Optimal auctions maximize a seller's expected revenue subject to individual rationality and strategyproofness for the buyers. Myerson's seminal work in 1981 settled the case of auctioning a single item; however, subsequent decades of work have yielded little progress moving beyond a single item, leaving the design of revenue-maximizing auctions as a central open problem in the field of mechanism design. A recent thread of work in "differentiable economics" has used tools from modern deep learning to instead learn good mechanisms. We focus on the RegretNet architecture, which can represent auctions with arbitrary numbers of items and participants; it is trained to be empirically strategyproof, but the property is never exactly verified leaving potential loopholes for market participants to exploit. We propose ways to explicitly verify strategyproofness under a particular valuation profile using techniques from the neural network verification literature. Doing so requires making several modifications to the RegretNet architecture in order to represent it exactly in an integer program. We train our network and produce certificates in several settings, including settings for which the optimal strategyproof mechanism is not known.

中文翻译：

---

认证 Strategyproof 拍卖网络

最优拍卖会最大化卖方的预期收入，这取决于买方的个人理性和策略证明。迈尔森在 1981 年的开创性工作解决了拍卖单品的案子；然而，随后几十年的工作几乎没有取得超越单个项目的进展，使收入最大化拍卖的设计成为机制设计领域的一个核心未决问题。最近在“可微经济学”方面的一项工作使用现代深度学习中的工具来学习良好的机制。我们专注于 RegretNet 架构，它可以代表任意数量的物品和参与者的拍卖；它被训练为具有经验性的策略证明，但该属性从未被完全验证，从而为市场参与者留下潜在的漏洞来利用。我们提出了使用神经网络验证文献中的技术在特定估值配置文件下明确验证策略证明的方法。这样做需要对 RegretNet 架构进行多次修改，以便在整数程序中准确地表示它。我们训练我们的网络并在多种设置中生成证书，包括最佳策略证明机制未知的设置。