Revealing POMDPs: qualitative and quantitative analysis for parity objectives

Asadi, Ali, Chatterjee, Krishnendu, Lurie, David and Saona, Rai (2025) Revealing POMDPs: qualitative and quantitative analysis for parity objectives. Proceedings of the AAAI Conference on Artificial Intelligence. ISSN 2159-5399 (In Press)

Text (main) - Accepted Version Pending embargo until 1 January 2100. Download (260kB)

Abstract

Partially observable Markov decision processes (POMDPs) are a central model for uncertainty in sequential decision making. The most basic objective is the reachability objective, where a target set must be eventually visited, and the more general parity objectives can model all ω-regular specifications. For such objectives, the computational analysis problems are the following: (a) qualitative analysis that asks whether the objective can be satisfied with probability 1 (almost-sure winning) or probability arbitrarily close to 1 (limit-sure winning); and (b) quantitative analysis that asks for the approximation of the optimal probability of satisfying the objective. For general POMDPs, almost-sure analysis for reachability objectives is EXPTIME-complete, but limit-sure and quantitative analyses for reachability objectives are undecidable; almost-sure, limit-sure, and quantitative analyses for parity objectives are all undecidable. A special class of POMDPs, called revealing POMDPs, has been studied recently in several works, and for this subclass the almost-sure analysis for parity objectives was shown to be EXPTIME-complete. In this work, we show that for revealing POMDPs the limit-sure analysis for parity objectives is EXPTIME-complete, and even the quantitative analysis for parity objectives can be achieved in EXPTIME.

Item Type:	Article
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	01 Dec 2025 17:39
Last Modified:	09 Jan 2026 11:30
URI:	http://eprints.lse.ac.uk/id/eprint/130382

Actions (login required)

View Item