Paper: Incentivized Collaborative Learning: Architectural Design and Insights (ICLR-2024)

Reviewer comment (Novelty):
The novel contributions and the new insights from the unified framework need further clarification.

Author response:
Thanks for your query about new insights from our framework. We extract some concrete examples from the paper to demonstrate the insights of our approach.

Insight 1: suitable incentives can improve collaboration performance. Unlike prior work that treats incentives as a separate problem, our framework integrates incentives into the learning process itself. For example, in the federated learning use case, we developed a theory-guided algorithm for simultaneously optimizing the pricing plan and performing federated learning (Appendix D). The insight is that a client, especially an adversarial client, will opt out of the selection process if participation costs are too high. This reduces system exploration costs and improves collaboration efficiency.

In the assisted learning use case, we showed the insight that entities could be incentivized to autonomously collaborate to enhance personal learning objectives, even without a central coordinator (Section 3.2.1 and Appendix E). 

In the multi-armed bandit use case (Appendix F), we showed the insight that screening at both participation and selection stages could simultaneously achieve the following goals: 1) prevent the laggard arms from participating by leveraging their incentives, which can further improve the collaboration gain, 2) encourage the medium-performing arms to participate to enjoy the collaboration gain, which can boost the overall profit, and 3) reward the top-performing arms to participate to make sure that they can be consistently selected to be active. Consequently, incentives reduce the complexity of exploration, which can further improve the quality of generated outcomes and engage a broader range of entities.

Insight 2: Each participant can simultaneously play the roles of contributor and beneficiary of the collaboration gain. Each entity’s participation cost can be positive or non-positive to reward those who contribute positively and charge those who hinder collaboration or disproportionately benefit from it. An interesting case is to have the system incur a net zero cost, as exemplified in Section 3.2.2. The insight is that a system can still engage entities to achieve the maximum collaborative gains even without incurring net costs.

Insight 3. The joint architecture of pricing and selection plans could manage free-riders and adversarial participants.
 
A free-rider is an entity that hopes to participate and enjoy the collaboration gain realized by other more capable participants with a relatively small participation cost. By ensuring a minimum probability of being active and incurring a related cost, one could effectively prevent entities from exploiting the system without contributing. Additionally, for adversarial participants, the pricing plan may impose a high cost whenever the realized local gain revealed after the collaboration exceeds a pre-specified threshold, so no adversary would dare to risk paying an excessively high cost after participating in the game. 

These insights, derived from our case studies and theoretical work, illustrate how the unified ICL framework fosters win-win situations in collaborative settings, a perspective not extensively explored in existing literature. We believe these contributions significantly advance the understanding and application of incentivization in collaborative learning.

Reviewer comment (Writing):
The pricing plan formulation and its dependency on the individual outcomes of active and non-active participants is not clearly elaborated in the paper.

Author response:
Thank you for this question. Yes, our pricing plan is designed to differentiate between active participants based on their contribution levels to ensure proper incentives. An example of this is Equation (18) of Appendix D. Here, participants with higher $z_m$ values, indicating greater contributions, can pay less costs or receive more rewards than those with lower values. For participants who are not active, the pricing is more uniform since their specific contributions (realized gains) are not directly observable. However, they are still incentivized to contribute, considering the potential of being selected as active and thus facing related costs. This aspect is further illustrated in the multi-armed bandit example in Appendix F, where the potential of incurring costs influences participant behavior even when they are not currently active.

Reviewer comment (Theory):
The pricing plan \(\mathcal{P}\) looks at the realized collaboration gain from the outcomes of the active participants in \(I_A\) to charge all participants in \(I_P\). Does the pricing differentiate participants with high \(z_m\) from those with low \(z_m\)?

Author response:
Thank you for this question. Yes, our pricing plan is designed to differentiate between active participants based on their contribution levels to ensure proper incentives. An example of this is Equation (18) of Appendix D. Here, participants with higher $z_m$ values, indicating greater contributions, can pay less costs or receive more rewards than those with lower values. For participants who are not active, the pricing is more uniform since their specific contributions (realized gains) are not directly observable. However, they are still incentivized to contribute, considering the potential of being selected as active and thus facing related costs. This aspect is further illustrated in the multi-armed bandit example in Appendix F, where the potential of incurring costs influences participant behavior even when they are not currently active.

Reviewer comment (Theory):
It appears problematic that the pricing for the non-active participants depends on the individual gains of the active participants \(z_m\), stated in (1). Clarification is needed on whether this understanding is correct.

