Reviews: An Improved Analysis of Alternating Minimization for Structured Multi-Response Regression

This paper studies the multi-response regression model, and in particular, the alternating minimization algorithm for the problem . In contrast to prior work, this paper makes the following improvements: 1. It does not require the resampling assumptions that usually abound in showing results on alternating procedures. With good initialization, the procedure without resampling is able to achieve what is usually the minimax rate of such problems. The major technique is that of generic chaining, which allows the authors to prove bounds that hold uniformly over all iterates. I liked the paper and the result overall seems quite interesting, in particular points 1 and 2 above.