Robust Learning of Optimal Auctions

TL;DR

This paper develops algorithms for learning revenue-optimal auctions that are robust to adversarial corruption and distribution perturbations, providing tight bounds and guarantees for regular and MHR distributions.

Contribution

It introduces new algorithms capable of learning near-optimal auctions under adversarial conditions with proven bounds, extending beyond bounded distributions.

Findings

Algorithms achieve near-optimal revenue with adversarially corrupted data.

Proven tight upper and lower bounds for revenue under distribution perturbations.

Sample complexity bounds for learning auctions in adversarial settings.

Abstract

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.