Reducing mechanism design to algorithm design via machine learning

  • Authors:
  • Maria-Florina Balcan;Avrim Blum;Jason D. Hartline;Yishay Mansour

  • Affiliations:
  • Carnegie Mellon University, Pittsburgh, PA 15213, USA;Carnegie Mellon University, Pittsburgh, PA 15213, USA;Microsoft Research, Mountain View, CA 94043, USA;School of Computer Science, Tel-Aviv University, Israel

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2008

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Abstract

We use techniques from sample-complexity in machine learning to reduce problems of incentive-compatible mechanism design to standard algorithmic questions, for a broad class of revenue-maximizing pricing problems. Our reductions imply that for these problems, given an optimal (or @b-approximation) algorithm for an algorithmic pricing problem, we can convert it into a (1+@e)-approximation (or @b(1+@e)-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 class of allowable pricings. We apply these results to the problem of auctioning a digital good, to the attribute auction problem which includes a wide variety of discriminatory pricing problems, and to the problem of item-pricing in unlimited-supply combinatorial auctions. From a machine learning perspective, these settings present several challenges: in particular, the ''loss function'' is discontinuous, is asymmetric, and has a large range. We address these issues in part by introducing a new form of covering-number bound that is especially well-suited to these problems and may be of independent interest.