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

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.

利用可区分经济学、遗憾预测模型和一种能确保拍卖机制具有战略不可篡改性的拍卖接受规则，本研究提出了一种新方法来确保拍卖过程中买家被鼓励出真实估值，以实现最优且公平的拍卖结果，并通过数值实验证明了该方法的适用性和有效性。

基于一致性预测的无操纵拍卖策略

Strategy-Proof Auctions through Conformal Prediction

Optimal auction design is a fundamental problem in algorithmic game theory.
This problem is notoriously difficult already in very simple settings. Recent
work in differentiable economics showed that neural networks can efficiently
learn known optimal auction mechanisms and discover interesting new ones. In an
attempt to theoretically justify their empirical success, we focus on one of
the first such networks, RochetNet, and a generalized version for affine
maximizer auctions. We prove that they satisfy mode connectivity, i.e., locally
optimal solutions are connected by a simple, piecewise linear path such that
every solution on the path is almost as good as one of the two local optima.
Mode connectivity has been recently investigated as an intriguing empirical and
theoretically justifiable property of neural networks used for prediction
problems. Our results give the first such analysis in the context of
differentiable economics, where neural networks are used directly for solving
non-convex optimization problems.

研究神经网络在拍卖设计及优化中的应用，证明了不可凸优化问题中局部最优解之间存在简单的分段线性路径，网络的表现满足模态连通性。