Venue: NeurIPS 2022 Conference

Reviews:

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 studies the problem of fair payoff allocation of compensation/cost among a group of collaborating parties which pool their data to jointly train a machine learning model. Specifically, the authors considered several fairness properties (including a linearity property which helps to uniquely determines an allocation scheme). The authors then presented a unique allocation scheme which satisfies these properties. From there, the authors considered and resolved a more general setting where parties may not have sufficient budget by balancing their budget and model performances.
strengths_and_weaknesses: Strengths:
- the collaborative machine learning setting is interesting and important.
- the considered fairness axioms are reasonable, for example, the budge balance that keeps the total payoff/cost to zero among the group of parties.
- the proposed payoff allocation scheme is unique and supported with theoretical fairness axioms

Weaknesses:
- there is limited empircal comparison and analysis with prior works.

Some minor comments:
- the uniqueness of the allocation scheme is largely a result from the linearity axiom, that draws a connection to the Shapley value. I can see that the advantage of imposing the linearity is that it utilises the fairness of the Shapley value (a classic solution concept), which is a reasonable constraint for finding a unique solution. However, I do not see why allocation schemes that do not exhibit the linearity dependency on the Shapley value are inferior in the particular setting. This may be beyond the scope of the current paper, but a more comprehensive analysis on the class of payoff allocation schemes (without the linearity property) may be explored further in future works.  I also acknowledge the motivation and overall contributions of the present paper.
- As far as I know, there are quite a few papers on payoff allocation with external funds, but only a few on fully collaborative settings. I find this topic to be interesting for the community. I would not argue for acceptance weighing the strengths/weaknesses, but I am slightly positive hence a weak accept.
questions: Can the authors comment on the payoff allocation schemes that do not satisfy the linearity property?
limitations: I do not observe any negative societal impact.
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 considers collaborative machine learners where multiple vendors combine their data so as the generate more accurate models than either of them can achieve on their own. The authors focus on tradeoffs between payoff and model rewards, including for budget restricted vendors. The method proposed can be derived from two methods,  based on desirable properties of the parties’ payoffs or based on the underlying payoff flows from one party to another (the second allows handling constraints on the budgets of vendors). The authors propose desiderata for buiding a fair adjustment of the payoff flows that trades off between the model reward’s performance and the payoff reward. The authors also support their claims on several collaborative ML scenarios. 

Thansk for the detailed author comments. 
strengths_and_weaknesses: I find the topic of the paper very interesting. There have recently been multiple works on mechanisms for allowing vendors to share their data, focusing on how to incentivize them to do so by fairly sharing the proceeds of the resulting model (or by yielding smaller models where the quality of a model a party receives depends on its contribution). The key strength of the paper is by combining key methodology from cooperative game theory, such as the Shapley value and the desiderata yielding this value, and applying them to this domain. 

However, given that there are already multiple papers on this topic, I believe the bar for additional work here is higher. The paper has some weaknesses. First, while taking an axiomatic (desiderata) approach, I'm not sure I fully by into the proposed desiderata here. Specifically, for the Shapley value which is a common theme here, one of the axioms is linearity across games. Other powre indices are triggered by alternative approaches. See, for e.g. (and I'd encourage the authors to discuss these, in more depth):

Dubey, Pradeep. "On the uniqueness of the Shapley value." International Journal of Game Theory 4.3 (1975): 131-139.
Dubey, Pradeep, and Lloyd S. Shapley. "Mathematical properties of the Banzhaf power index." Mathematics of Operations Research 4.2 (1979): 99-131.Feltkamp, Vincent. "Alternative axiomatic characterizations of the Shapley and Banzhaf values." International Journal of Game Theory 24.2 (1995): 179-186.
Monderer, Dov, and Dov Samet. "Variations on the Shapley value." Handbook of game theory with economic applications 3 (2002): 2055-2076.
(and see the very related discussion in Torra, Vicenç, and Yasuo Narukawa. Modeling decisions: information fusion and aggregation operators. Springer Science & Business Media, 2007.)

Further, regarding writing, I feel like a more detailed introduction in cooperative game theory is warranted. You build on these foundations, but the discussion is short. For example, what are the key differences between such power indices and other known methods such as the Core or Nucleolus? Why are these less applicable here? 

