Limit-sure reachability for small memory policies in POMDPs is NP-complete
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911004017819648 |
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| author | Asadi, Ali Chatterjee, Krishnendu Saona, Raimundo Shafiee, Ali |
| author_facet | Asadi, Ali Chatterjee, Krishnendu Saona, Raimundo Shafiee, Ali |
| contents | A standard model that arises in several applications in sequential decision making is partially observable Markov decision processes (POMDPs) where a decision-making agent interacts with an uncertain environment. A basic objective in such POMDPs is the reachability objective, where given a target set of states, the goal is to eventually arrive at one of them. The limit-sure problem asks whether reachability can be ensured with probability arbitrarily close to 1. In general, the limit-sure reachability problem for POMDPs is undecidable. However, in many practical cases the most relevant question is the existence of policies with a small amount of memory. In this work, we study the limit-sure reachability problem for POMDPs with a fixed amount of memory. We establish that the computational complexity of the problem is NP-complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00941 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit-sure reachability for small memory policies in POMDPs is NP-complete Asadi, Ali Chatterjee, Krishnendu Saona, Raimundo Shafiee, Ali Computational Complexity A standard model that arises in several applications in sequential decision making is partially observable Markov decision processes (POMDPs) where a decision-making agent interacts with an uncertain environment. A basic objective in such POMDPs is the reachability objective, where given a target set of states, the goal is to eventually arrive at one of them. The limit-sure problem asks whether reachability can be ensured with probability arbitrarily close to 1. In general, the limit-sure reachability problem for POMDPs is undecidable. However, in many practical cases the most relevant question is the existence of policies with a small amount of memory. In this work, we study the limit-sure reachability problem for POMDPs with a fixed amount of memory. We establish that the computational complexity of the problem is NP-complete. |
| title | Limit-sure reachability for small memory policies in POMDPs is NP-complete |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2412.00941 |