Mechanism Design via Machine Learning
Maria-Florina Balcan, Avrim Blum, Jason Hartline and Yishay Mansour
In: FOCS 2005, October 22-25, 2005, Pittsburgh, USA.

## Abstract

We use techniques from sample-complexity in machine learning to reduce problems of incentive-compatible mechanism design to standard algorithmic questions, for a wide variety of revenue-maximizing pricing problems. Our reductions imply that for these problems, given an optimal (or $\beta$-approximation) algorithm for the standard algorithmic problem, we can convert it into a $(1+\epsilon)$-approximation (or $\beta(1+\epsilon)$-approximation) for the incentive-compatible mechanism design problem, so long as the number of bidders is sufficiently large as a function of an appropriate measure of complexity of the comparison class of solutions. We apply these results to the problem of auctioning a digital good, the {\em attribute auction} problem, and to the problem of item-pricing in unlimited-supply combinatorial auctions. From a learning perspective, these settings present several challenges: in particular, the loss function is discontinuous and asymmetric, and the range of bidders' valuations may be large.