# Settling the Sample Complexity of Single-parameter Revenue Maximization

## TL;DR

This paper precisely characterizes the sample complexity for single-parameter revenue maximization, providing matching upper and lower bounds using a novel information-theoretic framework, advancing understanding of the fundamental limits in this domain.

## Contribution

It introduces a unified, information-theoretic approach to establish tight sample complexity bounds, differing from previous methods based on mechanism space discretization or virtual value approximation.

## Key findings

- Matching upper and lower bounds up to poly-logarithmic factors.
- A novel framework based on revenue monotonicity and information theory.
- First application of information-theoretic arguments for upper bounds in this context.

## Abstract

This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the literature. The upper bounds are unified under a novel framework, which builds on the strong revenue monotonicity by Devanur, Huang, and Psomas (STOC 2016), and an information theoretic argument. This is fundamentally different from the previous approaches that rely on either constructing an $\epsilon$-net of the mechanism space, explicitly or implicitly via statistical learning theory, or learning an approximately accurate version of the virtual values. To our knowledge, it is the first time information theoretical arguments are used to show sample complexity upper bounds, instead of lower bounds. Our lower bounds are also unified under a meta construction of hard instances.