Threshold probability of non-terminal type in finite horizon Markov decision processes

Akifumi Kira, Takayuki Ueno, Toshiharu Fujita

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We consider a class of problems concerned with maximizing probabilities, given stage-wise targets, which generalizes the standard threshold probability problem in Markov decision processes. The objective function is the probability that, at all stages, the associatively combined accumulation of rewards earned up to that point takes its value in a specified stage-wise interval. It is shown that this class reduces to the case of the nonnegative-valued multiplicative criterion through an invariant imbedding technique. We derive a recursive formula for the optimal value function and an effective method for obtaining the optimal policies.

Original languageEnglish
Pages (from-to)461-472
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - Feb 1 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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