Differentiable economics uses deep learning for automated mechanism design. Despite strong progress, it has remained an open problem 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 RochetNet [D\"utting et al., 2023] 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 undisturbed trained menus that already satisfy menu compatibility and reducing to RochetNet for a single bidder. Mixed-integer linear programs are used for menu transforms and through a number of optimizations, 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.

用可微经济学和深度学习实现自动机制设计，引入GEneral Menu-based NETwork (GemNet)来解决多竞标者、一般和全面策略性（SP）拍卖的学习问题，通过学习竞标者独立的菜单，使用Lipschitz平滑性确保菜单完整性，GemNet能够学习出收益更高、确切策略性的拍卖，并且具有较强的可解释性。

菜单式、无策略性、多竞标人拍卖的GemNet: 基于深度学习的实现