On polynomial-time preference elicitation with value queries

  • Authors:
  • Martin A. Zinkevich;Avrim Blum;Tuomas Sandholm

  • Affiliations:
  • Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA

  • Venue:
  • Proceedings of the 4th ACM conference on Electronic commerce
  • Year:
  • 2003

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Abstract

Preference elicitation --- the process of asking queries to determine parties' preferences --- is a key part of many problems in electronic commerce. For example, a shopping agent needs to know a user's preferences in order to correctly act on her behalf, and preference elicitation can help an auctioneer in a combinatorial auction determine how to best allocate a given set of items to a given set of bidders. Unfortunately, in the worst case, preference elicitation can require an exponential number of queries even to determine an approximately optimal allocation. In this paper we study natural special cases of preferences for which elicitation can be done in polynomial time via value queries. The cases we consider all have the property that the preferences (or approximations to them) can be described in a polynomial number of bits, but the issue here is whether they can be elicited using the natural (limited) language of value queries. We make a connection to computational learning theory where the similar problem of exact learning with membership queries has a long history. In particular, we consider preferences that can be written as read-once formulas over a set of gates motivated by a shopping application, as well as a class of preferences we call Toolbox DNF, motivated by a type of combinatorial auction. We show that in each case, preference elicitation can be done in polynomial time. We also consider the computational problem of allocating items given the parties' preferences, and show that in certain cases it can be done in polynomial time and in other cases it is NP-complete. Given two bidders with Toolbox-DNF preferences, we show that allocation can be solved via network flow. If parties have read-once formula preferences, then allocation is NP-hard even with just two bidders, but if one of the two parties is additive (e.g., a shopping agent purchasing items individually and then bundling them to give to the user), the allocation problem is solvable in polynomial time.