Algorithms for Deciding the Safety of States in Fully Observable Non-deterministic Problems: Technical Report

arXiv cs.AI / 3/17/2026

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Key Points

The paper introduces iPI, a policy-iteration algorithm that combines TarjanSafe's best-case performance with polynomial worst-case guarantees for safety testing in fully observable non-deterministic problems.
It defines safety as deciding whether a safe policy exists from a state and identifies faults as state-action pairs that transition from safe to unsafe.
TarjanSafe has exponential worst-case runtime, a linear-time alternative exists but is slower in practice, and iPI achieves polynomial worst-case performance while matching TarjanSafe's practical efficiency in favorable cases.
Experiments show iPI matches TarjanSafe on problems amenable to TarjanSafe and scales much better on ill-suited problems, confirming the approach's robustness.

Abstract

Learned action policies are increasingly popular in sequential decision-making, but suffer from a lack of safety guarantees. Recent work introduced a pipeline for testing the safety of such policies under initial-state and action-outcome non-determinism. At the pipeline's core, is the problem of deciding whether a state is safe (a safe policy exists from the state) and finding faults, which are state-action pairs that transition from a safe state to an unsafe one. Their most effective algorithm for deciding safety, TarjanSafe, is effective on their benchmarks, but we show that it has exponential worst-case runtime with respect to the state space. A linear-time alternative exists, but it is slower in practice. We close this gap with a new policy-iteration algorithm iPI, that combines the best of both: it matches TarjanSafe's best-case runtime while guaranteeing a polynomial worst-case. Experiments confirm our theory and show that in problems amenable to TarjanSafe iPI has similar performance, whereas in ill-suited problems iPI scales exponentially better.