Paper: RealFM: A Realistic Mechanism to Incentivize Data Contribution and Device Participation (ICLR-2024)

Reviewer comment (Theory):
This work builds on [Karimireddy et.al. (2022)]. The derivation to model accuracy in (1) and (2), following [Karimireddy et al., 2022] and moreover, [Mohri et al., 2018] assumes for m i.i.d. samples. Will it enjoy generalization to the non-i.i.d. case?

Author response:
Currently our mechanism does not fully generalize to the non-i.i.d case. The reason stems from the fact that our assumptions on $\hat{a}(m)$, detailed above, may fail in the non-i.i.d case ($\hat{a}(m)$ may not necessarily increase with more non-i.i.d data). However, there may be scenarios where adding non-i.i.d data still allows $\hat{a}(m)$ to be increasing with respect to $m$. Under this scenario our mechanism *would* generalize to the non-i.i.d case.

Reviewer comment (Theory):
Some inconsistencies and incompleteness due to unclear representation. For instance, the authors mention generalizing $\phi_i$ to become a convex and increasing function (but in which variable), and also, in actuality, the utility is modelled as a concave function. Following that, Assumption 2 needs further clarity. Another concern is Fig. 2, which is not well-justified for the said "payoff function." I don't see this claim has been experimentally validated apart from numerical evaluation.

Author response:
We provide clarification that **(1)** $\phi_i(a)$ is *convex* with respect to the accuracy $a$, however **(2)** $\phi_i(\hat{a}(m))$ must remain concave with respect to $m$. 

As detailed in our paper, we can define the accuracy function $\hat{a}(m)$ as either Equation 1 or 40 and the accuracy-payoff function $\phi_i(a) := \frac{1}{(1-a)^2} - 1$ and this will satisfy both **(1)** and **(2)**. There are other variants of $\hat{a}(m)$ and $\phi_i(a)$ which work, but these are backed up by generalization bounds (Proposition 1) and intuition respectively.

The convex and increasing requirement for $\phi_i(a)$ is intuitive as rational devices heavily desire models with accuracies approaching 100%. This is much more intuitive than a linear $\phi_i(a)$, as described in the paper, since rational devices would place much greater value in a model increasing in accuracy from 99 to 99.5% than 30 to 30.5%.

Reviewer comment (Theory):
If the profit margin of the central server, defined as $p_m$, is fixed and known by all devices, I am not sure why it is used after all. In the later experiments, this is used to indicate the degree to which the server is greedy. Assuming this is unknown would be an interesting analysis. Also, the definition of profit margin should be made more rigorous.

Author response:
The profit margin $p_m$ details the percent of utility kept by the server after federated training is complete. The remaining $(1-p_m)$ percent is distributed uniformly as a monetary reward to all participating devices. It is important for devices to know the profit margin $p_m$, since a smaller $p_m$ will result in larger rewards for each device and may provide further incentive to participate. As noted by the reviewer, we showcase that device utility and contributions increase *even when the server is greedy and maintains all of its gained utility*.

We agree with the reviewer that assuming an unknown profit margin would be interesting analysis and we leave this as important future research. As detailed at the beginning of the rebuttal, our main goal was to construct the first FL mechanism of its kind. Once planted, we aim to further relax some of the assumptions initially used.

Reviewer comment (Theory):
As the authors mentioned, it is hard to bound the composition function $\phi$, and I am still not sure how, particularly with this framework, we can ensure increased data production leads to better payoffs. In principle, one has to factor in the quality of data or limit combinatorial properties.

Author response:
Accuracy function $\hat{a}(m)$ is increasing with respect to the amount of data $m$ (due to its concavity). The accuracy-payoff function $\phi_i(a)$ is increasing with respect to accuracy $a$. Therefore, $\phi_i(a(m))$ is increasing with respect to $m$. This is how, given our assumptions on data quality, we ensure "increased data production leads to better payoffs".

Reviewer comment (Theory):
The assumption that the closed form of each device's utility function is known, which may not always be realistic.

