Optimal Constrained sc-LTL Planning in MDPs via Switching Policies

Abstract:We study the synthesis of optimal policies for planning problems on Markov decision processes with both objectives and safety constraints specified in co-safe linear temporal logic (sc-LTL). Our problems are inherently non-Markovian due to the complexity of the sc-LTL specification and may require policy randomization to balance the objective and constraint. We propose a novel approach that reduces the constrained sc-LTL planning problem to a constrained reachability problem on an extended model. We then show that a class of switching policies constructed from stationary policies for the individual sc-LTL specifications is sufficient for optimality for the constrained reachability problem. Our finding enables a tractable linear program to compute the optimal policy. A grid world case study demonstrates that our switching policies can achieve the optimal trade-off between the objective and the safety constraint and validates both optimality and tractability.

12 pages, 6 figures. Author's accepted version; accepted for publication in the IEEE Transactions on Automatic Control

Robotics (cs.RO); Systems and Control (eess.SY)

arXiv:2608.05021 [cs.RO]

(or arXiv:2608.05021v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2608.05021 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1109/TAC.2026.3709203 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.