Title: Enhancing Affine Maximizer Auctions with Correlation-Aware Payment
Venue: NeurIPS 2025
Accepted: no
Keywords: Automated Mechanism Design

Affine Maximizer Auctions

Correlated Valuations

Differential Economics
Abstract: Affine Maximizer Auctions (AMAs), a generalized mechanism family from VCG, are widely used in automated mechanism design due to their inherent dominant-strategy incentive compatibility (DSIC) and individual rationality (IR). However, as the payment form is fixed, AMA's expressiveness is restricted, especially in distributions where bidders' valuations are correlated. In this paper, we propose Correlation-Aware AMA (CA-AMA), a novel framework that augments AMA with a new correlation-aware payment. We show that any CA-AMA preserves the DSIC property and formalize finding optimal CA-AMA as a constraint optimization problem subject to the IR constraint. Then, we theoretically characterize scenarios where classic AMAs can perform arbitrarily poorly compared to the optimal revenue, while the CA-AMA can reach the optimal revenue. For optimizing CA-AMA, we design a tailored loss function with a two-stage training algorithm. We derive that the target function's continuity and the generalization bound on the degree of deviation from strict IR. Finally, extensive experiments showcase that our algorithm can find an approximate optimal CA-AMA in various distributions with improved revenue and a low degree of violation of IR.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces Correlation-Aware AMA (CA-AMA), being a modification of affine-maximizer auctions (AMA) that adds a payment term for each bidder that depends on the valuations of all other bidders. The authors nicely motivated the need for enhancing AMA’s expressiveness and transitioning from bidder-independent settings to bidder-correlated settings. The authors proved (under certain assumptions) that their method satisfies DSIC, but IR can be high.\nThis motivated the formulation of an optimization framework to maximize revenue subject to IR.  The authors prove in Theorem 3.3 the following under single-item auctions: when bidders are independent, CA-AMA offers no advantage over classic AMA, but there exist correlated distributions  CA-AMA can achieve optimal revenue, whereas AMAs fail. Unfortunately, this analysis formally holds only for single-item auctions.\n\nThe authors also presented training methods: a two-stage gradient-based algorithm with a loss that balances revenue against IR-violation.  Theorem 4.1 states that, under certain assumptions, the optimal correlation-payment function $p^{\\text{OPT}}_{\\text{Cor}}(V^{-i})$ is continuous in the AMA parameters and $V^{-i}$. The authors also present in Theorem 4.2 a Rademacher-complexity bound for IR-regret.  Empirical results on synthetic correlated distributions (Gaussian mixtures withlinear correlations) illustrate that CA-AMA gets noticeably improved revenue than several baseline methods while having IR-regret near target.\n\nSTRENGTHS AND WEAKNESSES:\nBelow I give a list of strengths and weakeness that I wanted to reflect; I should note that I’m not an expert in this field.\n\n**Strengths**\n\nS1. Novelty: As far as I understand, the idea of including a correlation-dependent payment term is new in the AMA literature.\n\nS2. Theory: The authors provide a good theoretical basis for their proposed method: DSIC (Prop. 3.3), optimal revenue in a special case (Theorem 3.3), continuity (Theorem 4.1), and generalization bound (Theorem 4.2).\n\nS3. Well-motivated optimization method for CA-AMA.\n\nS4. Empirical analysis shows consistent gains in revenue, although somewhat modest.\n\n**Weaknesses**\n\nW1 (main concern). The proposed mechanism is only approximately IR by design. How do violations of IR affect the practical use of the proposed method? It seems unreasonable for a bidder to participate in an auction where they might end up with negative utility: it means a bidder could end up paying more than their actual bid, which I find unjustified.\n\nW2. I wonder how the method performs on real data, and how the limited expressivity of standard AMA is problematic in practice. Currently, the experiments are conducted using simulated data, which is valuable but not necessarily representative of real-world bidder-correlation structures.\n\nW3. Related to the above, are there standard errors for Table 1? Same for Figure 2 and Figure 5.\n\nW4. Still in the context of the experiments, the authors compared their approach to AMA methods and classical mechanisms, but did not compare it to the popular RegretNet method. The authors argue in the discussion in the appendix that RegretNet is not DSIC and thus such a comparison is less appropriate. But, on the other hand, RegretNet is IR in contrast with the proposed CA-AMA method. So, which method should one use?\n\nW5. The theory holds under a single-item assumption, but I understand the challenge of moving beyond this setup.\n\nQUESTIONS:\nSee weaknesses.\n\nLIMITATIONS:\nThe authors discussed the limitations of the work in the appendix. I’d also include the need to know the true valuations for training, and issues with robustness to train/test distribution shifts, and most importantly -- violations of IR.