Valid Stopping in Adaptive Generator-Verifier Loops

Abstract:Numerous agentic workflows are based on a generator-verifier loop: a generator proposes candidates, a cheap verifier scores them, and the workflow terminates when a proposal is verified as good enough. The verifier typically proxies a more costly ground-truth oracle, and as the generator searches adaptively against it, false acceptances may accumulate. Proposals can pass the proxy but fail under the costlier ground-truth check. We study when to stop these loops while controlling the false discovery rate of the accepted proposals. Our construction introduces tools of independent interest in distribution-free statistical testing and conformal risk control, including analysis of $e$-values constructed through index betting and a novel conformal risk control procedure for non-monotone losses. We validate the approach in synthetic settings and on a protein-design benchmark.

Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME)

arXiv:2610.06432 [stat.ML]

(or arXiv:2610.06432v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.06432 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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