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.
Original language | English |
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Article number | 58 |
Number of pages | 25 |
Journal | Applied Mathematics and Optimization |
Volume | 89 |
Issue number | 3 |
Early online date | 12 Apr 2024 |
DOIs | |
Publication status | Published - Jun 2024 |
Keywords
- 90C40
- Continuity
- Projection mapping
- Markov decision processes
- 60J05
- Absorbing model