Bounding the probability of resource constraint violations in multi-agent MDPs

Frits De Nijs, Erwin Walraven, Mathijs M. De Weerdt, Matthijs T.J. Spaan

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

11 Citations (Scopus)
84 Downloads (Pure)


Multi-agent planning problems with constraints on global resource consumption occur in several domains. Existing algorithms for solving Multi-agent Markov Decision Processes can compute policies that meet a resource constraint in expectation, but these policies provide no guarantees on the probability that a resource constraint violation will occur. We derive a method to bound constraint violation probabilities using Hoeffding's inequality. This method is applied to two existing approaches for computing policies satisfying constraints: the Constrained MDP framework and a Column Generation approach. We also introduce an algorithm to adaptively relax the bound up to a given maximum violation tolerance. Experiments on a hard toy problem show that the resulting policies outperform static optimal resource allocations to an arbitrary level. By testing the algorithms on more realistic planning domains from the literature, we demonstrate that the adaptive bound is able to efficiently trade off violation probability with expected value, outperforming state-of-the-art planners.

Original languageEnglish
Title of host publicationProceedings of the 31st Conference on Artificial Intelligence, AAAI 2017
PublisherAmerican Association for Artificial Intelligence (AAAI)
Number of pages7
ISBN (Print)978-1577357803
Publication statusPublished - 2017
Event31st AAAI Conference on Artificial Intelligence: AAAI 2017 - Hilton San Francisco Union Square, San Francisco, United States
Duration: 4 Feb 201710 Feb 2017
Conference number: 31


Conference31st AAAI Conference on Artificial Intelligence
Abbreviated title AAAI Conference on Artificial Intelligence
Country/TerritoryUnited States
CitySan Francisco
Internet address


  • Markov Decision Process
  • Resource constraints
  • Planning under uncertainty


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