Automated mechanism design (AMD) uses computational methods for mechanism design. Differentiable economics is a form of AMD that uses deep learning to learn mechanism designs and has enabled strong progress in AMD in recent years. Nevertheless, a major open problem has been to learn multi-bidder, general, and fully strategy-proof (SP) auctions. We introduce GEneral Menu-based NETwork (GemNet), which significantly extends the menu-based approach of the single-bidder RochetNet (D\"utting et al., 2024) to the multi-bidder setting. The challenge in achieving SP is to learn bidder-independent menus that are feasible, so that the optimal menu choices for each bidder do not over-allocate items when taken together (we call this menu compatibility). GemNet penalizes the failure of menu compatibility during training, and transforms learned menus after training through price changes, by considering a set of discretized bidder values and reasoning about Lipschitz smoothness to guarantee menu compatibility on the entire value space. This approach is general, leaving trained menus that already satisfy menu compatibility undisturbed and reducing to RochetNet for a single bidder. Mixed-integer linear programs are used for menu transforms, and through a number of optimizations enabled by deep learning, including adaptive grids and methods to skip menu elements, we scale to large auction design problems. GemNet learns auctions with better revenue than affine maximization methods, achieves exact SP whereas previous general multi-bidder methods are approximately SP, and offers greatly enhanced interpretability.

翻译：自动化机制设计（AMD）利用计算方法进行机制设计。可微分经济学是AMD的一种形式，它通过深度学习学习机制设计，近年来推动了AMD领域的显著进展。然而，一个主要的开放性问题是如何学习多投标人、通用且完全策略证明（SP）的拍卖机制。本文提出通用菜单网络（GemNet），它将单投标人RochetNet（D\"utting等人，2024）的菜单方法显著扩展至多投标人场景。实现SP的关键在于学习独立于投标人的可行菜单，使得每个投标人的最优菜单选择在组合使用时不会过度分配物品（我们称之为菜单兼容性）。GemNet在训练过程中对菜单兼容性失败进行惩罚，并在训练后通过价格调整对学习到的菜单进行转换——该方法通过考虑一组离散化的投标人估值，并基于Lipschitz平滑性推理来保证整个估值空间上的菜单兼容性。此方法具有通用性：对已满足菜单兼容性的训练菜单保持原状，并在单投标人场景下退化为RochetNet。我们采用混合整数线性规划进行菜单转换，并通过深度学习实现的多种优化技术（包括自适应网格和菜单元素跳过方法）将框架扩展至大规模拍卖设计问题。GemNet学习的拍卖机制相比仿射最大化方法具有更高收益，在先前通用多投标人方法仅能实现近似SP的情况下达到精确SP，并大幅提升了可解释性。