Applying learning algorithms to preference elicitation

We consider the parallels between the preference elicitation problem in combinatorial auctions and the problem of learning an unknown function from learning theory. We show that learning algorithms can be used as a basis for preference elicitation algorithms. The resulting elicitation algorithms perform a polynomial number of queries. We also give conditions under which the resulting algorithms have polynomial communication. Our conversion procedure allows us to generate combinatorial auction protocols from learning algorithms for polynomials, monotone DNF, and linear-threshold functions. In particular, we obtain an algorithm that elicits XOR bids with polynomial communication.

[1]  David C. Parkes,et al.  Iterative Combinatorial Auctions: Theory and Practice , 2000, AAAI/IAAI.

[2]  Avrim Blum,et al.  On polynomial-time preference elicitation with value queries , 2003, EC '03.

[3]  Noam Nisan,et al.  Bidding and allocation in combinatorial auctions , 2000, EC '00.

[4]  David Levine,et al.  CABOB: A Fast Optimal Algorithm for Combinatorial Auctions , 2001, IJCAI.

[5]  N. Littlestone Learning Quickly When Irrelevant Attributes Abound: A New Linear-Threshold Algorithm , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[6]  Yoav Shoham,et al.  Taming the Computational Complexity of Combinatorial Auctions: Optimal and Approximate Approaches , 1999, IJCAI.

[7]  Umesh V. Vazirani,et al.  An Introduction to Computational Learning Theory , 1994 .

[8]  Noam Nisany,et al.  The Communication Requirements of E¢cient Allocations and Supporting Lindahl Prices¤ , 2003 .

[9]  Avrim Blum,et al.  Preference Elicitation and Query Learning , 2004, J. Mach. Learn. Res..

[10]  Dana Angluin,et al.  Learning Regular Sets from Queries and Counterexamples , 1987, Inf. Comput..

[11]  David C. Parkes,et al.  Auction design with costly preference elicitation , 2005, Annals of Mathematics and Artificial Intelligence.

[12]  Sushil Bikhchandani,et al.  The Package Assignment Model , 2002, J. Econ. Theory.

[13]  David C. Parkes,et al.  Price-Based Information Certificates for Minimal-Revelation Combinatorial Auctions , 2002, AMEC.

[14]  Linda Sellie,et al.  Learning sparse multivariate polynomials over a field with queries and counterexamples , 1993, COLT '93.

[15]  Tuomas Sandholm,et al.  Using value queries in combinatorial auctions , 2003, EC '03.

[16]  Tuomas Sandholm,et al.  Partial-revelation VCG mechanism for combinatorial auctions , 2002, AAAI/IAAI.

[17]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[18]  Arne Andersson,et al.  Integer programming for combinatorial auction winner determination , 2000, Proceedings Fourth International Conference on MultiAgent Systems.

[19]  Dana Angluin,et al.  Queries and concept learning , 1988, Machine Learning.