  We study the problem of learning revenue-optimal multi-bidder auctions from
samples when the samples of bidders' valuations can be adversarially corrupted
or drawn from distributions that are adversarially perturbed. First, we prove
tight upper bounds on the revenue we can obtain with a corrupted distribution
under a population model, for both regular valuation distributions and
distributions with monotone hazard rate (MHR). We then propose new algorithms
that, given only an ``approximate distribution'' for the bidder's valuation,
can learn a mechanism whose revenue is nearly optimal simultaneously for all
``true distributions'' that are $\alpha$-close to the original distribution in
Kolmogorov-Smirnov distance. The proposed algorithms operate beyond the setting
of bounded distributions that have been studied in prior works, and are
guaranteed to obtain a fraction $1-O(\alpha)$ of the optimal revenue under the
true distribution when the distributions are MHR. Moreover, they are guaranteed
to yield at least a fraction $1-O(\sqrt{\alpha})$ of the optimal revenue when
the distributions are regular. We prove that these upper bounds cannot be
further improved, by providing matching lower bounds. Lastly, we derive sample
complexity upper bounds for learning a near-optimal auction for both MHR and
regular distributions.
