Budget-feasible mechanism design for non-monotone submodular objectives: Offline and online

Georgios Amanatidis, Pieter Kleer, Guido Schäfer

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

Abstract

The framework of budget-feasible mechanism design studies procurement auctions where the auctioneer (buyer) aims to maximize his valuation function subject to a hard budget constraint. We study the problem of designing truthful mechanisms that have good approximation guarantees and never pay the participating agents (sellers) more than the budget. We focus on the case of general (non-monotone) submodular valuation functions and derive the first truthful, budget-feasible and O(1)-approximation mechanisms that run in polynomial time in the value query model, for both offline and online auctions. Since the introduction of the problem by Singer [40], obtaining efficient mechanisms for objectives that go beyond the class of monotone submodular functions has been elusive. Prior to our work, the only O(1)-approximation mechanism known for non-monotone submodular objectives required an exponential number of value queries. At the heart of our approach lies a novel greedy algorithm for non-monotone submodular maximization under a knapsack constraint. Our algorithm builds two candidate solutions simultaneously (to achieve a good approximation), yet ensures that agents cannot jump from one solution to the other (to implicitly enforce truthfulness). Ours is the first mechanism for the problem where-crucially-the agents are not ordered according to their marginal value per cost. This allows us to appropriately adapt these ideas to the online setting as well. To further illustrate the applicability of our approach, we also consider the case where additional feasibility constraints are present, e.g., at most k agents can be selected. We obtain O(p)-approximation mechanisms for both monotone and non-monotone submodular objectives, when the feasible solutions are independent sets of a p-system. With the exception of additive valuation functions, no mechanisms were known for this setting prior to our work. Finally, we provide lower bounds suggesting that, when one cares about non-trivial approximation guarantees in polynomial time, our results are asymptotically best possible.

Original languageEnglish
Title of host publicationACM EC 2019 - Proceedings of the 2019 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Pages901-919
Number of pages19
ISBN (Electronic)9781450367929
DOIs
Publication statusPublished - 17 Jun 2019
Event20th ACM Conference on Economics and Computation, EC 2019 - Phoenix, United States
Duration: 24 Jun 201928 Jun 2019

Conference

Conference20th ACM Conference on Economics and Computation, EC 2019
CountryUnited States
CityPhoenix
Period24/06/1928/06/19

Keywords

  • Budget-feasible mechanism design
  • Non-monotone submodular maximization
  • Procurement auctions

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