Auctions are key for maximizing sellers' revenue and ensuring truthful bidding among buyers. Recently, an approach known as differentiable economics based on deep learning shows promise in learning optimal auction mechanisms for multiple items and participants. However, this approach has no guarantee of strategy-proofness at test time. Strategy-proofness is crucial as it ensures that buyers are incentivized to bid their true valuations, leading to optimal and fair auction outcomes without the risk of manipulation. Building on conformal prediction, we introduce a novel approach to achieve strategy-proofness with rigorous statistical guarantees. The key novelties of our method are: (i) the formulation of a regret prediction model, used to quantify at test time violations of strategy-proofness; and (ii) an auction acceptance rule that leverages the predicted regret to ensure that for a new auction, the data-driven mechanism meets the strategy-proofness requirement with high probability (e.g., 99\%). Numerical experiments demonstrate the necessity for rigorous guarantees, the validity of our theoretical results, and the applicability of our proposed method.

翻译：拍卖是最大化卖方收益并确保买方真实出价的关键机制。近期，一种基于深度学习的可微分经济学方法在针对多物品和多参与者的最优拍卖机制学习方面展现出潜力。然而，该方法无法保证在测试阶段具有策略证明性。策略证明性至关重要，因为它能激励买方按其真实估值出价，从而在不被操纵风险的情况下实现最优且公平的拍卖结果。基于保形预测，我们提出了一种具有严格统计保证的策略证明性实现新方法。我们方法的核心创新在于：(i) 构建了一个遗憾预测模型，用于在测试时量化策略证明性的违反程度；(ii) 设计了一种拍卖接受规则，该规则利用预测的遗憾值来确保对于新的拍卖，数据驱动的机制能够以高概率（例如99%）满足策略证明性要求。数值实验证明了严格保证的必要性、我们理论结果的有效性以及所提方法的适用性。