ResearchResearch paperEfficiency & Inference · Safety & Alignment · Reinforcement Learning1 source · Oct 20, 2026

Anytime-Valid Runtime Monitoring of Learned Barrier Certificates

We propose an anytime-valid runtime monitor that audits a learned barrier certificate using observed closed-loop trajectories.

Learned barrier certificates provide a principled mechanism for establishing safety of stochastic systems, but their validity may deteriorate during deployment when the underlying dynamics differ from those used for training.
Specifically, the conditional barrier-drift condition is formulated as an episode-wise sequential hypothesis test, and observed barrier increments are transformed into a nonnegative test supermartingale, yielding finite-sample false-alarm control under arbitrary stopping times.
Inspired by finite-horizon safety verification, we further introduce a deterministic temporal shaping of the monitoring boundary, making the monitor more conservative early in a prescribed deployment horizon while preserving anytime-validity.
To assess the monitor empirically, we evaluate empirical alarm behavior under valid and invalid certificates.

[1]Anytime-Valid Runtime Monitoring of Learned Barrier Certificates
arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 06:46 AM
We propose an anytime-valid runtime monitor that audits a learned barrier certificate using observed closed-loop trajectories.
Learned barrier certificates provide a principled mechanism for establishing safety of stochastic systems, but their validity may deteriorate during deployment when the underlying dynamics differ from those used for training.

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