Data Market Design through Deep Learning

Summary

This paper studies the market design problem, specifically for data markets. In particular, different from existing analytic approaches, the proposed approach is based on (deep) learning to recover/discover market designs. They adopt and extend an existing RochetNet architecture to both single- and multi-buyer setting and empirically demonstrate the effectiveness of the approach in recovering/discovering the market design.

Strengths

- The paper studies the problem of market design and it is relevant for data market. - The proposed learning-based approach is interesting in that it can recover some analytic solutions. - There are relatively extensive empirical results.

Weaknesses

- The motivation and justification of a (deep) learning-based approach can be made stronger. In lines 40-42, "The difficulty of using analytical tools for this problem of data market design is highlighted by this example, and it remains an open problem to obtain theoretical results for richer multi-buyer settings. This motivates the need for computational approaches." While it is perceived that analytic solutions are difficult, and computational approaches seem a viable alternative. Is it really necessary to use deep learning? In other words, are there less complex computational approaches that can be tried first or reasons why they would not work as well? In particular, (how) can the assumption of i.i.d. samples from $\mathcal{P}$ for training the deep learning model be satisfied? It requires the type of the buyer (i.e., both belief and the $v$) to remain fixed throughout observing the signals. Does this assumption have conflicts with "Upon receiving a signal, the buyers update their prior beliefs and choose an optimal action accordingly" (lines 143-144)? - The inline equations in the paper can break the flow of the writing and make it more difficult for the reader to catch the most important points. For instance, equations (1)-(4) are used to discuss (different variants of) incentive compatbility. It is not so clear which equation the reader should pay most attention to. Furthermore, it seems that equation (4) (i.e., ex post incentivie compatible) is not interpreted after the equation. - Some experimental results can be difficult to interpret (or understand their significance), due to the lack of (existing) analytic characterization of optimum solution. For instance, in lines 294-296, "We are aware of no theoretical characterization of optimal data market designs when both $v$ and $\theta$ vary. In such cases, we can use RochetNet to conjecture the structure of an optimal solution." As a result, it is not clear to the reader how to understand whether the proposed method is effective. It further goes to the first point regarding the motivation/justification of a learning based approach: There lacks a solution or ground truth (i.e., analytic optimum or approixmate optimum) to evaluate the approach. Hence, it seems appealing to first establish such a solution before a computational approach, otherwise, how to effectively evaluate the proposed computational approach?

Questions

- In lines 20-22, "... hold vast quantities of data about individuals. In turn, this has led to data markets, where information about an individual can be purchased in real-time to guide decision-making (e.g., LiveRamp, Segment, Bloomreach)." This seems to hint at that the aforementioned companies are selling data about individuals, is it what it means? - In lines 60-62, "Further, we give a training method that enables the efficient reuse of computed interim allocations and payments from other samples to swiftly calculate the interim utility of misreporting, dramatically speeding up training." Is this empirically or theoretically demonstrated, specifically about "dramatically speeding up training"? What is it comparing against, in terms of speed of training? - In line 122, "The state of the world, $\omega$, is unknown and is drawn from a finite state space ... " Is there an assumption on the distribution of this? - In line 127, "where each $v_i$ is drawn independently from a distribution $\mathcal{V}_i$". What is the interpretation of $v_i$ and what does the distribution $\mathcal{V}_i$ depend on? - In lines 137-138, it seems that the negative externality is in the form of decreasing payment for one buyer $i$ as the gain for some other buyers. In other words, if another buyer $j$ gains (in ex post payoff), this buyer $i$ "loses" (i.e., has a lower utility), is this correct? How should this be interpreted in an example? - In line 139, "There is a data seller who observes the world state ... " How to justify or realize this assumption that the actual world state is exactly known by the data seller? - In line 159 (5-th bulletin point), "$u_i(a,\omega, V_i, \theta_i)$", is it meant to be $V_i$ or $v_i$? - In line 192, "... an unsupervised learning problem." Is it referring to optimizing the softmax version of Equation (9)? If so, it looks more like an optimization problem (i.e., parametric fitting) instead of a learning problem. Often, unsupervised learning is to learn about the inter or intra structure of the data instead of to fit a functional form. Please help interpret why the loss function in line 222 is an unsupervised learning problem.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

2 fair

Presentation

2 fair

Contribution

2 fair

Limitations

- Typically in an optimization approach, if the objective is non-convex (or more complex), it is difficult to establish theoretical guarantees in terms of the optimality or quality of the final solution obtained. This is also mentioned by the authors in lines 374 - 375. The implication is that, it is difficult to obtained a principled understanding of how good the solution (i.e., learnt market design) is, obtained from the gradient-based optimization. - With regard to lines 378-380, "we return to where we started, and underline that markets for trading data about individuals raise a number of ethical concerns." In light of the potential ethical concerns of data trading, a (deep) learning-based approach potentially makes it even more difficult to manage and parse the working mechanism of the data trading. As a result, such an approach can make it even more difficult to reliably/verifably address those concerns.

