Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: This paper covers a somewhat interesting and novel problem: learning constraints of an auction setting, and then learning to run an auction that respects those. Fairness in allocations is cited as a justification for this in practice, where it may be beneficial to learn from a human’s choices to determine how to decide who should win in the auction, for example to determine similar allocations across demographics.

The approach builds on the RegretNet line of work that learns to run revenue maximizing auctions. The approach broadly is to learn a feasibility constraint that is scored by human subjects, and then use that in the RegretNet architecture to learn to generate auctions that respect that constraint. In this work, the motivating constraint is a binary classification of fairness. The implementation is a composition of learning then constraint, followed by leveraging RegretNet to learn according to that function. 

To support the approach, the authors first compare PreferenceNet to RegretNet trained with the exact constraints, and see similar performance suggesting some amount of usefulness. The authors then train PreferenceNet on responses from human subjects in two surveys regarding the binary qualitative fairness of allocations. 

main_review: The paper delivers on a novel use for machine learning in auctions. The significance of the approach remains a little open to interpretation: I don’t know that fairness is the constraint that makes the most sense for this approach, but there is no reason for the approach to be limited to fairness as the measure used - in such cases is it better to have the biases explicit or implicit as a result of human responses? In some ways it seems that the decision of what is fair is moved from the explicit constraint to the survey question, either explicitly here or implicitly in any use of this approach.

The paper is generally well written and comprehensive in exploring the performance of PreferenceNet in the fairness area, both comparing to a baseline RegretNet with perfect knowledge of the constraint and then examples trained based on human input. 

Evaluating the architecture choices is outside of my area of expertise. 

Small notes:
Fig 1: doesn't seem to be particularly helpful as a comparison, or I am missing the intuition that would give this a half page here.
Line 193: eval[u]ate
limitations_and_societal_impact: The work has one primary potential for negative societal impact: human responses should not be expected to be unbiased. The authors do address this, though perhaps a stronger statement regarding where such approaches would be deemed to be appropriate would be helpful.
review_title: null

final_score: rating: 5: Marginally below the acceptance threshold
review_content: summary: This paper proposes PreferenceNet, which is a new deep learning approach for designing revenue-maximizing auctions that encodes human preferences. PreferenceNet extends RegretNet [Duetting et al. 2019] with modified loss functions and additional constraints. 
main_review: Overall I find the paper well-written and clear to follow.  The PreferenceNet proposed by the authors extends from RegretNet, with additional MLP layers that are trained to capture implicit human preferences, modified loss functions and constraints. The authors also conducted  two surveys to further study human preferences for auction outcomes, and I find the conduction of the surveys useful and important, as they provide actual feedbacks from human participants. Below are a few questions and concerns I have.

First is about the scalability and flexibility of PreferenceNet. In the current formulation, the ground truth labeling function based on the underlying preference ( s(b) ) is constrained to be a binary label, and the input is a whole vector of allocations for the given bid. However, in practice the decision ("good" or "bad") could be hard to provided by human, especially when the number of items is large. For example, human could be bad at deciding if two vectors of allocations are actually similar or not. This can make the preference feedbacks obtained very noisy. I would also be curious to see more details on experimentally how much additional computation PreferenceNet requires compared to the RegretNet.

Second is, the deep learning based approach estimates violations of the strategyproofness and fairness constraints using a gradient-based method which is effective during training, but may not accurately reflect the true extent to which strategyproofness or fairness constraints are violated. Therefore I find the design of the loss functions and constraints for PreferenceNet intuitive, but it is unclear theoretically how these affect the generalization bound for strategyproofness. Besides, will the fairness constraints render the optimal auction infeasible in some cases? Is it possible that each agent has incompatible preferences, and PreferenceNet cannot satisfy the overall preferences for all agents? I would be interested in seeing more elaboration on this side.

typos:
Eq(3) c, C_k undefined
Eq(4) numerator missing index
limitations_and_societal_impact: The authors have addressed the limitations and potential negative societal impact of this work.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper describes how we can encode socially desirable constraints in auction mechanisms learned using the regretNet framework.   The paper has two main contributions:  
(1) A metric that quantifies how well these mechanisms adhere to these constraints.  
(2) An neural network and a training procedure (called the preferenceNet) that can encode these constraints using exemplars of the desired allocation

The authors demonstrate the efficacy of the proposed approach by showing that it can match the performance of standard approaches on both synthetic preferences as well as human preferences
main_review: Pros:
- Unlike existing/related work, they attempt to capture socially desirable properties through data (rather than formally defining them).  
- Results are quite promising - they either match or beat standard approaches (despite only being trained using weaker and noisy signals) 
- Significance: This paper studies an important problem at the intersection of mechanism design and human in the loop learning
- Clarity: The paper is well written and easy to understand


Comments:
- My main concern is the inability of preferenceNet to learn the preference function exactly (which happens to play a key role in the training pipeline)
- It is unclear how $\alpha$,  $\beta$ and $\gamma$ were chosen.
- Is there an intuition behind why some constraints are harder than others?