Author response:
We agree with the reviewer that assuming the form of $u_i$ can be unrealistic in some instances for each device. However, we believe that using a closed-form $u_i$ is an important first step towards realistic FL. Using a closed-form $u_i$ for each device is much more realistic than assuming that devices will always participate in federated training regardless of its costs. The majority of FL papers do not even attempt to model device or server utility, which is quite unrealistic. Furthermore, there is usage of closed-form utility functions in economics literature [Trout (1963) & Orsborn et al. (2009)] as well as with mechanism design in ML [Karimireddy et al. (2022) and Zhan et al. (2021; 2020b)] to name a few. Removing the closed-form assumption is a great future research direction.

Reviewer comment (Evaluation):
RealFM distributes model accuracy and rewards based on the amount of data provided by each device. This may raise questions about potential cheating. It would make more sense to depend on each device's marginal contribution to model accuracy, provided that it can be easily and accurately determined.

Author response:
We are wary that many other avenues to determine each device's marginal contribution, like Federated Shapley Value Wang et al. (2020), can be cheated as well. The issues surrounding honesty are an *important* future research direction in FL. We set out to accomplish quite a bit in our work, as **it is the first FL mechanism which more realistically models device utility (non-linear function of model accuracy) and provably improves device participation and contributions (eliminating the free-rider effect) without the need of a payment mechanism**. Specific novelties are listed in our rebuttal for Reviewer A7vi.

In summary, we aim to address honesty in future works but we first wanted to establish a foundational base for FL mechanisms which incentivize device participation and contributions.

Reviewer comment (Novelty):
Theorem 4, which claims that RealFM eliminates the free-rider phenomena, may not be particularly thrilling. Designing a contract to incentivize individuals when their exact contribution is known is not a challenging task.

Author response:
As mentioned within our paper, contract-theory approaches require construction of a payment mechanism. Pricing of the contracts is especially difficult and can often result in sub-optimal utility gained by both the devices and servers (too low of a reward does not incentivize devices to participate and too high of a reward can cause the server to attain low or negative utility).

The importance of our work is that our mechanism allows free-riding to be eliminated **without having to construct a payment mechanism prior to training**. Using accuracy shaping, devices are incentivized to contribute more data because they will achieve a higher-performing model than they would by training alone. Theory 4 provably eliminates free-riding while also guaranteeing that devices will *increase* their contributions under a new accuracy-shaping scheme, differing from Karimireddy et al. (2022), which enables flexible modeling of diverse device utilities that accommodate non-linear relationships between model accuracy and utility. Furthermore, this mechanisms allow for monetary rewards to be received by devices after training.

Reviewer comment (Theory):
The comparison between linear RealFM and local training does not effectively demonstrate how well RealFM incentivizes non-linear devices' contribution to model training. It is understandable that the authors cannot be blamed for weak baseline algorithms, as this paper is the first to aim at incentivizing device data contribution in a non-linear setting. However, in such cases, it would be more valuable to have theoretical guarantees of data maximization to truly showcase the strength of RealFM, which the paper lacks, except for the linear setting.

Author response:
As mentioned by the reviewer, due to the dearth of FL mechanisms that allow for non-linear relationships between model accuracy and utility we were unable to compare against other mechanisms. **We believe this speaks volumes about the novelty and importance of our work**.

As mentioned by the reviwer, we prove data maximization under linear settings in Corollary 1. We were unable to guarantee tight theoretical guarantees in other settings due to the non-linearity. This stems from the proof of Theorem 3, specifically relaxing Equation 29. In fact, we assume $\phi_i(a)$ is convex with respect to the accuracy $a$ **in order to make the bound as tight as possible**. Therefore, the accuracy-shaping function proposed in Theorem 3 is close to data maximizing but falls slightly short.

We also mention that our empirical results showcase major improvement (up to 7x more) in device contributions relative to the available baselines even when the profit margin is set to 100%. Our results are even stronger when the server is not completely greedy. *We outperform all state-of-the-art mechanisms which is both novel and important.*

Reviewer comment (Theory):
Some assumptions are simplistic and limit the significance of the work. In equation 1, the accuracy is modelled to depend solely on the number of data points but in practice, devices may have data with different quality, diversity and noise. Moreover, it is hard to decide the difficulty of the learning task $k$ and the server would not have access to data for tuning (Sec. 6) before incentivization. As $a$ is an upper bound, the individual rationality for the upper bound does not translate to rationality for the expected/actual values.