Author response:
Thank you for raising this important point. You are correct in your understanding that the pricing for non-active participants can be influenced by the individual gains of the active participants, as reflected in (1). This design choice is intentional and stems from a key insight of our framework. The rationale is that when active participants achieve high performance, contributing significantly to the collaboration gain, they are deemed to merit greater rewards. These rewards could be, in part, sourced from the non-active participants. Non-active participants, in anticipation of potentially becoming active in future rounds and benefiting from the collaboration gains, are generally more willing to contribute to this reward pool. This approach ensures that all participants, active or not, are invested in the success of the collaborative effort and that high performers are appropriately compensated for their significant contributions. We hope this explanation clarifies the pricing mechanism in our framework.

Reviewer comment (Theory):
Under the formulation of this paper, the incentive of participation for \(m\) only depends on the utility income of \(m\) himself minus the participation cost, meaning the client is incentivized as long as (9) is fulfilled. However, in practice, a candidate’s incentive should also depend on other candidates (e.g., knowing that others have a higher expected gain with lower-quality data can deter participation). How does the framework address this scenario?

Author response:
Thank you for pointing out the aspect of interference between participants in our incentive mechanism. We recognize that this dynamic is not explored in our current work. Your insight is valuable, and we will mention this as future research.

Reviewer comment (Theory):
Clarification is needed regarding the statement at the end of Page 5: “if not selected, it will become an inactive participant with zero gain, which will contribute to the system’s profit but not harm the collaboration.” Why would the gain be zero? All participants will receive \(z_{I_A}\) and there might be a large utility income gain for this “inaccurate candidate.”

Author response:
Thanks for pointing out this. It was a typo and we will remove “with zero gain”.

Reviewer comment (Theory):
How does Theorem 1 translate to functional forms of the pricing plan in practice?

Author response:
Thanks for your question. Theorem 1 can be translated to particular forms of the pricing plan through more explicit assumptions of how the collaboration gain can be calculated or approximated. The paper demonstrates some specific use cases. For example, in the federated learning use case, we used Theorem 1 to derive Theorem 2 under a large-participation assumption (so a law of large numbers could be applied for approximation). We further translated it into an algorithm to automatically identify a concrete pricing plan from a parametric form of the pricing plan (Appendix D.1). We also translated Theorem 1 in the multi-armed bandit use case to quantify the conditions for the pricing plan (Appendix F.2).

Reviewer comment (Theory):
Why is it acceptable and reasonable to assume the utility functions (e.g., utility income \(\mathcal{U}\)) of the candidates are known to the system for pricing and selection? How practical is it to calculate \(E [ \mathcal{U}(z_{I_A}) - \mathcal{U}(z_m) ]\)?

Author response:
Thank you for raising this point. It is true that in the current framework, we need the utility functions to be known for designing the pricing and selection in concrete use cases. This assumption helps in demonstrating the theoretical aspects of our model more clearly. However, I acknowledge that in real-world scenarios, the exact utility functions of participants may not always be fully known. In those cases, utility functions can be approximated or inferred through data analysis, historical behavior patterns, or market research. We see a valuable future direction of research in developing methods to dynamically learn these utility functions within our framework. As for the calculation of the expected utility difference, we would like to refer to the same response in the above comment 7.

Reviewer comment (Theory):
It is better not to overload the collaborative gain function \(\mathcal{G}\) to take an individual \(z_m\) as input, since \(z_m\) should also depend on the outcomes of other active participants in \(I_A\).

Author response:
Thank you for your comment. We would like to clarify that in Section 2.2, the definition of collaboration gain function $G$ takes individual outcomes $x_m$ (rather than $z_m$) for $m \in I_A$ as input. This is designed to capture the interaction and interference between active participants. To maintain notational simplicity, we have also used the same symbol $G$ in a different context to represent the gain of an individual outcome. In this case, $G$ refers to the gain achieved when an individual operates independently, without being part of the collaborative effort.

Reviewer comment (Experiments):
The discussion in the paper cannot fully reflect the superiority of the proposed framework compared to previous methods. For example, there seems no specific comparative experiment to confirm that the proposed ICL framework is more efficient than previous works.

