Limit-Sure Reachability for Small Memory Policies in POMDPs Is NP-Complete
Abstract
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 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.
Cite
Text
Asadi et al. "Limit-Sure Reachability for Small Memory Policies in POMDPs Is NP-Complete." Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, 2025.Markdown
[Asadi et al. "Limit-Sure Reachability for Small Memory Policies in POMDPs Is NP-Complete." Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, 2025.](https://mlanthology.org/uai/2025/asadi2025uai-limitsure/)BibTeX
@inproceedings{asadi2025uai-limitsure,
title = {{Limit-Sure Reachability for Small Memory Policies in POMDPs Is NP-Complete}},
author = {Asadi, Ali and Chatterjee, Krishnendu and Saona, Raimundo and Shafiee, Ali},
booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence},
year = {2025},
pages = {238-256},
volume = {286},
url = {https://mlanthology.org/uai/2025/asadi2025uai-limitsure/}
}