### Abstract

In this paper, finite-state, finite-action, discounted infinite-horizon- cost Markov decision processes (MDPs) with uncertain stationary transition matrices are discussed in the deterministic policy space. Uncertain stationary parametric transition matrices are clearly classified into independent and correlated cases. It is pointed out in this paper that the optimality criterion of uniform minimization of the maximum expected total discounted cost functions for all initial states, or robust uniform optimality criterion, is not appropriate for solving MDPs with correlated transition matrices. A new optimality criterion of minimizing the maximum quadratic total value function is proposed which includes the previous criterion as a special case. Based on the new optimality criterion, robust policy iteration is developed to compute an optimal policy in the deterministic stationary policy space. Under some assumptions, the solution is guaranteed to be optimal or near-optimal in the deterministic policy space.

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

Title of host publication | Proceedings of the 2007 IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning, ADPRL 2007 |

Pages | 96-102 |

Number of pages | 7 |

DOIs | |

State | Published - 2007 |

Event | 2007 IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning, ADPRL 2007 - Honolulu, HI, United States Duration: Apr 1 2007 → Apr 5 2007 |

### Other

Other | 2007 IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning, ADPRL 2007 |
---|---|

Country | United States |

City | Honolulu, HI |

Period | 4/1/07 → 4/5/07 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Software

### Cite this

*Proceedings of the 2007 IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning, ADPRL 2007*(pp. 96-102). [4220820] https://doi.org/10.1109/ADPRL.2007.368175

**Robust dynamic programming for discounted infinite-horizon markov decision processes with uncertain stationary transition matrice.** / Li, Baohua; Si, Jennie.

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

*Proceedings of the 2007 IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning, ADPRL 2007.*, 4220820, pp. 96-102, 2007 IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning, ADPRL 2007, Honolulu, HI, United States, 4/1/07. https://doi.org/10.1109/ADPRL.2007.368175

}

TY - GEN

T1 - Robust dynamic programming for discounted infinite-horizon markov decision processes with uncertain stationary transition matrice

AU - Li, Baohua

AU - Si, Jennie

PY - 2007

Y1 - 2007

N2 - In this paper, finite-state, finite-action, discounted infinite-horizon- cost Markov decision processes (MDPs) with uncertain stationary transition matrices are discussed in the deterministic policy space. Uncertain stationary parametric transition matrices are clearly classified into independent and correlated cases. It is pointed out in this paper that the optimality criterion of uniform minimization of the maximum expected total discounted cost functions for all initial states, or robust uniform optimality criterion, is not appropriate for solving MDPs with correlated transition matrices. A new optimality criterion of minimizing the maximum quadratic total value function is proposed which includes the previous criterion as a special case. Based on the new optimality criterion, robust policy iteration is developed to compute an optimal policy in the deterministic stationary policy space. Under some assumptions, the solution is guaranteed to be optimal or near-optimal in the deterministic policy space.

AB - In this paper, finite-state, finite-action, discounted infinite-horizon- cost Markov decision processes (MDPs) with uncertain stationary transition matrices are discussed in the deterministic policy space. Uncertain stationary parametric transition matrices are clearly classified into independent and correlated cases. It is pointed out in this paper that the optimality criterion of uniform minimization of the maximum expected total discounted cost functions for all initial states, or robust uniform optimality criterion, is not appropriate for solving MDPs with correlated transition matrices. A new optimality criterion of minimizing the maximum quadratic total value function is proposed which includes the previous criterion as a special case. Based on the new optimality criterion, robust policy iteration is developed to compute an optimal policy in the deterministic stationary policy space. Under some assumptions, the solution is guaranteed to be optimal or near-optimal in the deterministic policy space.

UR - http://www.scopus.com/inward/record.url?scp=34548772562&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548772562&partnerID=8YFLogxK

U2 - 10.1109/ADPRL.2007.368175

DO - 10.1109/ADPRL.2007.368175

M3 - Conference contribution

AN - SCOPUS:34548772562

SN - 1424407060

SN - 9781424407064

SP - 96

EP - 102

BT - Proceedings of the 2007 IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning, ADPRL 2007

ER -