### Abstract

Infinite-horizon non-stationary Markov decision processes provide a general framework to model many real-life decision-making problems, e.g., planning equipment maintenance. Unfortunately, these problems are notoriously difficult to solve, due to their infinite dimensionality. Often, only the optimality of the initial action is of importance to the decision-maker: once it has been identified, the procedure can be repeated to generate a plan of arbitrary length. The optimal initial action can be identified by finding a time horizon so long that data beyond it has no effect on the initial decision. This horizon is known as a solution horizon and can be discovered by considering a series of truncations of the problem until a stopping rule guaranteeing initial decision optimality is satisfied. We present such a stopping rule for problems with unbounded rewards. Given a candidate policy, the rule uses a mathematical program that searches for other possibly optimal initial actions within the space of feasible truncations. If no better action can be found, the candidate action is deemed optimal. Our rule runs faster than comparable rules and discovers shorter, more efficient solution horizons.

Original language | English |
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Title of host publication | Proceedings of the Twenty-Ninth International Conference on Automated Planning and Scheduling |

Editors | J. Benton, N. Lipovetzky, E. Onaindia, D.E. Smith, S. Srivastava |

Publisher | Association for the Advancement of Artificial Intelligence (AAAI) |

Pages | 292-300 |

Number of pages | 9 |

Volume | 29 |

Publication status | Published - 2019 |

Event | 29th International Conference on Automated Planning and Scheduling - Berkeley, United States Duration: 11 Jul 2019 → 15 Jul 2019 Conference number: 29 |

### Conference

Conference | 29th International Conference on Automated Planning and Scheduling |
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Abbreviated title | ICAPS |

Country | United States |

City | Berkeley |

Period | 11/07/19 → 15/07/19 |

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## Cite this

Neustroev, G., de Weerdt, M., & Verzijlbergh, R. (2019). Discovery of Optimal Solution Horizons in Non-Stationary Markov Decision Processes with Unbounded Rewards. In J. Benton, N. Lipovetzky, E. Onaindia, D. E. Smith, & S. Srivastava (Eds.),

*Proceedings of the Twenty-Ninth International Conference on Automated Planning and Scheduling*(Vol. 29, pp. 292-300). Association for the Advancement of Artificial Intelligence (AAAI). https://aaai.org/ojs/index.php/ICAPS/article/view/3491