Review for NeurIPS paper: Lower Bounds and Optimal Algorithms for Personalized Federated Learning

The example derived for the lower bound and its idea behind are quite similar to that of Nesterov in [36]. And I have some questions about the example for the lower bound. In line 432, I didn't figure out why the expression of M is matrix dependent on the parity of n. Is there something wrong with my understanding? What's more, there are two identity matrices without specifying its dimension, making it hard to understand. Besides, 2. It seems that AL2SGD works well empirically.