Paper:
Federated Learning (FL) refers to learning a high quality global model based on decentralized data storage, without ever copying the raw data. A natural scenario arises with data created on mobile phones by the activity of their users. Given the typical data heterogeneity in such situations, it is natural to ask how can the global model be personalized for every such device, individually. In this work, we point out that the setting of Model Agnostic Meta Learning (MAML), where one optimizes for a fast, gradient-based, few-shot adaptation to a heterogeneous distribution of tasks, has a number of similarities with the objective of personalization for FL. We present FL as a natural source of practical applications for MAML algorithms, and make the following observations. 1) The popular FL algorithm, Federated Averaging , can be interpreted as a meta learning algorithm. 2) Careful fine-tuning can yield a global model with higher accuracy, which is at the same time easier to personalize. However, solely optimizing for the global model accuracy yields a weaker personalization result. 3) A model trained using a standard datacenter optimization method is much harder to personalize, compared to one trained using Federated Averaging, supporting the first claim. These results raise new questions for FL, MAML, and broader ML research.

Review:
Update: I thank authors for the rebuttal. I agree that direction of exploring personalization in FL is interesting. With a stronger methodological contribution, this could become a good paper.
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The main contribution of this paper is to notice the connection between Federated Averaging (FedAvg) and Model Agnostic Meta Learning algorithms (MAML). Authors also consider an algorithm that first trains with FedAvg and then continues training using Reptile.
Pros:
Interpretation of FedAvg as a meta-learning algorithm is interesting.
Cons:
Very limited methodological contribution. Proposed algorithm is essentially two existing algorithms applied one after another.
Experiments are not conducted rigorously enough. There are many arbitrary hyperparameter choices which may bias the conclusions made in the paper. Statement "We tried SGD with a range of other learning rates, and in all cases we observed this value to work the best." is alarming suggesting that authors tried a variation of settings observing test data performance and reported a few selected runs. Although "each experiment was repeated 9 times with random initialization", the train/test split of the clients was fixed. Randomizing over client train/test split could help to improve the reliability of the results.
EMNIST-62 is the only dataset analyzed in some detail. This dataset has drastically varying P(y|x) across clients, i.e. some people write zeros as some others write 'o's. This suggests that it is very hard to train a good global model and personalization is necessary. However this doesn't mean that Shakespeare dataset "does not provide any interesting insights". Perhaps, it is indeed more interesting and challenging, demanding more advanced methodology.
In Figure 1, number of communication rounds may be impractical for FL (considering also addition 200 Reptile rounds). On Shakespeare, FedAvg paper reports 54% accuracy achieved in under 50 communication rounds in one of the settings. There are also recent works on improving communication efficiency that were not discussed or studied for personalization quality, e.g. FedProx from "Federated Optimization in Heterogeneous Networks" and PFNM from "Bayesian Nonparametric Federated Learning of Neural Networks".
Questions about Figure 2 experiments:
1. Fine-tuning requires 200 extra epochs over the initially trained model. What's the initial model accuracy when FedAvg is further trained with Adam optimizer for 200 extra communication rounds?
2. The personalized test accuracy with FedAvg and Reptile fine-tuning reaches the same value in 10 update epochs, even when Reptile fine-tuning gets 200 extra initial training epochs. Does Reptile fine-tuning provide additional benefits to the initial model as compared to running FedAvg for more number of epochs?