Learning Revenue-Maximizing Auctions with Neural Affine Maximizer

Learning truthful, revenue-maximizing auctions is a central challenge in automated mechanism design and differentiable economics. Existing learning approaches that guarantee truthfulness typically discretize the outcome space into a finite menu, which tends to favor deterministic but suboptimal auctions. In this work, we propose *Neural Affine Maximizer* (NAM), a discretization-free approach for learning truthful auctions. NAM guarantees truthfulness by building on affine maximizer auctions (AMAs) while replacing the conventional finite menu with a boosting function over the outcome space. NAM then parameterizes the boosting function with neural networks and derives unbiased gradient estimators to enable first-order optimization. Experiments show that NAM consistently improves revenue over state-of-the-art baselines. In the 2-bidder 2-item setting, NAM discovers a randomized, truthful auction with a 2.4\% revenue improvement over known optimal deterministic, truthful auctions. In larger-scale settings up to $10$ buyers or $30$ goods, NAM continues to achieve revenue gains over existing approaches with comparable computation costs. Our codes are available at \url{https://github.com/YunxuanMaPKU/NAM}.