One-Hit Detection in Generative Sampling: Optimal Stopping and Conformal Calibration

Generative models can produce candidates for scientific discovery, but most lack the desired property, and determining which ones qualify often requires costly experiments. In practice, predictive models help assess whether at least one hit—a candidate satisfying the target property—has been generated, thereby guiding when to stop generation and reducing unnecessary experimental validation. We formulate this task as a finite-horizon optimal stopping problem that maximizes expected reward for early detection while controlling the probability of false alarms, i.e., stopping before any hit appears. Given a sequence of independent $p$-values, we first construct a monotone family of stopping times based on Lagrangian duality, each optimal for the Lagrangian problem at its corresponding multiplier. We then propose a novel method Conformalized Optimal Stopping, applying the monotone family to conformal \(p\)-values constructed from screening scores and selecting the multiplier by calibration on simulated global-null trajectories. Under suitable assumptions, the resulting stopping strategy achieves nearly optimal expected reward with exact finite-sample false-alarm control. Experiments on QED–HGraph and TargetDiff candidates demonstrate substantial improvements over competing methods with the same finite-sample false-alarm guarantees.