Exact Model-Free Policy Iteration for Co-safe LTL Planning

Abstract:This work studies model-free reinforcement learning for co-safe linear temporal logic (sc-LTL) objectives in finite Markov decision processes, which can be reduced to maximal reachability objectives via the standard product construction. For this problem, direct sample-based bootstrap methods (e.g., TD or Q-learning) may fail to converge to optimal policies due to the noncontractive nature and nonuniqueness of solutions to the Bellman equation. We develop a new two-step model-free reinforcement learning method that first uses a discounted surrogate to identify a clamp set that resolves this nonuniqueness, and then applies undiscounted policy evaluation and greedy policy improvement with guarantees of finding an optimal solution. We prove almost-sure convergence of the policy evaluation step and finite termination of the policy iteration algorithm at an optimal policy. These theoretical results are validated through numerical experiments on a stochastic grid world.

7 pages, 1 figure. Accepted for publication in IEEE Control Systems Letters. To be presented at the 2026 IEEE Conference on Decision and Control

Systems and Control (eess.SY); Formal Languages and Automata Theory (cs.FL); Robotics (cs.RO)

arXiv:2608.05047 [eess.SY]

(or arXiv:2608.05047v1 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2608.05047 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1109/LCSYS.2026.3702192 Focus to learn more DOI(s) linking to related resources

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