Transience in countable MDPs
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 counta...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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Schloss Dagstuhl
2021
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| _version_ | 1797057568939442176 |
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| author | Kiefer, SM Mayr, R Shirmohammadi, M Totzke, P |
| author_facet | Kiefer, SM Mayr, R Shirmohammadi, M Totzke, P |
| author_sort | Kiefer, SM |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T19:38:18Z |
| format | Conference item |
| id | oxford-uuid:1fc859e7-78fa-4ab0-92b3-aa3d2ba3ebc7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:38:18Z |
| publishDate | 2021 |
| publisher | Schloss Dagstuhl |
| record_format | dspace |
| spelling | oxford-uuid:1fc859e7-78fa-4ab0-92b3-aa3d2ba3ebc72022-03-26T11:23:57ZTransience in countable MDPsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:1fc859e7-78fa-4ab0-92b3-aa3d2ba3ebc7EnglishSymplectic ElementsSchloss Dagstuhl2021Kiefer, SMMayr, RShirmohammadi, MTotzke, PThe 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. |
| spellingShingle | Kiefer, SM Mayr, R Shirmohammadi, M Totzke, P Transience in countable MDPs |
| title | Transience in countable MDPs |
| title_full | Transience in countable MDPs |
| title_fullStr | Transience in countable MDPs |
| title_full_unstemmed | Transience in countable MDPs |
| title_short | Transience in countable MDPs |
| title_sort | transience in countable mdps |
| work_keys_str_mv | AT kiefersm transienceincountablemdps AT mayrr transienceincountablemdps AT shirmohammadim transienceincountablemdps AT totzkep transienceincountablemdps |