Making the Most of Your Samples


June 16, 2015


Zhiyi Huang


University of Hong Kong


We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution D. The seller has “data” about D in the form of m >= 1 i.i.d. samples, and the algorithmic challenge is to use these samples to obtain expected revenue as close as possible to what could be achieved with advance knowledge of D.

Our first set of results quantifies the number of samples m that are necessary and sufficient to obtain a (1-eps)-approximation. For example, for an unknown distribution that satisfies the monotone hazard rate (MHR) condition, we prove that ˜Theta(eps-3/2) samples are necessary and sufficient. Remarkably, this is fewer samples than is necessary to accurately estimate the expected revenue obtained for such a distribution by even a single reserve price. We also prove essentially tight sample complexity bounds for regular distributions, bounded-support distributions, and a wide class of irregular distributions. Our lower bound approach, which applies to all randomized pricing strategies, borrows tools from differential privacy and information theory, and we believe it could find further applications in auction theory.

Our second set of results considers the single-sample case. While no deterministic pricing strategy is better than 1/2-approximate for regular distributions, for MHR distributions we show how to do better: there is a simple deterministic pricing strategy that guarantees expected revenue at least 0.589 times the maximum possible. We also prove that no deterministic pricing strategy achieves an approximation guarantee better than e/4 ≅ 0.68.


Zhiyi Huang

Zhiyi is an assistant professor in Computer Science at the University of Hong Kong. He works broadly on theoretical computer science. Before joining HKU, Zhiyi was a postdoc at Stanford University from 2013 to 2014, working with Tim Roughgarden. He obtained his Ph.D. from the University of Pennsylvania under Sampath Kannan and Aaron Roth in 2013, interned at Microsoft Research Redmond under Nikhil R. Devanur in the summers of 2011 and 2012, and got his bachelor degree from the first “Yao Class” under Andrew Yao at Tsinghua University in 2008.