Kiefer, S, Mayr, R, Shirmohammadi, M and Totzke, P 
ORCID: 0000-0001-5274-8190
(2021)
Transience in Countable MDPs.
In: 32nd International Conference on Concurrency Theory (CONCUR 2021), 2021-8-23 - 2021-8-27, Paris.
Abstract
The Transience objective is not to visit any state infinitely often. While this is not possible in any finite Markov Decision Process (MDP), it can be satisfied in countably infinite ones, e.g., if the transition graph is acyclic. We prove the following fundamental properties of Transience in countably infinite MDPs. 1. There exist uniformly ϵ-optimal MD strategies (memoryless deterministic) for Transience, even in infinitely branching MDPs. 2. Optimal strategies for Transience need not exist, even if the MDP is finitely branching. However, if an optimal strategy exists then there is also an optimal MD strategy. 3. If an MDP is universally transient (i.e., almost surely transient under all strategies) then many other objectives have a lower strategy complexity than in general MDPs. E.g., ϵ-optimal strategies for Safety and co-Büchi and optimal strategies for {0, 1, 2}-Parity (where they exist) can be chosen MD, even if the MDP is infinitely branching.
| Item Type: | Conference or Workshop Item (Unspecified) |
|---|---|
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 15 Nov 2021 08:30 |
| Last Modified: | 27 Apr 2024 13:20 |
| DOI: | 10.4230/LIPIcs.CONCUR.2021.11 |
| Open Access URL: | https://drops.dagstuhl.de/opus/volltexte/2021/1438... |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3143103 |
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