Paper:
Federated learning involves training statistical models in massive, heterogeneous networks. Naively minimizing an aggregate loss function in such a network may disproportionately advantage or disadvantage some of the devices. In this work, we propose q-Fair Federated Learning (q-FFL), a novel optimization objective inspired by fair resource allocation in wireless networks that encourages a more fair (i.e., more uniform) accuracy distribution across devices in federated networks. To solve q-FFL, we devise a communication-efficient method, q-FedAvg, that is suited to federated networks. We validate both the effectiveness of q-FFL and the efficiency of q-FedAvg on a suite of federated datasets with both convex and non-convex models, and show that q-FFL (along with q-FedAvg) outperforms existing baselines in terms of the resulting fairness, flexibility, and efficiency.

Review:
The problem of fairness in federated learning (FL) is important given the popularity of the topic and its immediate impact on the society. Vanilla FL approaches may be subject to poor performance for clients whose data is under-represented across all participants. This paper proposes a new algorithm for federated learning to reduce variance in performance across clients. The inspiration for the algorithm comes from the problem of uniform  resource allocation in wireless networks.
While the problem and the motivation for the algorithm are interesting on the high level, I think this paper does not deliver the key ideas in sufficient detail and clarity.
On the algorithms side, I am still unclear on how the Lipschitz constant L is estimated on the first run with q=0. Are the results for q=0 in the experiments reported for this run or is it repeated with the learned L? Further, this procedure suggests that the number of communication rounds is at least doubled for the end-to-end training. Tuning q, which seems to be necessary, may require even more communication rounds.
While there are a lot of experiments in the paper (across main text and supplementary), none seem to be carried out sufficiently well. Understanding the complete experimental setup for at least one of them is also quite hard due to numerous supplementary references throughout the experiments section. I would recommend to focus on fewer experiments, but present more thorough results. Below are some suggestions.
The importance of resource allocation in FL appears to me to be directly related to the key FL aspects such as degree of data heterogeneity and number of clients. This submission is lacking experiments comparing FedAvg to the proposed method under these settings (which can be simulated using available datasets). To argue in favor of the proposed approach it is important to demonstrate failure modes of the existing algorithms under some realistic scenarios and present a solution using new algorithm.
Accuracies in Fashion MNIST and Shakespeare experiments seem quite poor suggesting some problems with the setup. FedAvg paper reports 54% on Shakespeare, whereas this paper reports 52%. It also appears that the number of considered "devices" on Shakespeare is significantly smaller than in the FedAvg paper (31 vs 1146) - what is the reason for this?
On Fashion MNIST, AFL paper reports 80%+ accuracy while achieving 90%+ on the combined dataset seems relative easy based on the results mentioned on the Github repository of the dataset. This paper reports 78% for the proposed method and AFL. Why is there a discrepancy with AFL paper and what is the performance of FedAvg on this dataset (assuming some suitable CNN architecture)? Is there a reason to believe that this dataset is much harder for federated learning than MNIST, where FedAvg roughly matches full data training?
This statement is ambiguous "uniform sampling is a static method and can easily overfit to devices with very few data points, whereas q-FFL has better generalization properties due to its dynamic nature." If there is a device with very few data points it is easy to overfit to it and q-FFL will essentially ignore that device since the loss on this device is very small. Why does this not lead to more severe overfitting behavior?