Solving Robust POMDPs with Omega-regular Objectives via Partially Observable Stochastic Games

Abstract:Robust POMDPs (RPOMDPs) generalize classical POMDPs to the setting where exact transition probabilities are not known -- rather, they are only known to belong to some uncertainty set of values. In this work, we study the problem of solving RPOMDPs with general omega-regular objectives, which subsume a broad class of objectives such as reachability, safety, and linear temporal logic (LTL) objectives. We show that, for (s,a)-rectangular RPOMDPs with polytopic uncertainty sets, the problem of solving RPOMDPs under omega-regular objectives can be reduced to solving partially observable stochastic games (POSGs) under omega-regular objectives. Moreover, we show for the first time that reductions can be constructed in both directions, establishing the semantic equivalence between (s,a)-rectangular RPOMDPs with polytopic uncertainty sets and POSGs. This allows us to derive a range of new computational complexity results, including both upper and lower complexity bounds, on solving RPOMDPs with different omega-regular objectives. As a corollary, we also derive new computational complexity results for RMDPs.

Artificial Intelligence (cs.AI)

arXiv:2608.24986 [cs.AI]

(or arXiv:2608.24986v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2608.24986 Focus to learn more arXiv-issued DOI via DataCite

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