Summary

This paper introduces a deep learning application to the data market designs that find optimal signaling schemes to maximize the revenue of data sellers. The proposed method is designed to handle truthfulness and obedience (i.e., buyers following recommendations). The overall approach follows the prior frameworks of RochetNet and RegretNet for auction design. The authors are able to demonstrate the method’s ability to recover existing analytical optimal solutions and extend to cases where analytical results are not available. Some experimental results are provided for both single-buyer and multiple-buyer settings.

Strengths

1. The paper applies deep learning to the new domain of data market design, illustrating the feasibility of learning solutions to optimal data market design. 2. It considers the obedience of data buyers in the design. This makes the approach more practical. 3. The paper provides a sound analysis of Individual Rationality for the mechanism and payments.

Weaknesses

1. The writing could be improved. Preliminaries could be better structured to explain essential terms like menu entry, signaling, state of the world, how the mechanism works, etc. Interpretations could be added after Lemmas and computation equations (e.g., (10)) to improve clarity. 2. The scales of the experiments are not large enough to be convincing. If larger experiments are not possible, challenges and limitations should be clearly stated.

Questions

**Major** 1. Are there any references to support the assumptions made in the preliminaries section? For example, why is the matching utility payoff reasonable in data market design? How do you interpret that in the binary-state setting in the real world? How about a more complex non-binary setting? 2. For the single buyer setting Lemma 3.1, it is claimed that the mechanism is Incentive Compatible as it is agent optimizing. Why is it agent optimizing when the objective is to maximize the payment by the agents? 3. How to access the validity of the results from the networks when there is no analytical solution (more complex settings)? For example, for the price of 0.14 outputted for setting C, how do you know whether it is close to optimal? Also, could you provide a more intuitive interpretation of the price and results? 4. What are the challenges in conducting experiments on binary states, actions? Also, can you perform experiments on more than two buyers? Can the method be extended to much more complex scenarios with a large number of players, actions and states? **Minor** 5. Grammar. Lines 80, 103, 242. Punctuations and formats: Lines 146, 153-160, 239. 6. Some notations can be confusing, especially the subscripts, superscripts and brackets. 7. What is $\Delta$ in Line 129, never explained before.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

2 fair

Limitations

The authors have sufficiently discussed the limitations of the approach in the limitation section. Additionally, I wonder how well this framework applies in real-world scenarios. Could the author clarify the limitations of adopting the method in real life for data pricing, or provide a practical example/application?

Summary

The authors are concerned with a problem of "data market design". In such a setting, a mechanism designer with access to an unknown world state interacts with buyers who have private types, and need to take actions whose payoffs vary depending on the world state. These buyers purchase (in the single buyer case) or bid on (in the multi-buyer case) access to a signaling scheme which, given reports from the agents and the world state, sends a signal to the buyers (which without loss of generality can just be a recommended action). This mechanism, treated as a direct-revelation mechanism, needs to be both truthful (incentivizing honest reporting by the buyers) and obedient (once the buyers receive their signal, they should be incentivized not to deviate from the recommendation). Subject to those constraints (either Bayesian or ex post), the mechanism designer wants to maximize their revenue. This problem shares some similarities to truthful revenue-maximizing auction design. In that domain, there has been recent progress using the tools of "differentiable economics" to approximately learn high-performing (and sometimes even provably optimal) auctions, in both single- and multi-bidder settings. The authors apply very similar techniques to this data market problem. In single-buyer settings (as in auctions) they are able to ensure exact IC; for multi-buyer settings they use a Lagrangian during training to approximately enforce IC constraints. They experiment on a relatively wide variety of problem instances, reproducing known results, finding new optimal mechanisms, and conjecturing optimal mechanisms where they cannot find them.

Strengths

The paper comprehensively shows how to successfully apply differentiable economics to a new domain where it has not previously been applied. The authors are able to reproduce optimal mechanisms and find new ones, showing that their adaptation of these technique is in fact useful in producing novel results. This helps to further push these techniques towards being practically helpful tools for theorists and modelers.

Weaknesses

The network architectures here are essentially the same as those used in previous work for auctions, only adapted slightly for the data market setting. This is fine, but it does mean that from the perspective of differentiable economics, there is no novel methodological contribution. The experiments appear to consider at most 2 buyers. While (as in the case of multi-parameter auctions) even selling to just two buyers may be a very challenging case, it would be more interesting to consider a slightly larger number of buyers.

Questions

Can the method in fact scale to larger (even just 3-5 buyers) settings, or not? This should be discussed.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

4 excellent

Presentation

2 fair

Contribution

3 good

Limitations

See questions.