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-15"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThere has been many recent works on differentiable economics focusing on the affine maximizer auctions (AMA). The key idea of this literature is to \"model an auction as a multi-layer\nneural network, frame optimal auction design as a constrained learning problem\", and then solve the said problem \"using standard machine learning pipeline\" (Duetting et al 2017)[Optimal Auctions through Deep Learning: Advances in Differentiable Economics]. This paper considers a variant of the AMA with additional parameters designed to maximize revenue better with interdependent bids. It builds on the ideas of Cr\\'{e}mer and McLean (1987), to augment the VCG pivot payment by a term that depends only on other bids, called the correlation-aware payment. This preserves DSIC but not IR (individual rationality), so a regret penalty on IR is added. \n\nThe paper's main contributions are the following. \n\n1. A constructed example to demonstrate that VCG-style AMA can fail to optimize revenue when bids are sufficiently negatively correlated. \n2. Introduce an additional term in the VCG payment in the style of Cremer-McLean, generalizing it. \n3. Add a regret penalty to the standard AMA revenue optimization to encourage the IR constraint, in th style of Duetting et al. \n4. Give some theoretical results to show that the new optimization problem (CA-AMA) has some reasonable properties (continuous w.r.t. parameters, a K^{1/2} regret bound). \n5. Demonstrate experimentally that CA-AMA stays close to the targetted Regret threshold (ie keeps IR violation within a specified amount). Though CA-AMA is not optimal in close to $\\pm 1$ correlation, it is better than AMA in strongly correlated settings and seems less sensitive to correlation strength compared to other methods (eg ItemCAN). AMA is better in independent settings.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: natural setup (interdependent values), decent solution (Cremer-McLean inspiration), good exposition. \n\nWeaknesses: experimental results show minor improvements over Randomized AMA except for strongly correlated (negative or positive) values, which might not be too realistic. It seems unlikely to me for this to dislodge randomized AMA as the standard benchmark in practice, so from that view the literature impact could be limited.\n\nQUESTIONS:\nMinor comment: I find it a bit hard to keep track of all of the competitor's methods and assumptions, so could you please mention in your results table which of the competing methods also have a non-zero regret for IR (and if so how much), and which guarantees IR ? This way we can have a fair comparison, ie that the new method CA-AMA is not obtaining better revenue at the expense of loosening the constraints. Probably showing the loss (-revenue + regret) would help, I would expect CA-AMA to be optimal there, but it would be helpful to have an understanding such as \"for every X unit of revenue gained, some Y united of regret must be paid for\".\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel family of DSIC and IR multi-item auctions with additive valuations that generalizes Affine Maximizer Auctions (AMAs), a widely used auction family in automated mechanism design. The paper focuses on the Bayesian auction setting with additive valuations: there are many items and many buyers, each buyer has a private value for each item, and buyers’ valuations are drawn from a possibly correlated prior distribution. The goal is to design individually rational (IR) and dominant strategy incentive compatible (DSIC) mechanisms that maximize expected revenue. In general, finding the optimal IC mechanism in the multi-item setting is notoriously difficult. A common approach is to restrict to a specific family of IC and IR mechanisms and optimize within that family for the given instance. One notable example is the AMA, an extension of the VCG mechanism. A key limitation of AMA is that a bidder’s payment is positively correlated with the bids of others. This is not an issue when valuations are independent, but when valuations are negatively correlated, the paper shows that the performance of AMA can be arbitrarily bad. To address this, the authors propose Correlation-Aware AMA (CA-AMA), which introduces a new payment term for each bidder that depends only on the other bidders' reports. This added term increases the expressiveness of the mechanism but comes at the cost of not always satisfying IR. The authors provide examples with correlated valuations where CA-AMA significantly outperforms AMA. They also present an empirical framework for learning the optimal CA-AMA for a given instance, and conduct numerical experiments to demonstrate the effectiveness of their learning approach.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper is well-written and easy to follow.\n2. The problem is well-motivated.\n3. The numerical experiments are comprehensive.\n\nWeaknesses:\n\n1. The problem looks a bit incremental, it simply adds a payment term to AMA. \n2. IMHO, one major downside is that is makes the optimization problem much more complicated by introducing the IR constraint. In the original AMA formulation, IR is not a constraint of optimization since AMAs guarantee IR.\n3. The theoretical analyses and guarantees of CA-AMA is not very strong -- it mainly covers the single-bidder case.\n\nQUESTIONS:\nIt seems that the correlation-aware payment is an arbitrary function of other bidders' valuation. What are the major benefits of such a big freedom? Can you limit correlation-aware payment to a simpler form?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}