Author response:
> (1) Accuracy is modeled to depend solely on the number of data points... devices may have data with different quality, diversity and noise.
> (2) The central server has to compute $m_i^o$ and $m_i^*$ based on the declared $\phi_i$ and $c_i$. Device $i$ may misreport the cost to get a better reward.

The overarching goal of our work is to create a foundational FL mechanism which solves many of the issues detailed in our paper as well as above. There remain many frontiers to improve how realistically device utility is modeled. Data and truthfulness are two of them. We agree that in practice devices have different data distributions and data quality can vary both inter- and intra-device. We also agree that devices can be dishonest and report untruthful costs in practice. Relaxing our assumptions on data quality and truthfulness is an important follow-up to our work. The literature provided by reviewer A7vi on data quality is a great place to begin tackling the data quality assumptions.

> Hard to decide the difficulty of the learning task $k$ and the server would not have access to data for tuning (Sec. 6) before incentivization. As $a$ is an upper bound, the individual rationality for the upper bound does not translate to rationality for the expected/actual values.

The use of $a$ in our paper was, in part, to allow for empirical analysis of our mechanism. What is most important about $a$ is that it must hold under reasonable and mild assumptions: continuous, non-decreasing, and concave (along a certain interval) with respect to the amount of data $m$. As shown in empirical studies Sun et al. (2017), accuracy grows with the amount of data used (continuous and non-decreasing) yet the growth experiences diminishing returns (concave). In practice, $a$ can be tuned by the server to align with test accuracy curves (as the accuracy improves with more contributions and updates).

Reviewer comment (Novelty):
The advantage of this work over the existing work has to be made clearer. There needs to be a deeper discussion about Shapley value based/collaborative fairness approaches including Xu et. al. (2021) and Wang et. al. (2020). In appendix A, it is suggested that these work “assume that devices are already willing to contribute all of their data”. This claim may be inaccurate — these work guarantees that contributing less (nothing) leads to less (no) reward thus devices would respond by contributing more data as in this work. The difference is that there is no closed form function for device $i$ utility.

Author response:
> Shapley value and collaborative fairness based approaches in existing work may not assume that devices are willing to contribute data... rational devices should contribute more data as in this work. Can you clarify and make the differences/advantages of your work more specific?

We detail the novelty of our work in the first part of our rebuttal. Wang et al. (2020) proposes a method to estimate the federated Shapley Value (which holds similar properties as the regular Shapley Value) in order to determine data quality from the devices participating in FL training. Thus, Wang et al. (2020) and other Shapley Value works seek to evaluate each data source in the FL setting. *Our work seeks to incentivize and increase device participation, through mechanism design, within FL. This is fundamentally different.*

Collaborative fairness works such as Lyu et al. (2020) are closer to our own in that they seek to fairly allocate models with varying performance depending upon how much devices contribute to training in FL settings. There are a few **key** differences between this line of work and our own, namely:
1. Our mechanism incentivizes devices to both participate in training and increase their amount of contributions. There are no such incentives in collaborative fairness.
2. We model device and server utility. Unlike collaborative fairness, we do not assume that devices will always participate in FL training.
3. Our mechanism design **provably** eliminates the free-rider phenomena unlike collaborative fairness, since devices who try to free-ride receive the same model performance as they would on their own (Equations 12 & 13).
4. No monetary rewards are received by devices in current collaborative fairness methods.

Reviewer comment (Writing):
Some notations are used before they are defined or explained (e.g., $[\mathcal{M}^U(\cdot)]_i $ in Theorem 2). This makes the claims unclear and harder to understand.

Author response:
> (1) There needs to be a deeper discussion about Shapley value based/collaborative fairness approaches including Xu et. al. (2021) and Wang et. al. (2020)
> (2) Some notations are used before they are defined or explained (e.g., $[\mathcal{M}^U(\cdot)]_i$ in Theorem 2). This makes the claims unclear and harder to understand.

We appreciate the review's feedback and have expanded our related works and fixed our mistaken claim in Appendix A. $[\mathcal{M}^U(\cdot)]_i$ is the utility received by a device $i$ participating in the mechanism. We added or moved definitions of notations to ensure they are defined when they first appear. We have fixed all minor suggestions.