Summary

This paper introduces a deep learning framework for the automated design of data markets, a novel and timely application in the field of economics. The authors address the data market design problem, which involves designing a set of signaling schemes to maximize expected revenue. The paper extends previous work on deep learning for auction design by learning signaling schemes and handling obedience constraints that arise from the actions of agents.

Strengths

- Innovative Application: The paper introduces a novel application of deep learning to the data market design problem, expanding the scope of machine learning in the field of economics. - The paper is well-written overall.

Weaknesses

-Incremental work: It seems that the core contribution, the proposed neural network architecture, is a simple extension of existing model called RochetNet, by slightly modifying the loss function. -Lack of comparison with baselines: mechanism design for information acquisition is a long standing problem. I was surprised to see no baseline comparison in the experiments, and no discussion on how/why existing approaches may not work in the methodology.

Questions

What are some baseline methods to compare with? For example, how does the standard rochetnet perform on the proposed market settings?

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

Yes.

Summary

The authors present a novel approach to the problem of data market design, which seeks to find a set of signaling schemes, each revealing some of the information known to a seller and having a corresponding price, where the goal is to maximize expected revenue. Then, the authors introduce the application of a deep learning framework to the automated design of the data market. The paper discusses the importance of data market design and its potential applications in real-world settings, such as data marketplaces where sellers sell data to buyers for ML tasks. The authors demonstrate that their new learning framework can replicate known solutions from theory, expand to more complex settings, and establish the optimality of new designs. The paper also highlights some limitations of the approach, such as the need for interpretability of the mechanisms learned by the RegretNet approach for larger problems, the potential for local optima in non-convex problems, and the challenge of achieving exact incentive alignment in multi-buyer settings.

Strengths

+ The paper presents a novel approach to the problem of data market design, which uses deep learning to automate the design of data markets. + The authors demonstrate that their new learning framework can almost precisely replicate all known solutions from theory, which shows that the approach is effective and reliable. + The paper shows that the new learning framework can be used to establish the optimality of new designs and conjecture the structure of optimal designs, which is a significant contribution to the field.

Weaknesses

+ The paper acknowledges that for the approach to provide insights into the theoretically optimal design for larger problems, it will be important to provide interpretability to the mechanisms learned by the approach. However, the RegretNet approach used in the paper is not immediately interpretable, which limits its usefulness in this regard. + The paper notes that the approach uses gradient-based approaches, which may suffer from local optima in non-convex problems. This suggests that the approach may not always find the global optimum and may be limited in its ability to handle more complex problems. + The paper attains in the multi-buyer setting approximate and not exact incentive alignment, which leaves the question as to how much alignment is enough for agents to follow the intended advice of a market design. This suggests that the approach may not be able to achieve exact incentive alignment in all settings, which could limit its effectiveness.

Questions

+ Could you provide more details on how the RegretNet approach can be made more interpretable for larger problems? Are there any specific techniques or methods that could be used to achieve this? + Have you considered using other optimization techniques besides gradient-based approaches to address the potential for local optima in non-convex problems? If so, what are some alternative approaches that could be used? + What are some potential ways to provide more practical or theoretical guidance on how much alignment is enough for agents to follow the intended advice of a market design? Are there any existing frameworks or approaches that could be used to address this issue?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

4 excellent

Presentation

3 good

Contribution

3 good

Limitations

The authors acknowledge the ethical concerns raised by markets for trading data about individuals and suggest that machine learning frameworks such as those introduced in this paper can be used to strike new kinds of trade-offs, such as allowing individuals to benefit directly from trades on data about themselves. This shows that the authors are aware of the broader implications of their work and are thinking critically about its potential impact.

Regarding ethical concerns

Indeed, there are important ethical concerns concerning markets for trading data about individuals, and we can use the additional page in the camera-ready copy to give an expanded discussion. Perhaps most interesting, we expect that the techniques introduced in this paper can also easily be extended to identify market designs that make additional, explicit tradeoffs between welfare and concerns regarding user welfare, including privacy. This can be done by modulating the loss function to incorporate additional considerations, for example, providing a continuous tradeoff between revenue and user (privacy-based or otherwise) welfare. This seems very interesting for future work. In light of the inherent importance of privacy considerations, properly designed and functioning data markets could be an improvement over the many “hidden markets” in the present day, where the quid pro quo trade, for example, between preference information and free content or services, may not be clear to users. We also note that data markets for selling information already exist and are typically subject to regulatory control and that markets for data will likely continue to exist as an important part of the business landscape. Thus, they are worthy of study, and thorough computational approaches that can afford additional considerations from reality relative to theoretical approaches are necessary.

