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

GemNet: Menu-Based, Strategy-Proof Multi-Bidder Auctions Through Deep  Learning

Effectively predicting molecular interactions has the potential to accelerate
molecular dynamics by multiple orders of magnitude and thus revolutionize
chemical simulations. Graph neural networks (GNNs) have recently shown great
successes for this task, overtaking classical methods based on fixed molecular
kernels. However, they still appear very limited from a theoretical
perspective, since regular GNNs cannot distinguish certain types of graphs. In
this work we close this gap between theory and practice. We show that GNNs with
directed edge embeddings and two-hop message passing are indeed universal
approximators for predictions that are invariant to translation, and
equivariant to permutation and rotation. We then leverage these insights and
multiple structural improvements to propose the geometric message passing
neural network (GemNet). We demonstrate the benefits of the proposed changes in
multiple ablation studies. GemNet outperforms previous models on the COLL,
MD17, and OC20 datasets by 34%, 41%, and 20%, respectively, and performs
especially well on the most challenging molecules. Our implementation is
available online.

本研究介绍了一种新型的 Geometric Message Passing Neural Network（GemNet）结构，采用了定向边嵌入和双跳消息传递，展现出图神经网络在预测分子动力学方面的强大效果和广阔前景。