Characterizing revenue-optimal auctions for multi-item, multi-bidder settings remains a fundamental open problem, with no known closed-form solution existing beyond restrictive binary-type instances. This has motivated interest in computational approaches to optimal auction design. In this paper, we introduce the first computational framework that directly tackles the dual problem for multi-item, multi-bidder auctions and dominant-strategy incentive compatibility (DSIC), generating certified revenue upper bounds. Our approach parametrizes Lagrange multipliers with a structurally guaranteed strict flow-conservation property using neural networks, enabling efficient optimization over feasible dual solutions via gradient descent. To bridge the gap between discrete computational methods and theoretical guarantees for continuous types, we develop a novel lifting technique that maps dual certificates from coarse discretizations to fine refinements. We prove that lifting gives valid revenue upper bounds for multi-item, multi-bidder auctions with continuous uniform valuations. Furthermore, we give a generalized lifting construction for arbitrary continuous distributions and demonstrate that these lifted duals converge to the revenue of the original continuous problem in the discrete limit. We validate this computational framework for the dual auction design problem by recovering known analytical mechanisms for canonical instances. For multi-item multi-bidder problems, our framework establishes a small gap between the optimal revenue and best-known DSIC mechanisms, providing computational certificates of near-optimality.

翻译：刻画多物品、多竞拍者场景下的收益最优拍卖机制仍是一个基础性开放问题，除受限的二元类型实例外，尚无已知的闭式解。这推动了计算最优拍卖设计领域的研究兴趣。本文提出首个直接处理多物品多竞拍者拍卖及占优策略激励相容（DSIC）对偶问题的计算框架，生成经认证的收益上界。该方法利用神经网络对拉格朗日乘子进行参数化，并赋予其结构上严格保证的流守恒性质，从而通过梯度下降实现对可行对偶解的高效优化。为弥合离散计算方法与连续类型理论保证之间的鸿沟，我们开发了一种新颖的提升技术，可将对偶凭证从粗离散化映射至精细划分。我们证明，对于具有连续均匀估值的多物品多竞拍者拍卖，提升后的对偶解能够给出有效的收益上界。此外，我们针对任意连续分布给出广义的提升构造，并证明这些提升后的对偶解在离散极限下收敛至原始连续问题的收益。通过恢复经典实例的已知解析机制，我们验证了该对偶拍卖设计计算框架的有效性。对于多物品多竞拍者问题，本框架确立了最优收益与已知最优DSIC机制之间的微小差距，提供了近最优性的计算凭证。