Learning Reserve Prices in Second-Price Auctions

TL;DR

This paper establishes the tight sample complexity for learning reserve prices in second-price auctions across various distribution families, showing dependence on precision but not on the number of bidders, and allowing correlated distributions in some settings.

Contribution

It provides the first tight sample complexity bounds for second-price auctions with anonymous reserves, extending to correlated distributions and improving upon prior bounds for Myerson auctions.

Findings

Sample complexity depends on precision, not number of bidders.

Allows correlated distributions in bounded-support settings.

Achieves tight bounds matching information-theoretic limits.

Abstract

This paper proves the tight sample complexity of {\sf Second-Price Auction with Anonymous Reserve}, up to a logarithmic factor, for each of all the value distribution families studied in the literature: $[0,\, 1]$-bounded, $[1,\, H]$-bounded, regular, and monotone hazard rate (MHR). Remarkably, the setting-specific tight sample complexity $\mathsf{poly}(\varepsilon^{-1})$ depends on the precision $\varepsilon \in (0, 1)$, but not on the number of bidders $n \geq 1$. Further, in the two bounded-support settings, our learning algorithm allows {\em correlated} value distributions. In contrast, the tight sample complexity $\tilde{\Theta}(n) \cdot \mathsf{poly}(\varepsilon^{-1})$ of {\sf Myerson Auction} proved by Guo, Huang and Zhang (STOC~2019) has a nearly-linear dependence on $n \geq 1$, and holds only for {\em independent} value distributions in every setting. We follow a similar framework as the Guo-Huang-Zhang work, but replace their information theoretical arguments with a direct proof.