### Abstract

A continuous-time average-reward Markov-decision-process problem is most easily solved in terms of an equivalent discrete-time Markov decision process (DMDP). Customary hypotheses include that the process is a Markov jump process with denumerable state space and bounded transition rates, that actions are chosen at the jump points of the process, and that the policies considered are deterministic. An analogous uniformization result is derived which is applicable to semi-Markov decision process (SMDP) under a (possibly) randomized stationary policy. For each stationary policy governing an SMDP meeting certain hypotheses, a past-dependent policy on a suitably constructed DMDP is specified. The new policy carries the same average reward on the DMDP as the original policy on the SMDP. Discrete-time reduction is applied to optimization on a SMDP subject to a hard constraint, for which the optimal policy has been shown to be stationary and possibly randomized at no more than a single state. Under some convexity conditions on the reward, cost, and action space, it is shown that a nonrandomized policy is optimal for the constrained problem.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | IEEE |

Pages | 1122-1123 |

Number of pages | 2 |

State | Published - 1985 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 1122-1123). IEEE.

**DISCRETE-TIME EQUIVALENCE FOR CONSTRAINED SEMI-MARKOV DECISION PROCESSES.** / Beutler, Frederick J.; Ross, Keith.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Conference on Decision and Control.*IEEE, pp. 1122-1123.

}

TY - GEN

T1 - DISCRETE-TIME EQUIVALENCE FOR CONSTRAINED SEMI-MARKOV DECISION PROCESSES.

AU - Beutler, Frederick J.

AU - Ross, Keith

PY - 1985

Y1 - 1985

N2 - A continuous-time average-reward Markov-decision-process problem is most easily solved in terms of an equivalent discrete-time Markov decision process (DMDP). Customary hypotheses include that the process is a Markov jump process with denumerable state space and bounded transition rates, that actions are chosen at the jump points of the process, and that the policies considered are deterministic. An analogous uniformization result is derived which is applicable to semi-Markov decision process (SMDP) under a (possibly) randomized stationary policy. For each stationary policy governing an SMDP meeting certain hypotheses, a past-dependent policy on a suitably constructed DMDP is specified. The new policy carries the same average reward on the DMDP as the original policy on the SMDP. Discrete-time reduction is applied to optimization on a SMDP subject to a hard constraint, for which the optimal policy has been shown to be stationary and possibly randomized at no more than a single state. Under some convexity conditions on the reward, cost, and action space, it is shown that a nonrandomized policy is optimal for the constrained problem.

AB - A continuous-time average-reward Markov-decision-process problem is most easily solved in terms of an equivalent discrete-time Markov decision process (DMDP). Customary hypotheses include that the process is a Markov jump process with denumerable state space and bounded transition rates, that actions are chosen at the jump points of the process, and that the policies considered are deterministic. An analogous uniformization result is derived which is applicable to semi-Markov decision process (SMDP) under a (possibly) randomized stationary policy. For each stationary policy governing an SMDP meeting certain hypotheses, a past-dependent policy on a suitably constructed DMDP is specified. The new policy carries the same average reward on the DMDP as the original policy on the SMDP. Discrete-time reduction is applied to optimization on a SMDP subject to a hard constraint, for which the optimal policy has been shown to be stationary and possibly randomized at no more than a single state. Under some convexity conditions on the reward, cost, and action space, it is shown that a nonrandomized policy is optimal for the constrained problem.

UR - http://www.scopus.com/inward/record.url?scp=0022290735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022290735&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0022290735

SP - 1122

EP - 1123

BT - Proceedings of the IEEE Conference on Decision and Control

PB - IEEE

ER -