Reviews: High-Dimensional Optimization in Adaptive Random Subspaces

Post-rebuttal update: The author's rebuttal addresses my (minor) concerns well, and my overall score remains the same. The approach is similar to earlier work such as: - M. Pilanci and M. J. Wainwright. The main innovations here are to extend this sketching technique to a wider class of convex objectives and to introduce a data-adaptive sketching technique that greatly improves the error bounds on the solution relative to a data-oblivious sketch. The proposed technique can also be performed iteratively to improve the accuracy of the solution without having to change the sketch matrix, so the sketch on the data only has to be performed once. Overall, I thought this was a high-quality paper.