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: The paper addresses multi-agent performative prediction (Multi-PfD), focusing on a setting where multiple agents are learning a common decision vector from data that can be influenced by their decisions. The paper formulates this as a decentralized optimization problem and identifies a necessary and sufficient condition for a unique multi-agent performative stable (Multi-PS) solution. The paper demonstrates that the consensus effect results in a relaxed requirement compared to the single agent case. As a solution to the problem, the paper studies a decentralized extension to a greedy deployment scheme (DSGD-GD), demonstrates that it converges to the Multi-PS solution, and analyzes the non-asymptotic convergence rate. The analysis reveals that heterogeneous users and poor graph connectivity may impair convergence but do not affect the asymptotic rate. Some numerical experiments on synthetic and real data are provided as validation of the analysis. 
strengths_and_weaknesses: Strengths

1.	The paper studies an interesting problem and provides a thorough and useful theoretical analysis that addresses key questions of interest (existence of stable solution, convergence + rate). Although parts of the proofs are similar to those of related results in decentralized optimization and performative prediction, there are additional challenges in the analysis and these are handled in an elegant fashion.   
2.	There is valuable discussion associated with the theoretical results. Going beyond expressions for bounds, the papers discusses key contributing factors to various terms. This leads to a specification of how factors such as graph connectivity impact the behaviour. 
3.	The assumptions underpinning the analysis do not impose unreasonable constraints that make the setting impractical, although the strongly convex loss assumption and the local decision impact do impose limitations. 
4.	The paper is very well written. The key theoretical results are presented in a clear manner and there is enough discussion of the proof procedure to provide the reader with an understanding of the general strategy. 
5.	The numerical experiments, while limited and not the main focus of the paper, do provide a validation of the theoretical analysis. 

Weaknesses

1.	There is a relatively weak motivation for the setting under study in the paper. In the introduction, the paper cites Hardt et al., Dong et al., and Kleinberg et al. in providing an example scenario, but the extension to the multi-agent setting is not clearly motivated. The example is a spam classifier and the proposed multi-agent context is regional servers with users that respond in different ways. In this case, it’s not obvious why the consensus solution is desirable. If there is sufficient data, then it would seem that individual classifiers for each region would be preferable. If not, then I would think that it would be natural to explore compromises with some parameters being shared and others permitting a suitable response to the local data.    
2.	Experiments: While the experiments are primarily illustrative and serve the role of validating the theory, it is misleading and incorrect to claim that the paper “illustrate[s] the Multi-PfD problem in a real application” (l. 302). While the analyzed dataset is from a real application, neither the division into multiple agents nor the users’ proposed adaptation are.

questions: 1.	Is there a clear example where the consensus solution is clearly superior and desirable? i.e., Can the authors provide a stronger motivation for the studied problem?
2.	There is relatively limited discussion of the assumption that the local distribution is only affected by the agent’s decision vector. Can the authors elaborate on how this restricts the application of the results to multi-agent problems? Is it possible to extend the results to handle this setting?
3. As the authors acknowledge, the assumption of strong convexity is limiting. Can the authors comment on how the results might be extended to incorporate weaker requirements?

limitations: Yes.
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 consider the problem of multi-agent performative prediction (Multi-PfD), and formulate Multi-PfD as a decentralized optimization problem. The authors first prove the necessary and sufficient condition for the Multi-PfD problem to admit a unique multi-agent performative stable (Multi-PS) solution, show that enforcing consensus leads to a laxer condition for existence of Multi-PS solution with respect to the distributions’ sensitivities, compared to the single agent case. Then, they study a decentralized extension to the greedy deployment scheme [Mendler-Dünner et al., 2020], called the DSGD-GD scheme. They show that DSGD-GD converges to the Multi-PS solution and analyze its non-asymptotic convergence rate.  



strengths_and_weaknesses: Pros: this paper provides the study and analysis of Multi-PfD with consensus seeking agents via a practical DSGD-GD scheme. The results indicate that when agents are consensus seeking, Multi-PfD admits a performative stable solution with laxer condition and DSGD-GD achieves linear speedup. 