Reviewer comment (Theory):
The central server has to compute $m_i^o$ and $m_i^*$ based on the declared $\phi_i$ and $c_i$. Device $i$ may misreport the cost to get a better reward.

Author response:
> (1) Accuracy is modeled to depend solely on the number of data points... devices may have data with different quality, diversity and noise.
> (2) The central server has to compute $m_i^o$ and $m_i^*$ based on the declared $\phi_i$ and $c_i$. Device $i$ may misreport the cost to get a better reward.

The overarching goal of our work is to create a foundational FL mechanism which solves many of the issues detailed in our paper as well as above. There remain many frontiers to improve how realistically device utility is modeled. Data and truthfulness are two of them. We agree that in practice devices have different data distributions and data quality can vary both inter- and intra-device. We also agree that devices can be dishonest and report untruthful costs in practice. Relaxing our assumptions on data quality and truthfulness is an important follow-up to our work. The literature provided by reviewer A7vi on data quality is a great place to begin tackling the data quality assumptions.

Reviewer comment (Novelty):
In related works, it is mentioned that Karimireddy et al. (2022) “requires data sharing between devices and the central server”. Is the amount of data sharing the same as centralised FL? How does the amount of sharing in this work differ?

Author response:
> Karimireddy et al. (2022) “requires data sharing between devices and the central server”. Is the amount of data sharing the same as centralised FL? How does the amount of sharing in this work differ?

No data is shared within centralized FL. Instead, gradient updates are communicated between the devices and a central server. In Karimireddy et al. (2022), devices share their actual data with a server *which violates the fundamental underpinning of FL*.

Reviewer comment (Novelty):
The Shapley value and collaborative fairness based approaches in existing work may not assume that devices are willing to contribute data. They just guarantee if they are unwilling and contribute less (nothing), they receive less (no) reward. Resultingly, rational devices should contribute more data as in this work. Can you clarify and make the differences/advantages of your work more specific?

Author response:
> Shapley value and collaborative fairness based approaches in existing work may not assume that devices are willing to contribute data... rational devices should contribute more data as in this work. Can you clarify and make the differences/advantages of your work more specific?

We detail the novelty of our work in the first part of our rebuttal. Wang et al. (2020) proposes a method to estimate the federated Shapley Value (which holds similar properties as the regular Shapley Value) in order to determine data quality from the devices participating in FL training. Thus, Wang et al. (2020) and other Shapley Value works seek to evaluate each data source in the FL setting. *Our work seeks to incentivize and increase device participation, through mechanism design, within FL. This is fundamentally different.*

Collaborative fairness works such as Lyu et al. (2020) are closer to our own in that they seek to fairly allocate models with varying performance depending upon how much devices contribute to training in FL settings. There are a few **key** differences between this line of work and our own, namely:
1. Our mechanism incentivizes devices to both participate in training and increase their amount of contributions. There are no such incentives in collaborative fairness.
2. We model device and server utility. Unlike collaborative fairness, we do not assume that devices will always participate in FL training.
3. Our mechanism design **provably** eliminates the free-rider phenomena unlike collaborative fairness, since devices who try to free-ride receive the same model performance as they would on their own (Equations 12 & 13).
4. No monetary rewards are received by devices in current collaborative fairness methods.

Reviewer comment (Theory):
Does the mechanism _need_ monetary rewards to incentivise devices (can the profit margin be set to 1)?

Author response:
> Does the mechanism need monetary rewards to incentivise devices (can the profit margin be set to 1)?

No. Monetary rewards are not required. In fact, for ease of empirical analysis, *we set the profit margin equal to 1 in all of our experimental results*. Thus, device contributions and utility would **increase** further if we had set the profit margin to a lower value. This showcases how strong our mechanism works empirically.

Reviewer comment (Theory):
In Eq 10, must $\phi_C(a(\sum m))$ be less than $\sum m$ to ensure a profit margin?

Author response:
> In Eq 10, must $\phi_C(a(\sum m))$ be less than $\sum m$ to ensure a profit margin?

