Generalization Guarantees for Multi-Item Profit Maximization: Pricing, Auctions, and Randomized Mechanisms.

This article focuses on providing generalization guarantees for multi-item profit maximization mechanisms when the seller has only sample access to the distribution of buyers' values, rather than full knowledge of it. It identifies a common structural property across diverse mechanism classes—including nonlinear pricing mechanisms, affine maximizer auctions (AMAs), virtual valuation combinatorial auctions (VVCAs), mixed-bundling auctions with reserves (MBARPs), and lotteries—namely that profit is a piecewise linear function of the mechanism’s parameters. Leveraging this structure, the authors develop a general theorem that bounds the difference between empirical average profit on samples and expected profit over the true distribution, using the concept of pseudo-dimension to quantify mechanism complexity. The paper also presents stronger, distribution-dependent bounds for settings with additive buyers and item-independent value distributions, and discusses how to optimize the tradeoff between mechanism complexity and sample size to avoid overfitting. These results unify and extend prior work by offering the first generalization guarantees for many important multi-item mechanism classes and provide a framework applicable to a broad range of economic and computational settings.