Finally, I suggest addressing computational constraints. What is the exact time (and memory) complexity of the proposed approaches? Are you computing Shapley values exacly, or approximating? Can alternative computational mechanisms be used? 

questions: Are there any guarantees on the shared data? Can one vendor "poison" the data given to others so as to achieve its goals? See discussion in: Meir, Reshef, Ariel D. Procaccia, and Jeffrey S. Rosenschein. "Algorithms for strategyproof classification." Artificial Intelligence 186 (2012): 123-156.

Further, can other foundations of mechanism design (such as auctions or the Vickery-Clarke-Groves mechanism) be used here for similar applications (e.g. auction off the data by a vendor, rather than redistributing payments). 

Could there be other constraints (e.g. computational ones) that be tackled here, rather than the budget constraints. 

Finally, you show that your solutions are "sensible" and result with reasonable outcomes. What kind of additional metrics could quantify that? What could one show in future work to demonstrate an even "more fair" outcome? 
limitations: This builds heavily on earlier work and foundations from cooperative game theory. The empirical analysis is illuminating but limited (few domains, few metrics). The authors should do more to justify their choices of desiderata (and surey relevant game theory work on how different desiderata yield different solutions). 

While the question of whether budget constraints are reasonable ones for ML vendors is subjective, the authors focus on this one constraint.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: This paper considered the setting where there exists a tradeoff between payoff and model rewards in collaborative machine learning. Inspired by the observation that the difference between the contributions of parties should take into consideration during reward allocation, they proposed a new solution concept \emph{conditional Shapley value}, and proved their payoff function is unique for reasonable properties. Additionally, they decide their allocation based on the payoff function, and consider the settings that the parties have budget constraints, or without budget constraints, and empirically demonstrate the performance of their allocation scheme. 
strengths_and_weaknesses: This paper has many strengths:
1. They consider a more general setting when the given model should of different payments based on the parties' contribution.  
2. Their characterization of the desirable properties for a payoff reward vector produces a provable \emph{unique} payoff reward vector. 
3. Their payoff allocation also satisfies replication-robustness that is studied in the previous literature.
4. The paper includes experiments on MNIST, CIFAR-10, and IMDB datasets. 

Weaknesses:
1. The paper doesn’t compare against the existing benchmark either in theoretical statements or empirically. 
2. No contribution section in the introduction. ([line 65-90] has an overview of the sections, but doesn't include the theoretical results of this paper. 
3. The descriptions of the payoff functions are hard to follow. 
4. No running time analysis. 

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After review rebuttal period, the reviewer would like to add more weakness as follows:

1. Results for similar settings, though not explicitly stated as "Fair Allocation", has been published in 2019, see [1]. 

2. Many of the concepts in this paper are stated without appropriate references, for example, "Individual Rationality", "Marginal contribution consistency", "balance", "linear Value", "dummy party" etc. These concepts are widely used metrics for mechanism design and beyond. 
3. The conditional Shapley value seems to be similar to Shapley value, as in stated in Remark 3.5. Additionally, for the properties introduced in this paper, i.e., balance, linear Value, dummy party, similar properties are already been proved as in [2] for Shapley value, which makes the theoretical contributions for providing such metric incremental. 

3. This paper doesn't have comprehensive references, at least existing literature on collaborative learning/ allocations rules. From the reviewer's perspective, while there are total 17 references, many of them are not directly related to collaborative learning. Additionally, the current references are informal, i.e., without the conference/ journal name, e,g. [15], [16], [8] in the paper. 

The reviewer is from a more theoretical background, so my evaluations are more on the theoretical contributions of this paper, i.e., the novelty of the proof for theorem statements, and how the results are different from existing metrics. From the reviewer's perspective, the writing of this paper itself (references, connection to existing results ) needs a major revision. 

[1] Ghorbani, A., & Zou, J. (2019, May). Data Shapley: Equitable valuation of data for machine learning. In International Conference on Machine Learning (pp. 2242-2251). PMLR.

