Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper introduces a definition for fairness between agents in federated learning that is derived from social choice theory. The authors name it core-stability. Intuitively, core-stability ensures that there is no incentive for any subgroup $S$ of agents to defect from the rest and create their own centralized model. The authors point out how core stability ensures that two basic conditions of proportionality, and Pareto optimality are satisfied. Moreover, the authors offer an optimization objective CoreFed which provably converges to a core-stable network under a set of reasonable assumptions (the definition of core-stability can be slightly relaxed to be local in order for the theory to extend more diverse settings). Finally, the authors provide some empirical results to show that CoreFed does better than the existing FedAvg objective at achieving core-stable fairness.
strengths_and_weaknesses: ## Originality
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### Strengths
- Though I am not familiar with the literature on the intersection of fair federated learning schemes and social choice theory, I was unable to find any work that used this notion of core-stability. As far as I can tell, this goal of essentially subgroup indifference has not been proposed before in federated learning. Moreover, I believe this is a fresh perspective that should be further explored in future work.

## Quality and Clarity
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### Weaknesses
- Some of the writing in the paper was needlessly wordy, particularly in the introduction and the abstract, and there were some minor grammatical issues throughout the paper. I think for the camera ready version it would be good to trim down these sections and polish the prose a bit further, but these problems do not get in the way of understanding the paper.
- The authors could have performed more empirical results to further investigate CoreFed on more commonly used and complex models than the simple CNN used for section 5.2. More comprehensive empirical results in general would be a great avenue for future work.

### Strengths
- The quality of the theoretical analysis in this paper is exceptional. The authors demonstrate that they have thought deeply about this problem from many different angles, and the math in the main body was all easy to follow (intuition for omitted proofs was quite good too). Though I didn't carefully read the proofs in the appendix, everything looked sound at a glance.

## Significance
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It's difficult for me to assess the significance of this work in the absence of experience in this line of research. What I can say is the claims are ostensibly sound, and the idea is very well motivated. 


questions: I have decided to accept this paper. I would raise my score even further if the authors could better contextualize their work to offer an explanation of perhaps why this notion of core-stability (which is quite natural) has not been used in the past, and the impact they believe it will have now.
limitations: Yes.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper studies core stability, where no subset of agents can benefit much from forming a new coalition, in federated learning. This paper shows that:
1. Core-stable solution exists when the utilities are continuous and the set of maximizers of any conical combination of the utilities is convex.
2. Maximizing $\sum \log(u_i(\theta))$ derives a core stable solution when $u_i$s are concave. The objective can be maximized efficiently through SGD. Interestingly, the gradient update is similar to FedAvg.
3. The work then extend the core-stability to approximate core-stability in the non-convex case.
strengths_and_weaknesses: The paper studies the core-stability in federated learning, showing the existence of core-stable solutions and providing an efficient algorithm to find the solution. The results are novel and clean. The presentation is clear. The algorithm CoreFed is quite subtle as it is similar to FedAvg only with different weight updates. Overall, it is a good work.

My only concern is about the definition of core-stability, where players are incentivized to form a new coalition only when $\frac{|S|}{n}u_i(\theta')\geq u_i(\theta)$. That is to say, a single player would prefer to learn by herself only if her utility can be increased to $n$ times the currently utility. The multiplier $\frac{|S|}{n}$ seems a little weird to me. It seems like that the results make more sense when $n$ is small.
questions: For the definition of core-stability, could the authors explain the intuition/motivation that the multiplicative constant is $\frac{|S|}{n}$? Intuitively, the players in $S$ have incentives to form a new coalition if $u_i(\theta')>u_i(\theta)$ for all $i\in S$ or approximately $u_i(\theta')>(1+\alpha)u_i(\theta)$ for some $\alpha>0$. 

Is there any technical challenge of extending the results to the setting where core stability is defined as $\nexists \theta', u_i(\theta')>(1+\alpha)u_i(\theta)$ for all $i\in S$? If so, could the authors list some of them?
limitations: NA
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper introduces a new notion of fairness dubbed as core-stable fairness in FL setting, by borrowing ideas from game theory and social choice theory. Core-stable fairness indicates there is no subset of agents that can benefit significantly by forming a coalition. The authors propose a new FL Protocol based on this new notion of fairness called CoreFed. The authors prove that CoreFed finds a core-stable model when the loss functions of agents are convex, and CoreFed can find an approximate model when loss functions are non-convex.  Finally the authors do an empirical comparison between CoreFed and FedAvg in which they show CoreFed achieves higher core-stable fairness than FedAvg while maintaining similar accuracy.  
strengths_and_weaknesses: **Strengths:**
* The paper appears to be theoretically sound as well as the claims seem to be supported by theoretical proofs. 
* The paper introduces a new notion of fairness in FL settings, that has not been studied in the literature.  

**Weaknesses:**

Mainly is due to limited empirical evaluation. In particular:
* The proposed protocol/algo only compared to FedAvg, and not with some existing recent works in the Literature, e.g., Ref 20 [Li et al., 2020].
* Limited experiments and few number of agents (i.e., 3 agent in Table 1 ).
* Lack of experiments in settings with low quality data from some agents. This was a promise of the proposed algorithm to be robust against low quality agents in the summary and main body of the paper but was not supported by experiments. 

*Minor Comments (not affecting review score):*

Duplicate references in introduction [32, 23, 8, 35, 36, 26, 23] 

questions: 1. What are the $privacy$ implications of Core-stable fairness ? Some discussion around this in the paper would be useful. 
2. Similarly, What are the implications of CoreFed protocol, in regards to communication-cost given that in addition to local updates, local losses need to be also communicated back to the server. How scalable this protocol is in real world applications ?
limitations: NA
review_title: null

Meta-review: metareview: This paper introduces core stability as a fairness notion for federated learning, which is motivated by social choice theory. The reviewers all agreed that the paper provides a novel contribution to studying fairness in federated learning. The authors have also addressed reviewers' questions during the discussion period.
confidence: Certain
Decision: Accept