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Retrying a “Safe” Proposal Multiplied Its Risk

Per-candidate certification can inflate false admission under best-of-k selection; the paper derives a setwise condition that survives generator replacement.

Published Updated Story ID: mp-2026-09-09-003
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Summary

Per-candidate certification can inflate false admission under best-of-k selection; the paper derives a setwise condition that survives generator replacement.

The analysis asks when a runtime safety gate can remain trustworthy even if the learned policy or language-model planner behind it changes. Certifying each candidate separately does not compose: with k retries, a false-admission rate alpha can grow to one minus one-minus-alpha raised to k. The authors prove that simultaneous setwise soundness is necessary and sufficient for generator-independent admission soundness, provided there is a design-time certificate and no bypass path. A second result formalizes what partial observation makes impossible when different hidden states demand different safe actions. The contribution is a theoretical contract and risk ledger, not evidence from a deployed controller.

Why it matters

Per-candidate certification can inflate false admission under best-of-k selection; the paper derives a setwise condition that survives generator replacement.

Limits and context

  • The analysis asks when a runtime safety gate can remain trustworthy even if the learned policy or language-model planner behind it changes.
  • Certifying each candidate separately does not compose: with k retries, a false-admission rate alpha can grow to one minus one-minus-alpha raised to k.
  • The contribution is a theoretical contract and risk ledger, not evidence from a deployed controller.

Key claims

  1. Per-candidate certification can inflate false admission under best-of-k selection; the paper derives a setwise condition that survives generator replacement.

    Qualification: The analysis asks when a runtime safety gate can remain trustworthy even if the learned policy or language-model planner behind it changes.

    Evidence: source-2026-09-09-003

Sources

  1. arXiv preprint 2609.06036arXiv · primary research

Corrections

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