to read, and experiments show that the proposed method performs well.
Weaknesses:
1）Compared with LDS [1], this work seems to overlook the bi-level optimization problem for learning model parameters based on the optimal graph structure. The reason behind this method is expected. 
2）Although the paper claims that the dependence of raw node features for learning graph structure has been weakened,  empirical analysis on this point is not given. The feature matrices in experiments are not strictly independent with graph structures.
3) As shown in Appendix B, too many hyper-parameters are involved. I conjecture it will be difficult to reproduce the experimental results.
4) Eqs.(2), (3) and (10) are problematic. Node embeddings Z should be included in them. Eq.(10) does not have theoretical proof. According to Eq.(10), the method cannot handle graphs with noisy edges. In experiments, there are edge deletions, but no edge addings. Experiments with attacked graph are expected.
5) Although this method is claimed efficient, it is indeed slower than the classic GNNs due to the iterative operation. The details of training time comparison between this method and GNNs such as GCN and GAT will be helpful. I was wondering why this method is faster than LDS. Is it due to removing the bi-level optimization problem ? 
6) Although the method can handle inductive training, it is hardly scale to big networks. Pubmed is an open citation network with around 20,000 nodes similar to Cora and Citeseer. Those three datasets are popularly used in GNNs as testbed. However, Pubmed is not used in this work. I conjecture that the new method cannot handle such a big dataset efficiently.
Overall, this proposed method is well motivated, but the technical novelty is limited.