Thanks for the rebuttal

1. While it is claimed that the choice of “binary states/actions” and “matching utility” is not a necessary assumption for the framework (only adopted due to easy comparison with existing analytical works), no attempts to show the effectiveness of the proposed method on non-binary state problems are made. It is hard to be convinced without concrete support such as experiments. By the way, you mentioned about 10 agents and 10 states experiments in the global response, could you report the results for this experiment? Also, is there no way to assess the quality of the results (since you say visualizing + conjecturing is the way but we cannot do so in this complex case)? 2. Thanks for the clarification on “agent optimizing”, yes, please add a reference. 3. I am not entirely sure about the validity of the conjectures you have made. Further, could you explain about the “**price**” in your experiment outputs? If only one menu option is given, shouldn’t a higher price yield better revenue, which is the overall objective? What should be the optimum? Thanks for the real-world example, too!

Reponse to rebuttal

I thank the authors for their detailed feedback and response. Most of my concerns are addressed, so I will raise my rating to 5. Some additional notes: - I do think the deep learning approach is interesting, despite my concerns were over its jusitification as a design choice. I recommend the authors make clear in their revision what they have discussed in the rebuttals (specifically why deep learning, and what it is used for). - Regarding the term "unsupervised learning", I am still a bit unsure whether it's the most apt choice, primarily because unsupervised learning has a conventional meaning attached to it for the machine learning community. Since you do adopt an optimization objective, the name could be something related to optimization and specific to your setting. This is a suggestion.

Acknowledging rebuttal

Thanks for your response here. I acknowledge that the BIC techniques do constitute a new methodological contribution, although this is not the main point of the paper. Thanks also for checking that scaling up can generally work, at least for DSIC. My general conclusion about this paper has not changed.

On Scaling

As noted in the above comment during this rebuttal, our approach scales well in the _ex post_ IC setting but does not scale as easily with the number of buyers in the BIC setting. The challenge in the BIC setting comes from the "interim computations" $–$ involving conditional expectations over reports of others. For a given buyer and report, inference in regard to the "interim experiment" involves computing an expectation over the reports of the remaining buyers. For this reason, we only report results for 2 and 5 buyers in the BIC case (in regard to scaling the number of world states in the BIC case, there is a technical challenge preventing this in our current code framework but not an in-principle challenge). Scaling beyond this will require new techniques, for example, exploiting symmetry. Please note that the *ex post* IC case is in some ways more interesting because it provides an equilibrium concept that does not rely on common knowledge on the part of buyers about buyer types. This makes the learned mechanisms more robust (e.g., changes to the type distribution or deviations in participants' beliefs). Also noteworthy is that existing theory only provided results in the BIC case, which turns out to be easier to handle theoretically because the analytical problem becomes, in effect, smaller in dimension. Note that the revenue achieved in some cases, in reporting these new empirical results, is slightly larger than the optimal revenue because of the small empirical ex post regret. ### Ex post IC **Binary States with Matching Utility, $\theta = (0.5, 0.5)$, and $\alpha = 0.5$** | Num Buyers | Optimal revenue | Learned revenue | Empirical ex post Regret | Time Taken | |:----------:|:---------------:|:---------------:|:------------------------:|:----------:| | 3 | 0.39 | 0.40 | <0.001 | 11 minutes | | 5 | 0.64 | 0.65 | <0.001 | 21 minutes | | 10 | 1.26 | 1.27 | <0.001 | 34 minutes | The optimal revenue is computed through the optimal mechanisms from Theorem 6. The learned revenue and regret are from the multi-buyer architecture discussed in the paper with the same set of hyper-parameters in Appendix B.4 In the submitted paper, we conjecture and prove the structure of the optimal mechanism in the _ex post_ IC setting for binary world states, matching utility, and for any number of buyers. We can extend the proof for the matching utility case to non-binary states (and will extend the paper accordingly). We use this new theory to compute the optimal revenue in Column 1. **10 States with Matching Utility, $\theta = (0.1, ..., 0.1)$, and $\alpha = 0.5$** | Num Buyers | Optimal revenue | Learned revenue | Empirical ex post Regret | Time Taken | |:----------:|:---------------:|:---------------:|:------------------------:|:----------:| | 3 | 0.70 | 0.72 | <0.001 | 16 minutes | | 5 | 1.15 | 1.16 | <0.001 | 28 minutes | | 10 | 2.27 | 2.22 | <0.001 | 64 minutes | ### Bayes IC **Binary States with Matching Utility, $\theta = (0.5, 0.5)$, and $\alpha = 0.5$** | Num Buyers | Optimal revenue | Learned revenue | Empirical ex post Regret | Time Taken | |:----------:|:---------------:|:---------------:|:------------------------:|:----------:| | 3 | 0.52 | 0.52 | <0.001 | 13 minutes | | 5 | 0.78 | 0.82 | <0.001 | 40 minutes |