Minor Comments:   
- typo on line 193: evalate-> evaluate
- The augmented Lagrangian method is usually the sum of squares of the penalty term (rather than the square of the sum of penalty terms)
 $$\frac{\rho_r}{2}\left(\sum_{i} rgt_i(w)\right)^2 => \frac{\rho_r}{2} \sum_{i} \left(rgt_i(w)\right)^2$$

limitations_and_societal_impact: Yes. (For limitations see above)
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper studies of designing revenue optimizing auctions subject to the an additional constraint on fairness. Instead of algebraically capturing the fairness of an allocation, the authors train a neural network termed PreferenceNet that assign a fairness score to any allocation. The neural network for strategy-proof, revenue maximizing auction (RegretNet) is trained to trade-off revenue and regret with the preference loss.  The author evaluate this on small instances (2-4 bidders and 2-4 items) and contrast revenue, regret and fairness of simple RegretNet with one constrained to produce fair allocations. 

One primary motivation for a deep neural network based PreferenceNet is that it can capture real world preferences from humans. To explore this aspect, the authors conducted real world studies to get user preference samples and trained a PreferenceNet on that. They also correlate preference learned from humans with mathematical models of preference. 
main_review: The key idea in this paper is to train a deep neural network for scoring an allocation for fairness. This network is used to score allocations produced by RegretNet which is the deep neural network for computing revenue optimizing incentive compatible allocations. The authors provide empirical evaluation of their idea on small instances. 

The paper is closely related to the paper by Kuo et al. ProportionNet: Balancing Fairness and Revenue for Auction Design with Deep Learning. The key distinction is that paper uses only TVF and the allocation is scored using the mathematical definition, while in this work the authors approximate it using a neural network. 

I think this approach is interesting. The authors should explain their approach more fully and also evaluate it on a diverse set of inputs. In particular, fairness can become more restrictive if the advertisers preference for the different goods are very different. So it will be interesting to explore valuations that not identically distributed or with a larger spread of values such as exponential distributions.  

Another aspect that is worth evaluating is looking into what type of auctions are designed - how is the optimal auction different with the additional fairness constraint. 

Given these concerns, I believe the authors could strengthen paper a lot with a more thorough evaluation of their model. 

I also have a minor clarification question. The learning process describes re-training preference net about a few rounds of training regret-net. Is that relevant even for a preference-net trained for real world data. How does that work - does it require new data gathering or some sort of heuristic based approach, what if at all would be the impact of getting that part wrong.

Minor:
- Many of the references cite the authors as author A et al. It is preferred if the authors could include the full list of authors. 
- the definition of TVF is not clear. What's c, C_k, d^k(j, j')?
- please clarify that the experiment evaluation was done on bids drawn IID from U[0, 1].

Update based on author's response:
Authors provided a lot more evaluation of their approach with non-identical distributions, larger instance sizes. The authors should include this new data in the paper as it provides a more thorough evaluation of the approach. For example, we do see larger gaps emerge in the metrics with larger instances.  I had a some more questions about the results. 
1) In some cases RegretNet PCA is lower than PreferenceNet, is this expected. Shouldn't RegretNet perform better?
2) Can we still say that the two approaches are similar if the PCA is very far from each other or revenue is at times more than 5-6% different?

limitations_and_societal_impact: Authors do discuss limitations of their approach - in terms of human preference data gathering and model training. Particular for human preference data gathering - authors discussed the noise introduced and how they handled that. The authors also discuss the limitations of the PreferenceNet model and the situations in which it fails. One aspect lacking is looking deeper into the model trained and what it teaches about optimal auction design - this aspect is what makes the RegretNet approach interesting. Alternately the authors could discuss how this approach could scale to instances of arbitrary size.
review_title: null

Meta-review: The review team sentiment is positive about the paper: it is a new dimension to the problem of automated auction design via NN that makes it more practical and allows us to capture subtle notions like the perception of fairness? There were initial concerns around scalability and experiments on harder (non-iid) datasets, but those were adequately addressed by the authors in the discussion. Please incorporate those in the final version.

There are additional concerns on whether biases could be introduced in the model and that through this methodology biases would be harder to identify/correct since they are not explicitly written in a formula, but hidden in the data. While I share the concern of the reviewers, I think this is inherent from this type of approach, so we need to live with that. 

Finally, our recommendation is to accept the paper.
Decision: Accept (Poster)