NP-Hardness of checking the unichain condition in average cost MDPs

  • Authors:
  • John N. Tsitsiklis

  • Affiliations:
  • Massachusetts Institute of Technology, Room 32-D662, M.I.T., 77 Massachusetts Avenue, Cambridge, MA 02421, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 2007

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Abstract

The unichain condition requires that every policy in an MDP result in a single ergodic class, and guarantees that the optimal average cost is independent of the initial state. We show that checking whether the unichain condition fails to hold is an NP-complete problem. We conclude with a brief discussion of the merits of the more general weak accessibility condition.