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

The lower bounds established consider the number of oracle calls and the communication complexity. Also it is proven that there exists a method matching the lower bound. The rates are new and the paper is well-written. Interesting avenues for further research are a dependency on the number of clients. For a final version of the paper, besides the clarifications pointed out by reviewers discussing the range of parameters \lambda and \mu needs to be addressed, a discussion on how the number of clients affects convergence (i.e. in which constants the of the complexity estimates the nr. of clients has an influence) would further improve the paper.