Cons: In terms of optimization, the proposed methods are not novel, especially with limitations such as the requirement of synchronous updates among agents, strongly convex loss, etc. I would say the major contribution will be on the Multi-PfD problem formulation side, which I am not quite familiar with.  
questions: Please clearly state the status of area of multi-agent performative prediction (Multi-PfD) and demonstrate your contribution positions. From the optimization side, I don't see too much novelty of the paper.  
limitations: the authors adequately addressed the limitations and potential negative societal impact of their work
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: This paper studies a multi-agent performative prediction problem, where the agents want to learn an identical local decision parameter to minimize the average of all local loss functions. The main challenge is that the local data distribution, which is an input to the local loss function, will change as the agents update the local decision vectors. Before this work, similar performative prediction problems have been studied in single-agent settings and competitive multi-agent settings. In contrast, this work studies a cooperative multi-agent setting where all agents are willing to share local decision vectors and want to reach a consensus. The authors propose a decentralized learning scheme and provide a finite-time convergence bound. They also conduct numerical simulations on synthetic data to validate the theoretical results.
strengths_and_weaknesses: Strength: The paper is well-written and easy to follow, and the broad topic of performative predictive is interesting for the ML community. The authors explained the intuition behind the problem setting, the algorithm, and the main theoretical results very well. They also did a detailed comparison with related works to emphasize the novelties and challenges of this work.

Weakness: The multi-agent performative prediction problem setting proposed in this work is a novel and natural extension of the single agent setting, but the motivation is not sufficient in the following aspects: Since the local data distribution $D_i$ only depends on the local decision vector $\theta_i$, it seems unnatural to require all agents to reach a consensus on their local decision vectors. Besides, the graph $G$ of agents is only used as a communication graph. Compared with other works where the local data distribution $D_i$  can depend on non-local decision vectors, the multi-agent problem considered here looks more like a localized problem. More application examples are desired to motivate the setting considered in this work.

questions: As discussed in ``Weakness’’, I am concerned about the motivation behind the proposed problem setting in this work. The authors presented three examples in this paper: Example 1, multi-agent Gaussian mean estimation, and Email Spam Classification, but it looks like they are artificially constructed to fit in the Multi-PfD setting rather than coming from real-world applications. In rebuttal, I hope the authors can discuss why some core assumptions in the setting (e.g., the consensus and local communication with neighbors) are critical in these application examples.
limitations: Yes, the authors discussed the limitations of this work in the last paragraph. And I don’t see any negative social impact of this work.
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 formulate Multi-PfD as a decentralized optimization problem and admit a multiagent solution. Compared to the single-agent case, enforcing consensus leads to a laxer condition for the existence of Multi-PS solution with respect to the distributions’ sensitivity. This paper study the DSGD-GD scheme and analyze its convergence towards the Multi-PS solution, and show that the scheme is convergent under the same sufficient condition for existence of Multi-PS solution
strengths_and_weaknesses: originality:
Compared to multi-agent reinforcement learning algorithms, the proposed DSGD-DG method can converge to a unique Multi-PS solution.

quality, clarity:
The article is well organized.


significance:
The algorithm proposed in this paper has practical significance. In the dynamic classification task, it can dynamically adapt to some changes in the environment. Such as spam classification tasks. The algorithm was also experimented on this task, and achieved good results on the spambase-based multi-agent spam classification task.
questions: Can the method be used on reinforcement learning to change the unique convergence problem of reinforcement learning algorithm?
limitations: No
review_title: null

Meta-review: metareview: This paper received a mixed set of reviews. After reading the paper, the reviews, subsequent author-reviewer discussion, and discussing with the reviewers, I recommend that this paper be accepted. The paper studies a multi-agent version of the performative prediction problem. The paper contains original and interesting contributions, and we expect the community to appreciate this work. In particular, the theoretical contribution was appreciated by several reviewers. Although concerns were raised during the review process, my impression is that these were satisfactorily addressed through the rebuttals.

While preparing the camera ready, we strongly encourage the authors to address the main concerns that came up in reviews. These include:
* Strengthening the motivation for the particular multi-agent formulation studied in this paper
* Clarifying the relationship between performative prediction and prior work on distributed optimization
confidence: Certain
Decision: Accept