Author response:
Thank you for your valuable feedback regarding the comparative analysis of our ICL framework. We have included several experimental studies that compare incentivized and nonincentived/standard collaborative learning in federated learning (FL), assisted learning (AL), and multi-armed bandit (MAB) settings. We did not compare it with other incentivation techniques because the introduced architectural framework fundamentally differs from previous methods. The ICL framework is designed to address the under-explored area of when and why incentive mechanisms can enhance collaboration performance. The core contribution of our work is the establishment of general principles and insights into incentivized collaboration. Our experimental validation is strategically designed to corroborate the theoretical insights and principles developed in the ICL framework. Our experiments are not merely about efficiency comparisons but are aimed at demonstrating the practical applicability and benefits of the proposed framework in a variety of settings.

Reviewer comment (Experiments):
It’s kind of confusing that the description of the experiments is less detailed about their design. For example, the employed model and the meaning of the metrics in the first experiment are not very clear.

Author response:
Thank you for pointing this out. We will add more details such as model architectures, learning rates, and optimizers in the revised appendix. In particular, in the first experiment shown in Figure 2, we visualized the top-1 accuracy against communication rounds on the CIFAR10 dataset to show that a suitably incentivized FL algorithm in our framework can converge faster and better than the non-incentivized counterpart.

Reviewer comment (Evaluation):
Can you give more explicit evidences that the proposed ICL framework utilizes the incentive mechanism more effectively than previous works?

Author response:
Thank you for your valuable feedback regarding the comparative analysis of our ICL framework. We have included several experimental studies that compare incentivized and nonincentived/standard collaborative learning in federated learning (FL), assisted learning (AL), and multi-armed bandit (MAB) settings. We did not compare it with other incentivation techniques because the introduced architectural framework fundamentally differs from previous methods. The ICL framework is designed to address the under-explored area of when and why incentive mechanisms can enhance collaboration performance. The core contribution of our work is the establishment of general principles and insights into incentivized collaboration. Our experimental validation is strategically designed to corroborate the theoretical insights and principles developed in the ICL framework. Our experiments are not merely about efficiency comparisons but are aimed at demonstrating the practical applicability and benefits of the proposed framework in a variety of settings.

Reviewer comment (Theory):
A major concern I have over the work is that in stage 1 of the method, the coordinator needs to set a pricing plan based on prior knowledge of candidates potential gains from previous rounds. This means that first the client needs to participate first to know its incentives, and moreover, if the potential gain is erroneous, the ICL framework may not be able to properly incentivize the clients. This becomes even more trickier when clients have the flexibility to opt-in or opt-out which can often be the case for incentivized collaborative learning settings.

Author response:
Thank you for this comment. It is indeed a valid concern that the coordinator needs to set the pricing plan according to prior knowledge of candidates’ potential gains in order to optimize the system gain. In the experimental studies, we implemented this for each round using realized gains from previous rounds. Nevertheless, this does not necessarily mean that a client needs to participate first to know its incentives. For example, in the multi-armed bandit (MAB) use case, each candidate decides its incentive by observing the gains achieved by selected arms and contrast with its local potential to generate rewards; if it does not know its potential to generate reward, it could locally simulate to obtain an estimate of its potential. Similarly, in FL, a client could choose to run a local update to decide its incentive to participate, should local computation cost be not a matter of concern. In the paper, we did not specify the concrete way of obtaining such prior knowledge in the framework description, and instead, mentioned specific possible choices when introducing the three use cases. We will incorporate your comment in the revision.

Reviewer comment (Theory):
Lastly, the work seems mainly theoretical since the experimental validation is rather limited. However, the assumptions they use for the theoretical work such as having a three entity setting is rather restrictive. Moreover the implications of the main theoretical results such as Theorem 2 and 4 is unclear to me. In what conditions it is guaranteed that the clients benefit from the system for each corresponding theorems?

Author response:
Thank you for your comments. Section 3.1.1 “Consensus of Competing Candidates” studied the 3-entity setting only for developing the insights of how decentralized collaboration could be attained under suitable incentives. The results can be extended to multiple entities in a straightforward way. We would like to comment more on the implications of Theorems 2 and 4. Theorem 2 is a result to approximate the equilibrium conditions in Section 2.4 under a large number of participating clients. It is a very important result because it quantities the system's marginal profit increase attributed to an entity. In Appendix D, we had elaborated on this idea and proposed a concrete incentivized federated learning algorithm built on Theorem 2, whose  empirical performance was also studied. Theorem 4 develops a necessary and sufficient condition to reach a consensus among the participants. Specifically, the condition is the existence of a participant such that when it is active, the collaboration gain is maximized and every participant sees that the participation cost is worthwhile (to gain individual profits).

We appreciate your insightful feedback and hope that the above explanations have clarified our approach and findings. We are open to further discussions and would be glad to explore any additional questions or ideas you might have.