Abstract
Iterative-retrieval agents must decide whether another search justifies its cost. A comparison with full search alone cannot establish useful adaptation because accuracy may saturate at a smaller fixed budget. We therefore ask whether a learned rule improves the accuracy-cost frontier formed by development-selected fixed budgets and answer repetition. Our selection-aware audit studies four logit-free signals in four-search question-answering trajectories. Future-best gain (FBG) predicts the largest later improvement on one realized continuation. We compare it with binary future improvement, current-answer error, and evidence coverage. We cross-fit each score by trajectory, freeze selection on development questions, and evaluate untouched questions at matched calls, tokens, and wall time. Across 26 core cells, we find that a simple policy Pareto-dominates guarded FBG in 15, while the guard improves the selected fixed budget in five. Neither FBG rule has a positive cellwise equal-call interval in the 18-cell matched-cost family. No learned policy with an available simultaneous analysis retains a positive max-t interval. Our hindsight oracle still improves full search in all fourteen fully instrumented cells by 4.84 exact-match points on average, localizing the gap to signal identification rather than stopping opportunity. Our current-error head orders stopped-answer risk better than random in all 18 cells, compared with 7 for FBG, yet independent question draws still change the endpoint decision. Under answer-once accounting, fixed budgets become stronger because answer-dependent rules retain prefix-generation costs. We contribute a frontier-based protocol, a cross-signal diagnosis of the gap between prediction and policy utility, and an anonymous audit artifact. In this regime, we reserve deployment claims for learned controllers that improve tuned deterministic controls at matched cost on an independent population under simultaneous inference.