[2605.01051] Value Functions for Temporal Logic: Optimal Policies and Safety Filters
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Computer Science > Robotics
arXiv:2605.01051 (cs)
[Submitted on 1 May 2026]
Title:Value Functions for Temporal Logic: Optimal Policies and Safety Filters
Authors:Oswin So, William Sharpless, Sylvia Herbert, Chuchu Fan
View a PDF of the paper titled Value Functions for Temporal Logic: Optimal Policies and Safety Filters, by Oswin So and 3 other authors
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Abstract:While Bellman equations for basic reach, avoid, and reach-avoid problems are well studied, the relationship between value optimality and policy optimality becomes subtle in the undiscounted infinite-horizon setting, particularly for more complicated tasks. Greedily maximizing the Q-function can produce policies that indefinitely defer task completion for reach-avoid problems, or equivalently, Until specifications, even when the value function is optimal. Building upon recent results decomposing the value function for temporal logic (TL) into a graph of constituent value functions, we construct non-Markovian policies based on state history that avoid this pathology and prove their optimality with respect to the quantitative robustness score for nested Until, Globally, and Globally-Until specifications. We further show how the Q function can serve as a safety filter for complex TL specifications, extending prior results beyond simple avoid or reach-avoid tasks.
Subjects:
Robotics (cs.RO); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Logic in Computer Science (cs.LO); Optimization and Control (math.OC)
Cite as: arXiv:2605.01051 [cs.RO]
(or arXiv:2605.01051v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2605.01051
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arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Oswin So [view email] [v1] Fri, 1 May 2026 19:30:03 UTC (4,591 KB)
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