## Abstract

Uncertain partially observable Markov decision processes (uPOMDPs) allow the probabilistic transition and observation functions of standard POMDPs to belong to a so-called uncertainty set. Such uncertainty, referred to as epistemic uncertainty, captures uncountable sets of probability distributions caused by, for instance, a lack of data available. We develop an algorithm to compute finite-memory policies for uPOMDPs that robustly satisfy specifications against any admissible distribution. In general, computing such policies is theoretically and practically intractable. We provide an efficient solution to this problem in four steps. (1) We state the underlying problem as a nonconvex optimization problem with infinitely many constraints. (2) A dedicated dualization scheme yields a dual problem that is still nonconvex but has finitely many constraints. (3) We linearize this dual problem and (4) solve the resulting finite linear program to obtain locally optimal solutions to the original problem. The resulting problem formulation is exponentially smaller than those resulting from existing methods. We demonstrate the applicability of our algorithm using large instances of an aircraft collision-avoidance scenario and a novel spacecraft motion planning case study.

Original language | English |
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Title of host publication | Proceedings of the Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI-21) |

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

Pages | 11792-11800 |

Number of pages | 9 |

ISBN (Electronic) | 9781713835974 |

Publication status | Published - 2021 |

Event | 35th AAAI Conference on Artificial Intelligence, AAAI 2021 - ONLINE, Virtual, Online Duration: 2 Feb 2021 → 9 Feb 2021 |

### Conference

Conference | 35th AAAI Conference on Artificial Intelligence, AAAI 2021 |
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City | Virtual, Online |

Period | 2/02/21 → 9/02/21 |