Automated auction design seeks to discover empirically high-revenue and incentive-compatible mechanisms using machine learning. Ensuring dominant strategy incentive compatibility (DSIC) is crucial, and the most effective approach is to confine the mechanism to Affine Maximizer Auctions (AMAs). Nevertheless, existing AMA-based approaches encounter challenges such as scalability issues (arising from combinatorial candidate allocations) and the non-differentiability of revenue. In this paper, to achieve a scalable AMA-based method, we further restrict the auction mechanism to Virtual Valuations Combinatorial Auctions (VVCAs), a subset of AMAs with significantly fewer parameters. Initially, we employ a parallelizable dynamic programming algorithm to compute the winning allocation of a VVCA. Subsequently, we propose a novel optimization method that combines both zeroth-order and first-order techniques to optimize the VVCA parameters. Extensive experiments demonstrate the efficacy and scalability of our proposed approach, termed Zeroth-order and First-order Optimization of VVCAs (ZFO-VVCA), particularly when applied to large-scale auctions.

翻译：自动化拍卖设计旨在利用机器学习发现经验上高收益且激励兼容的机制。确保占优策略激励兼容（DSIC）至关重要，最有效的方法是将机制限制在仿射最大化拍卖（AMAs）框架内。然而，现有基于AMA的方法面临可扩展性问题（源于组合候选分配）以及收益不可微等挑战。本文为实现可扩展的AMA方法，进一步将拍卖机制约束为虚拟估值组合拍卖（VVCAs）——即参数数量显著减少的AMA子类。首先，我们采用可并行化的动态规划算法计算VVCA的中标分配；其次，提出一种结合零阶与一阶技术的新型优化方法来优化VVCA参数。大量实验表明，我们提出的方法（称为零阶-一阶优化的VVCAs，ZFO-VVCA）在应用于大规模拍卖时具有显著的有效性与可扩展性。