  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 $m \ge 1$ 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 $(1-\epsilon)$-approximation. For example,
for an unknown distribution that satisfies the monotone hazard rate (MHR)
condition, we prove that $\tilde{\Theta}(\epsilon^{-3/2})$ samples are
necessary and sufficient. Remarkably, this is fewer samples than is necessary
to accurately estimate the expected revenue obtained 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 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. For regular
distributions, we prove that no pricing strategy is better than
$\tfrac{1}{2}$-approximate, and this is optimal by the Bulow-Klemperer theorem.
For MHR distributions, we show how to do better: we give a simple pricing
strategy that guarantees expected revenue at least $0.589$ times the maximum
possible. We also prove that no pricing strategy achieves an approximation
guarantee better than $\frac{e}{4} \approx .68$.
