On the Continuity of the Projection Mapping from Strategic Measures to Occupation Measures in Absorbing Markov Decision Processes

Piunovskiy, A ORCID: 0000-0002-9683-4856 and Zhang, Y ORCID: 0000-0002-3200-6306 (2024) On the Continuity of the Projection Mapping from Strategic Measures to Occupation Measures in Absorbing Markov Decision Processes Applied Mathematics and Optimization, 89 (3). 58-. ISSN 0095-4616, 1432-0606

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Abstract

In this paper, we prove the following assertion for an absorbing Markov decision process (MDP) with the given initial distribution, which is also assumed to be semi-continuous: the continuity of the projection mapping from the space of strategic measures to the space of occupation measures, both endowed with their weak topologies, is equivalent to the MDP model being uniformly absorbing. An example demonstrates, among other interesting scenarios, that for an absorbing (but not uniformly absorbing) semi-continuous MDP with the given initial distribution, the space of occupation measures can fail to be compact in the weak topology.

Item Type:	Article
Uncontrolled Keywords:	4901 Applied Mathematics, 49 Mathematical Sciences
Divisions:	Faculty of Science & Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	04 Mar 2024 09:32
Last Modified:	23 Jan 2026 17:56
DOI:	10.1007/s00245-024-10124-7
Related Websites:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3179041
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