Reviews: Necessary and Sufficient Geometries for Gradient Methods

POST-AUTHOR FEEDBACK: I thank the authors for their explanations, which addresses my concerns. I look forward to seeing the camera-ready version with improved results and the clarifications. The paper is well-written, the technical results are precise and correct as far as I can tell, and the results are novel and interesting. However, I am slightly puzzled over a few points, some of which pertain to the interpretation of the results. I believe the paper would significantly benefit from clarifying the following points: * The authors refer to mirror descent with (fixed) weighted Euclidean distance as an adaptive gradient algorithm, but this connection is not clear to me.