Confidence-Based Stopping Rules: A General Primitive for Search, Inference, and Generation

We propose a simple, domain-agnostic primitive for deciding when to stop a search, inference,or generation process: stop when confidence that the current incumbent is (approximately) bestexceeds a threshold τ . Instantiated with an anytime-valid confidence process Ct adapted to theinformation observed up to time t, the stopping time Tτ = inf{t : Ct ≥ τ } enjoys nonasymptoticerror guarantees under optional stopping and admits efficient constructions in both Bayesian andfrequentist (e-process) styles. We formalize two common meanings of best—(i) ordinal optimalityover a finite or effectively finite candidate set and (ii) ontological centrality for tasks with astructural center (e.g., image captioning, regime identification). We give generic algorithmsand specialized instantiations for intellectual corpus mining, image captioning, change-pointdetection, feature selection, hyperparameter optimization, query expansion, and anomaly triage.We provide principled ways to choose τ via regret trade-offs and curvature (kink ) of the confidencecurve, and sketch proof techniques showing that optional stopping at Tτ achieves the targetmisidentification risk while reducing compute relative to exhaustive or ad hoc marginal-gainrules. The result is a compact stopping rule that turns confidence itself into the control surface.