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 practical 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.

翻译：仿射最大化拍卖（AMA）作为VCG机制的一种广义形式，因其固有的占优策略激励相容性（DSIC）与个体理性（IR）特性，在自动机制设计中得到广泛应用。然而，由于其支付形式固定，AMA的表达能力受限，尤其在竞拍者估值存在相关性的分布中表现尤为明显。本文提出相关性感知AMA（CA-AMA），这是一种通过引入新型相关性感知支付来增强AMA的全新框架。我们证明任何CA-AMA均保持DSIC特性，并将寻找最优CA-AMA形式化为在IR约束下的约束优化问题。随后，我们从理论上刻画了经典AMA相较于最优收益可能表现任意糟糕，而CA-AMA却能达到最优收益的场景。针对CA-AMA的优化，我们设计了一种实用的两阶段训练算法。我们推导了目标函数的连续性，以及偏离严格IR程度的泛化界。最后，大量实验表明，我们的算法能够在多种分布中找到近似最优的CA-AMA，在提升收益的同时保持较低的IR违反程度。