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

TL;DR

This paper establishes sample complexity bounds for multi-item profit maximization mechanisms, ensuring that sample-based optimization yields near-optimal expected profits by leveraging the piecewise linear structure of profit functions.

Contribution

It introduces a novel analysis framework based on the piecewise linearity of profit functions, providing new sample complexity bounds for various mechanism classes.

Findings

Derived bounds for sample complexity in mechanism design.

Demonstrated that profit functions are piecewise linear in mechanism parameters.

Improved or matched existing guarantees for multiple mechanism classes.

Abstract

We study multi-item profit maximization when there is an underlying distribution over buyers' values. In practice, a full description of the distribution is typically unavailable, so we study the setting where the mechanism designer only has samples from the distribution. If the designer uses the samples to optimize over a complex mechanism class -- such as the set of all multi-item, multi-buyer mechanisms -- a mechanism may have high average profit over the samples but low expected profit. This raises the central question of this paper: how many samples are sufficient to ensure that a mechanism's average profit is close to its expected profit? To answer this question, we uncover structure shared by many pricing, auction, and lottery mechanisms: for any set of buyers' values, profit is piecewise linear in the mechanism's parameters. Using this structure, we prove new bounds for mechanism classes not yet studied in the sample-based mechanism design literature and match or improve over the best-known guarantees for many classes.