Approximability of constant-horizon constrained POMDP

Majid Khonji, Ashkan Jasour, Brian Williams

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

14 Scopus citations

Abstract

Partially Observable Markov Decision Process (POMDP) is a fundamental framework for planning and decision making under uncertainty. POMDP is known to be intractable to solve or even approximate when the planning horizon is long (i.e., within a polynomial number of time steps). Constrained POMDP (C-POMDP) allows constraints to be specified on some aspects of the policy in addition to the objective function. When the constraints involve bounding the probability of failure, the problem is called Chance-Constrained POMDP (CC-POMDP). Our first contribution is a reduction from CC-POMDP to C-POMDP and a novel Integer Linear Programming (ILP) formulation. Thus, any algorithm for the later problem can be utilized to solve any instance of the former. Second, we show that unlike POMDP, when the length of the planning horizon is constant, (C)C-POMDP is NP-Hard. Third, we present the first Fully Polynomial Time Approximation Scheme (FPTAS) that computes (near) optimal deterministic policies for constant-horizon (C)C-POMDP in polynomial time.

Original languageBritish English
Title of host publicationProceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
EditorsSarit Kraus
Pages5583-5590
Number of pages8
ISBN (Electronic)9780999241141
DOIs
StatePublished - 2019
Event28th International Joint Conference on Artificial Intelligence, IJCAI 2019 - Macao, China
Duration: 10 Aug 201916 Aug 2019

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
Volume2019-August
ISSN (Print)1045-0823

Conference

Conference28th International Joint Conference on Artificial Intelligence, IJCAI 2019
Country/TerritoryChina
CityMacao
Period10/08/1916/08/19

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