PAC-CF: Calibrating Irreversible Frontier Pruning in LLM-Guided Search

LLM-guided search explores multiple candidate trajectories, but at substantial test-time cost. Pruning low-scoring frontier candidates can control this cost, yet it also turns potentially biased evaluator scores into irreversible decisions: systematic ranking errors can persist under repeated scoring and remove useful branches. We propose Probably Approximately Correct Conformal Filtering (PAC-CF). Its fixed-frontier analysis formulates elimination as an $(\varepsilon,δ)$-PAC problem under bounded evaluator bias; its operational rule separately calibrates a score-gap threshold on held-out tasks by running the original controller without PAC-CF and using post-search verifier labels to measure the deficit of solution-preserving candidates relative to the frontier leader. Conditional on exchangeable native-controller tasks with nonempty protected exposure, conformal calibration gives finite-sample coverage for retaining at least one verifier-defined valid continuation at every protected frontier on the native trajectory. At deployment, PAC-CF removes only candidates whose gap from the highest frontier score exceeds the frozen threshold. We evaluate PAC-CF across three domains, five controllers, and four request budgets from B100 to B500. In the cross-domain/controller macro averages, the point estimates for all three workload measures are lower at every budget; the paired-bootstrap 95\% confidence interval for utility excludes zero at B100 and B200. For pruning-aware ToolTree, the full-test-set cross-domain utility difference is $+4.38$ points at each tested budget; on the natural-termination sensitivity cohort, physical requests decrease by $18.94$--$18.95\%$ and end-to-end token usage by $23.57$--$23.76\%$.