Valid Stopping in Adaptive Generator-Verifier Loops

2026-10-05

AI Summary

This study addresses the challenge of false positive accumulation caused by verifiers in adaptive agent generation, as well as the absence of reliable stopping criteria within generate-verify loops. To overcome these limitations, this work proposes an e-value analytical framework based on exponential betting, coupled with a novel conformal risk control procedure tailored for non-monotonic losses. By integrating distribution-free statistical testing, the proposed theory rigorously bounds the false discovery rate (FDR) of accepted proposals. Experiments conducted on both synthetic scenarios and protein design benchmarks validate the effectiveness of the approach. Ultimately, this research provides a statistically guaranteed adaptive termination mechanism for agent workflows, ensuring robust and reliable generation processes without compromising theoretical safety guarantees.

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.

Problem

• generator-verifier loop
• false discovery rate
• valid stopping
• adaptive search
• proxy verifier

Innovation

• Generator-Verifier Loop
• False Discovery Rate
• Conformal Risk Control
• e-values
• Distribution-free Testing