There was a consensus among reviewers that this paper is sound and makes interesting contributions towards more personalized federated learning. After the author rebuttal, there was some discussion among reviewers regarding the "true" underlying objective that this approach is optimizing. It was decided that although very interesting, this point is beyond the scope of the paper. Therefore we accepted the paper, but I recommend that the authors add to the final version a discussion of potential future work along the lines of showing under which conditions the objective they propose can be provably useful (e.g., to improve generalization performance).