[2] Agarwal, A., Dahleh, M., & Sarkar, T. (2019, June). A marketplace for data: An algorithmic solution. In Proceedings of the 2019 ACM Conference on Economics and Computation (pp. 701-726).


questions: 1. Is there any rationale/literature on whether the party with more contributions should receive higher payoff rewards? From the reviewer's perspective, it's not a standard Fairness notion to assume this. 
limitations: See weakness section.
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: The authors considered an interesting and practical problem where groups of data owner contribute their data to collaborative build an ML model that is better than models they build on their own. The key contribution comes into designing a unique solution concept that simultaneously consider how monetary payoffs and model rewards should be assigned to each contributor using (Conditional) Shapley values.
strengths_and_weaknesses: Strengths:
- proposing a solution that handles monetary payoff + model rewards simultaneously is not something the literature has considered before. 
- Communication of ideas are mostly clear besides the use of payoff flows (see below).

Weaknesses:
- The introduction of payoff flow and conditional SVs weren't apparent to readers until getting to Sec.4, and it seemed to complicate the payoff allocation scheme. It was only made clear later in section 4 that we can handle the budget constraints by modifying the value functions of all parties in the Conditional SV. Maybe this intuition should be made a bit earlier to make it easier to follow.
questions: On the contrary, if a party has a constraint or minimal requirement on model performance instead of monetary budget, is your proposed optimisation framework applicable in this case? More concretely, if a party only requires the model to be as good as 90% of the best performing model in order to obtain some discounted payoffs, is your method applicable in this situation?

Another question: is the monotonicity assumption of s needed in your formulation? It seems to be needed to ensure joining the cooperation will be better than not joining, but in terms of Shapley values computation there is no such restriction needed when defining a value function? Can you comment a bit on this please? 
limitations: NA
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The paper studies collaborative machine learning, where data from multiple parties is aggregated to train a machine learning model with better performance. It is concerned with fairness in the sense that parties should receive a reward that accounts for how much they contributed to the quality of the model, as measured by the Shapley value. The paper notably presents a set of desirable properties of the payoff flows between parties from which it derives a fair allocation scheme. This approach allows to address settings with or without budget constraints. The method is evaluated on a simulation with segments from the MNIST dataset.
strengths_and_weaknesses: Strengths: The paper is overall well written. The fairness properties of payoff flows for fair allocation are interesting and allow to address both budgeted and non-budgeted settings. The scheme based on payoff rewards is limited to non-constrained problems but it is simpler to understand. The presentation of both types of allocation schemes allows to understand well the advantages and drawbacks of either approaches.

Weaknesses: The contribution of the paper is not very clear: How do the properties defined in the paper differ from classical axioms of cooperative game theory? This is important because the paper is not technical, and its main interest thus lies in the conceptual framework studied. 

Typos: L60 et -> It, L388 collaboration -> collaborative

questions: * What is the difference between this work and [Sim et al., 2020] ([14]), in the use of Shapley values to measure the contribution of a party? 

* Sec. 4: why should we consider fair to reduce the performance of the model a party receive, in the presence of budget constraints? 

limitations: The limitations and societal impact are not discussed in this work. In particular, the authors did not discuss the privacy issues involved when different parties share their data.
review_title: null

Meta-review: metareview: This paper lies in the borderline of acceptance, even with the help of an additional emergency expert reviewer (Reviewer GnPz) after the discussion phase:

On the positive side, the reviewers found the collaborative machine learning payoff problem studied in the paper interesting and relevant, and the fairness axioms reasonable, and the uniqueness proof of allocation schemes meaningful. 

On the negative side, the reviewers found the contributions of this paper not groundbreaking. They still have the following concerns:
- The work is not placed well enough with existing work (comparison with existing works on fairness and Shapley value raised by the reviewers, and the references Reviewer Bdvn gave)
- The empirical comparison between prior works is limited (Reviewer GnPz)
- The time complexity for computing the (conditional) Shapley value is exponential, so it's not a metric of practical use. Moreover, variants of Shapley value have been already studied in the literature, see (Xu et al, Gradient driven rewards to guarantee fairness in collaborative machine learning.) (Reviewer iwL1)
confidence: Less certain
Decision: Accept