Scalable Virtual Valuations Combinatorial Auction Design by Combining Zeroth-Order and First-Order Optimization Method

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.