There may be some confusion regarding the profit margin. The profit margin $p_m$ dictates what *percentage* of the overall utility gained by the server is kept by the server. The remaining $1-p_m$ percentage of the utility is uniformly returned (as a marginal monetary reward) to each participating device as defined in Equation 10. Overall, $\phi_C(a(\sum m))$ can be larger, equal to, or smaller than $\sum m$. This does not affect the profit margin, it only affects the amount of monetary rewards returned to each participating device.

Reviewer comment (Theory):
What does $\epsilon$ in Theorem 3 represent or control?

Author response:
> What does $\epsilon$ in Theorem 3 represent or control?

The parameter $\epsilon$ simply ensures that Equation 11 will be a **strict** inequality. This is crucial to ensure that devices are receiving more utility participating in our mechanism, via accuracy shaping, than on their own. If the inequality is not strict then devices are not incentivized to increase their contributions.

Reviewer comment (Theory):
In practice, how does the central server produce a model with accuracy $a(m_i^o) + \gamma_i(m_i)$? Is it guaranteed to be less than $a(\sum m)$? Does the server solve for the number of additional data points to use?

Author response:
> In practice, how does the central server produce a model with accuracy $a(m_i^o) + \gamma_i(m_i)$? Is it guaranteed to be less than $a(\sum m)$?

Via FL, the server will train a model using all contributions $\sum m$ which will result in a model with accuracy $a(\sum m)$. In order to provide devices with lower model performance, such as $a(m_i^o) + \gamma_i(m_i)$, the server can degrade the model using a variety of methods. Some examples of ways to do this include using noisy perturbations in a controlled manner or returning a model midway through training which has lower performance.

Reviewer comment (Experiments):
In the experimental setting, the number of devices is not large, which is not very consistent with the actual application scenario.

Author response:
> In the experimental setting, the number of devices is not large, which is not very consistent with the actual application scenario.

Due to the amount of compute resources, we could only use 16 CPUs and 8 GPUs (2 CPUs pinned to 1 GPU). We do lack the resources to perform realistic federated training in the realms of hundreds or thousands of devices. Furthermore, many existing FL papers use a similar scale as our own. Finally, other FL mechanism papers either use a similar number of devices *or do not perform truly federated experiments at all*. Our work is one of the first to provide truly federated empirical evidence to back up the claims of our proposed mechanism.

We also lack sufficient amounts of data to be split amongst devices if we have thousands of devices. The number of unique samples in the MNIST dataset is 60k, and this is even smaller since a fraction needs to be removed to evaluate test accuracy. In future work, with the proper compute power, we would love to showcase the efficacy of our mechanism on thousands of devices with extremely large real-world data.

Reviewer comment (Writing):
Intuitively I know roughly what Server Utility and Average Data Contribution mean. But in detail, I may still not fully understand how Server Utility and Average Data Contribution are Numerized. In particular, I don’t quite understand why Server Utility has been improved so much.

Author response:
> I may still not fully understand how Server Utility and Average Data Contribution are Numerized. 

Following literature in economics, mechanism design, and the intersection of both in FL, utility is often defined as a real-valued number. This number denotes the "net benefit" that a device attains. A larger real value denotes a larger net benefit received by the device.

> In particular, I don’t quite understand why Server Utility has been improved so much.

As detailed above, server utility drastically improves because our mechanism incentivizes devices to contribute more data. By contributing more data, the accuracy $a(\sum \mathbf{m})$ increases (due to our mild assumptions) which in turn increases server utility $\phi_C(a(\sum \mathbf{m}))$ since $\phi_C$ is also strictly increasing with respect to the accuracy $a$.

Reviewer comment (Experiments):
How will performance change when the number of devices increases?

Author response:
> How will performance change when the number of devices increases? 

Our mechanism should improve as the number of participating devices increases. The reason is that more devices means more data used during FL training. Through the mild assumptions on $a(m)$, increasing and concave, more overall data contributions $\mathbf{m}$ will result in higher final accuracies $a(\sum\mathbf{m})$. The higher final accuracy will create a larger window for accuracy shaping, $m_i^* := [ m ≥ m^o_i | a(m + \sum_{j \neq i} m_j) = a(m^o_i) + \gamma_i(m) ]$, which in turn will result in a stronger incentive for devices to contribute more.