Contributions: As nicely summarized by Reviewer 1: Incorporating side information is a practical and valuable extension to online matrix completion. The results specializing to specific structures are helpful, primarily coming into play by bounding the quasi-dimension of the matrix relative to the side information. Presentation: Based on my own reading of the paper, I partially disagree with the reviewers about the clarity of the presentation. I think the introduction and discussion of related work are actually quite good. The writing in the main body of the paper is not necessarily bad, but I do agree that it is mathematically quite terse, which is likely to reduce the audience to experts in this area. Further comments to the authors: The authors are strongly advised to see if they can make the writing less terse. For instance, try to reduce the reliance on technical notation at least in the main paper, and elaborate more on mathematical statements in their discussion. Appendix B.2 does contain an appropriate review of the related literature, but the reviewers are correct that it does not explain which parts of the proof are different.